CSE15 Abstracts

Abstracts are printed as submitted by the authors.

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CS15 Abstracts 1

IP1

Graph Data Analytics at Scale: Opportunities andChallenges

The four Vs of Big Data necessitate fundamentally differentdata analytics. A promising strategy toward understand-ing of a complex system’s dynamics and function aims toextract features and relationships between them and to an-alyze how their evolution causes different functional systemresponses. Discovery and forecasting of patterns in suchfeature graphs can provide insights about the vulnerabilityof our nations energy infrastructure to disturbances, thespread of a cyber-security attack, or the anomalies in in-ternode communication in high performance systems. Thistalk will present some opportunities and challenges in us-ing this strategy for computational science and engineeringapplications.

Nagiza SamatovaNorth Carolina State UniversityOak Ridge National Laboratorysamatova@csc.ncsu.edu

IP2

Model Reduction - Trouble with Scales?

Scientific and technological advances call for more andmore complex models as well as systematic ways of comple-menting them by observational data. Despite the ever in-creasing computing capacity, ironically, the need for quan-tifiable model reduction concepts is also gaining increasingimportance in numerous application contexts. Examplesare large scale design or online optimization tasks, uncer-tainty quantification or inversion problems some of whichmay only become feasible through employing reduced mod-els. Starting from a flow scenario with microscales thistalk highlights several aspects of related model reductionstrategies with particular focus on accuracy and stabil-ity guarantees, presence of small scales, singular pertur-bations, and high dimensionality. We address some of thekey ingredients, revolving around error-residual relations,rate-optimality as a benchmark notion, adaptive or greedymethods, separation of variables. The discussion is illus-trated by numerical examples.

Wolfgang DahmenRWTH AachenIGPMdahmen@igpm.rwth-aachen.de

IP3

Petascale Finite Element Simulation of RealWorlds Complex Structure with Billions DOFsModel

Leading supercomputers offer the computing power ofpetascale, and exascale systems are expected to be avail-able by the end of this decade. Supercomputers with morethan tens of thousands of computing nodes, each of whichhas many cores cause serious problems in practical finiteelement software. We have been developing an open sourceparallel finite element software known as ADVENTURE,which enables very precise analyses of practical structuresand machines using over 100 million to billions DOFs mesh.The basic parallel solution algorithms employed are the hi-erarchical domain decomposition method with balancingdomain decomposition as preconditioner. In this talk, Iexplain several key technologies and one practical applica-tion, i.e. seismic response of nuclear power plant subjected

to a strong earthquake.

Shinobu YoshimuraThe University of Tokyoyoshi@sys.t.u-tokyo.ac.jp

IP4

Extreme-scale Multigrid in Space and Time

Multigrid methods are important techniques for efficientlysolving huge linear systems and they have already beenshown to scale effectively on millions of cores. Future exas-cale architectures will require solvers to exhibit even higherlevels of concurrency (1B cores), minimize data movement,exploit machine heterogeneity, and demonstrate resilienceto faults. While considerable research and developmentremains to be done, multigrid approaches are ideal for ad-dressing these challenges. In this talk, we will discuss ef-forts to develop extreme-scale multigrid, including a newparallel time integration approach that has the potentialfor significant speedups over standard time stepping.

Robert FalgoutCenter for Applied Scientific ComputingLawrence Livermore National Laboratoryrfalgout@llnl.gov

IP5

Statistical and Computational Challenges of Con-straining Greenhouse Gas Budgets

Predicting future changes to the global carbon cycle (andtherefore climate) and quantifying anthropogenic emissionsof greenhouse gases (GHGs) both require an understand-ing of net GHGs emissions and uptake across a variety ofspatial and temporal scales. This talk will explore some ofthe core scientific questions related to understanding GHGbudgets through the lens of the statistical and computa-tional challenges that arise. The focus will be on the useof atmospheric observations, and applications will includethe natural and anthropogenic components of the methaneand carbon dioxide budgets. The discussion will include is-sues related to the solution of spatiotemporal inverse prob-lems, uncertainty quantification, data fusion, gap filling,and issues of “big data” arising from the use of satelliteobservations.

Anna MichalakCarnegie Institution for ScienceStanford, CAmichalak@stanford.edu

IP6

Scaling Open Systems for Future ComputationalChallenges

Computational models are changing rapidly, partially inresponse to growing data size and advances in high-performance computing. Open approaches are well suitedto this dynamic environment as they provide agile re-sponses to complex, evolving code, and support the greatergoal of ensuring reproducible science. This presentationintroduces some open initiatives addressing big data andHPC and the role that software architectures and processesplays in advancing scientific computation. Also discussedare emerging trends including competitive challenges andactive publications that will likely play an important rolein the creation, development and deployment of computa-

2 CS15 Abstracts

tional software.

Will SchroederKitware, Inc.will.schroeder@kitware.com

IP7

A Calculus for the Optimal Quantification of Un-certainties

The past century has seen a steady increase in the needof estimating and predicting complex systems and making(possibly critical) decisions with limited information. Withthis purpose, this talk will describe the development of aform of calculus allowing for the (computational) manip-ulation of infinite dimensional information structures andits application to the optimal quantification of uncertain-ties in complex systems and the scientific computation ofoptimal statistical estimators/models. Specific exampleswill be discussed to illustrate how this form of calculuscould also be used to facilitate/guide the process of scien-tific discovery.

Houman OwhadiApplied MathematicsCaltechowhadi@caltech.edu

IP8

The Power of Matrix and Tensor Decompositionsin Smart Patient Monitoring

Accurate and automated extraction of clinically relevantinformation from patient recordings requires an ingeniouscombination of adequate pretreatment of the data (e.g.artefact removal), feature selection, pattern recognition,decision support, up to their embedding into user-friendlyuser interfaces. The underlying computational problemscan be solved by making use of matrix and tensor decom-positions as building blocks of higher-level signal process-ing algorithms. A major challenge here is how to makethe mathematical decompositions “interpretable’ such thatthey reveal the underlying medically relevant informationand improve medical diagnosis. The application of thesedecompositions and their benefits will be illustrated in avariety of case studies, including epileptic seizure onset lo-calisation using adult and neonatal scalp EEG and Event-related potential analysis during simultaneous EEG-fMRIacquisition.

Sabine Van HuffelESAT-SCD(SISTA) Department of Electrical EngineeringKatholieke Universiteit Leuvensabine.vanhuffel@esat.kuleuven.ac.be

IP9

Implications of Numerical and Data IntensiveTechnology Trends on Scientific Visualization andAnalysis

Technology trends in numerically and data intensive com-puting have the potential to reshape and significantly ad-vance how we visualize and analyze the results of scientificsimulations. However, next generation numerically inten-sive supercomputers are bound by power and storage con-straints. These require us to transition from standard post-processing visualization and analysis approaches to intelli-gent, automated in-situ ones. In addition, data intensive

technology trends that support accessing and understand-ing our data using intuitive, web-based and query-driveninterfaces are now the norm. In this talk, I will discussthese trends and several freely available, open-source ap-proaches that leverage them.

James AhrensLos Alamos National Laboratoryahrens@lanl.gov

SP1

Celebrating 15 Years of SIAM CSE

There can be no doubt that SIAM CSE has been a bigsuccess! We examine the growth of CSE in SIAM, andmore broadly as a discipline, and look toward some of thechallenges and opportunities for the future.

Linda R. PetzoldUniversity of California, Santa Barbarapetzold@engineering.ucsb.edu

CP1

Computational Molecular Engineering: An Emerg-ing Technology in Process Engineering

Molecular modeling and simulation has become a powerfultool which can be applied to many physical processes andproperties of fluids on the molecular level. A shift in theaccessible length and time scales due to massively parallelhigh-performance computing has greatly increased its po-tential. The novel molecular dynamics code ls1 mardyn,which scales excellently on up to 146 000 cores, is pre-sented, highlighting the emergence of computational molec-ular engineering as a discipline.

Martin T. Horsch, Stephan WerthUniversity of Kaiserslautern, GermanyLaboratory of Engineering Thermodynamicsmartin.horsch@mv.uni-kl.de, stephan.werth@mv.uni-kl.de

Christoph Niethammer, Colin GlassHigh Performance Computing Center Stuttgart, Germanyniethammer@hlrs.de, glass@hlrs.de

Wolfgang Eckhardt, Philipp NeumannTechnische Universitat Munchen, GermanyScientific Computing in Computer Scienceeckhardw@in.tum.de, neumanph@in.tum.de

Hans-Joachim BungartzTechnische Universitat Munchen, Department ofInformaticsChair of Scientific Computing in Computer Sciencebungartz@in.tum.de

Jadran VrabecUniversity of Paderborn, GermanyThermodynamics and Energy Technologyjadran.vrabec@upb.de

Hans HasseUniversity of Kaiserslautern, GermanyLaboratory of Engineering Thermodynamics

CS15 Abstracts 3

hans.hasse@mv.uni-kl.de

CP1

A Numerical and Computational Frameworkfor Hierarchical Multi-Scale/multi-Physics Simula-tions

Multi-scale modeling (MSM) has become a dominantparadigm in materials modeling. The practical impact ofMSM depends on its ability to utilize modern computingplatforms. However, since there are no general numericaland computational frameworks for MSM, the vast major-ity of multi-scale material models or simulations are devel-oped on a case-by-case basis. We present a formulation ofan adaptive numerical and computational framework forMSM and analyze its performance for a number of chal-lenging problems.

Jaroslaw Knap, Oleg Borodin, Carrie E. Spear,KENNETH W. Leiter, DAVID A. Powell, RICHARD C.BeckerU.S. Army Research Laboratoryjaroslaw.knap@arl.army.mil, oleg.a.borodin.civ@mail.mil,carrie.e.spear.ctr@mail.mil, kenneth.w.leiter.civ@mail.mil,david.powell@survice.com, richard.c.becker.civ@mail.mil

CP1

Amr Strategies for Scft Algorithm

We introduce an adaptive mesh refinement technique forsolving the self consistent field theory mean-field optimiza-tion for an AB diblock copolymer. We use a 3D octreedata structure and a level set based refinement method tosolve a diffusion reaction equation. It reduces the requirednumber of points for fine polymeric 3D structures and thusthe data required to store is compressed consequently (1/3)without loss of accuracy on the physical observables.

Gaddiel OuakninUCSBgaddyouaknin18@gmail.com

Frederic G. GibouUC Santa Barbarafgibou@engineering.ucsb.edu

CP2

Robust Multigrid Methods for Magnetohydrody-namics

Magnetohydrodynamic models are used for a wide rangeof plasma physics applications. The system of PDEs thatcharacterizes these models is nonlinear, with strongly cou-pled fluid and electromagnetic interactions. The linearsystems that result from linearization and discretizationare typically difficult to solve. We consider multigrid-preconditioned GMRES to achieve efficient solution, andcompare results for two potential relaxation methods, bothmotivated by well-known relaxation techniques for incom-pressible fluid dynamics.

Thomas BensonDepartment of MathematicsTufts University

thomas.benson@tufts.edu

CP2

Dependance of the Convergence of MultigridMethods on the Used Discretization

A lot of effort has been put into analyzing the conver-gence rate of multigrid methods depending on the usedsmoother and coarse grid operator. Effectively, the conver-gence rate of the solver is already being influenced whenthe discretization of the PDE is chosen. In order to solvePDEs as computationally efficient as possible, the choice ofthe discretization matters. We present analyses of the con-vergence rate and computational cost of multigrid methodsfor different discretizations.

Matthias BoltenUniversity of WuppertalDepartment of Mathematicsbolten@math.uni-wuppertal.de

CP2

Support Graph Smoothing

Large scale-free data mining tasks often require an efficientlinear solver. Often standard iterative methods struggle doto the large size and complexity of the graphs. Computa-tion of an optimal preconditioner for CG is challenging fora general scale-free graph. Support graph preconditionershave been a popular subject of study, but deserve more indepth study within a multilevel setting. We employ a sup-port graph technique that serves as a relaxation methodfor AMG.

Alyson FoxUniversity of Colorado Boulderfox.alyson@gmail.com

CP2

On Teh Efficiency of Nonlinear Multigrid Methods

Nonlinear multigrid methods such as the Full Approxima-tion Scheme (FAS) and Newton-multigrid (Newton-MG)are widely-used as fast solvers for nonlinear PDEs of ellip-tic and parabolic type. This talk will consider Newton-MGand FAS iterations in a general setting to derive a the-oretical approximation of the execution time of the algo-rithms. Specific examples will then be used to demonstratethe sharpness of these estimates for a range of nonlineareliiptic and parabolic problems (the latter with implicittime-stepping). Our conclusion is that the Newton-MGapproach is almost always the superior choice.

Peter K. JimackSchool of ComputingUniversity of Leedsp.k.jimack@leeds.ac.uk

CP2

Large-Scale Sparse Inverse Covariance Estimation

The Sparse Inverse Covariance Estimation problem arisesin many statistical applications in Machine Learning. Inthis problem we estimate a sparse inverse of a covariancematrix of a multivariate normal distribution, by solvingan l1 regularized optimization problem. Because of mem-ory limitations, most algorithms are unable to handle large

4 CS15 Abstracts

scale instances of this problem. We present a block coor-dinate descent approach and a multilevel acceleration forsolving the problem for such large-scale data sets. We fur-ther show that an additional debiasing phase improves theestimated matrix.

Eran TreisterTechnion - Israel Institute of Technology, Israeleran@cs.technion.ac.il

Javier TurekComputer Science DepartmentTechnionjaviert@cs.technion.ac.il

Irad YavnehComputer Science Department, Technionirad@cs.technion.ac.il

CP3

CSE Education at JSC

Fostering a sound education of students and young re-searchers at bachelor, master and PhD level in high-performance computing, mathematics and computationalscience is an essential task of the Julich SupercomputingCentre (JSC). This talk will give an overview of the educa-tional activities and structures at JSC and informs aboutthe guest student programme, the summer/winter schoolsfor PhD students, joint bachelor and master courses withuniversities and the German Research School for Simula-tion Sciences (GRS).

Johannes GrotendorstForschungszentrum Juelichj.grotendorst@fz-juelich.de

CP3

Automatic Parallel Programming for ScientificSimulation

HiPro is an automatic parallel programming IDE designedfor developing scientific simulation based on JASMIN, adomain-specific computational framework. It supportsparallel programming through GUI and source code gen-eration.The unique parallel part and all interfaces of theapplication are generated and implementation of sequen-tial subroutines is the only part of the code left to be writ-ten manually for a programmer. It combines numericalmathematics with component-based programming to cre-ate ontological models for parallel simulations.

Li LiaoIAPCMliliao@iapcm.ac.cn

Aiqing ZhangInstitute of Applied Physics and ComputationalMathematicszhang aiqing@iapcm.ac.cn

Zeyao MoLaboratory of Computational Physics, IAPCMP.O. Box 8009, Beijing 100088, P.R. Chinazeyao mo@iapcm.ac.cn

CP3

Symbolic Representation and Automated Code

Generation for Discontinuous Galerkin Finite El-ement Methods

We consider the application of discontinuous Galerkin fi-nite element methods for the discretization of general fluidflow and multiphysics problems. By exploiting tools fromsymbolic differentiation, we present a simple programmingenvironment which automatically generates the necessarycode segments, leading to rapid development and testing ofdiscontinuous Galerkin methods for a wide variety of prob-lems. The proposed computational framework is demon-strated on a variety of problems arising in both incompress-ible and compressible fluid flows.

Nathan SimeSchool of Mathematical SciencesUniversity of Nottinghampmxns2@nottingham.ac.uk

Paul HoustonSchool of Mathematical SciencesUniversity of Nottingham, UKPaul.Houston@nottingham.ac.uk

CP3

PoKiTT: an Efficient, Platform Agnostic Pack-age for Thermodynamics, Kinetics, and TransportProperties within PDE Solvers

We introduce PoKiTT, a portable, lightweight library forperforming data parallel calculations of thermochemicalquantities commonly encountered in turbulent reactiveflow simulations. PoKiTT uses Nebo, a domain specificlanguage, to provide a platform agnostic implementationwhich will be ready for future exascale architectures. Wedemonstrate the performance benefits of using PoKiTTover Cantera in the context of a PDE solver for both CPUand GPU executions.

Nathan YonkeeThe University of Utahnathan.yonkee@chemeng.utah.edu

James C. SutherlandDepartment of Chemical EngineeringThe University of Utahjames.sutherland@chemeng.utah.edu

CP4

A Framework for Parallel Fast Matrix Multiplica-tion

We explore the performance of novel fast (Strassen-like)matrix multiplication algorithms in sequential and shared-memory parallel environments. We use a code generationframework to automatically implement over twenty fastmatrix multiplication algorithms and to rapidly test algo-rithmic variations for performance tuning. Our implemen-tations outperform Intel MKL for modest problem sizes.Furthermore, we find that Strassens algorithm is not al-ways optimal in practice; in particular, other algorithmsperform better for the multiplication of rectangular matri-ces.

Austin BensonStanford Universityarbenson@stanford.edu

Grey Ballard

CS15 Abstracts 5

Sandia National Laboratoriesgmballa@sandia.gov

CP4

Dynamic Runtime Scheduling for Dense Out-of-Core Matrix Computation on the Intel Xeon Phi

The talk describes the implementation of dense out-of-core matrix computations, such as Cholesky factorization,on the Intel Xeon Phi. The out-of-core algorithm is for-mulated as computation over submatrix tiles where thedependency is expressed as a directed acyclic graph. Amulti-threaded runtime system launches asynchronous of-fload computations on the Intel Xeon Phi. Examples andresults are presented.

Eduardo F. D’AzevedoOak Ridge National LaboratoryMathematical Sciences Sectiondazevedoef@ornl.gov

Ben Chan, Terrence ChongChinese University of Hong Kongss.sing@hotmail.com, tc92321@hotmail.com

Allan MoralesThe George Washington Universityarrm93@gwmail.gwu.edu

Kwai L. WongJoint Institute for Computational ScienceUniversity of Tennessee/ORNLkwong@utk.edu

CP4

Optimization of Singular Vectors Computation

New SVD routines based on a two-step reduction of a gen-eral matrix to bidiagonal form were developed for Intel R©MKL. In this talk we present some details of implementedoptimizations: dynamic parallelization of singular vectorscomputations, speculative computations in QR and LQfactorizations, dynamic parallelization of the reduction ofbanded matrix to bidiagonal form and how these tech-niques are combined for achieving high performance.

Sergey V Kuznetsov, Nadezhda MozartovaIntel Corporationsergey.v.kuznetsov@intel.com,nadezhda.mozartova@intel.com

CP4

Performance Study of a Randomized Dense Low-Rank Matrix Approximation Using Multiple Gpus

A standard method to compute low-rank approximationsfor dense matrices is truncated QR factorizations with piv-oting, such as LAPACK DGEQP3, an important kernel inmany scientific applications. In this talk, we study the per-formance of an algorithm based on randomized samplingto compute such factorizations of dense matrices for hybridCPU/GPU architectures and show it can have comparableaccuracy, better performance and reduced communicationsthan DGEQP3.

Theo MaryUniversite de Toulouse, INPT ENSEEIHTtheo.mary@etu.enseeiht.fr

Ichitaro Yamazaki, Jakub KurzakUniversity of Tennessee, Knoxvilleiyamazak@icl.utk.edu, kurzak@icl.utk.edu

Piotr LuszczekDepartment of Electrical Engineering and ComputerScienceUniversity of Tennessee, Knoxvilleluszczek@eecs.utk.edu

Stanimire TomovUniversity of Tennessee, Knoxvilletomov@icl.utk.edu

Jack J. DongarraDepartment of Computer ScienceThe University of Tennesseedongarra@cs.utk.edu

CP5

Variational Bayesian Formulations for High-Dimensional Inverse Problems

The present paper advocates a Variational Bayesian(VB) approach for approximating the posterior density instochastic inverse problems. In contrast to sampling tech-niques (e.g. MCMC, SMC), VB requires much fewer for-ward evaluations. Furthermore it enables learning of a suit-able lower-dimensional subspace where most of the poste-rior probability lies, and reducing dramatically the numberof unknowns. We demonstrate the accuracy and efficiencyof the proposed strategy in nonlinear problems and non-Gaussian posteriors in view of biomedical applications.

Isabell FranckTechnische Universitat Munchen, Germanyfranck@tum.de

Phaedon S. KoutsourelakisTechnische Universitat Muenchenp.s.koutsourelakis@tum.de

CP5

Surrogate-Based Bayesian Model Ranking ofAtomistic Models Incorporating the Fidelity ofSurrogates

Approximate modeling of atomistic systems is crucial indesigning new generation of material since ab initio simu-lations are prohibitively costly. We present how a Bayesianframework can rank a number of competing approximatemodels and also provide a basis concurrently exploit mul-tiple models for the same system. We make use of Poly-nomial Chaos surrogates to accelerate the calculation andalso account for the numerical error that is thus induced.

Hadi MeidaniUniversity of Southern Californiameidani@illinois.edu

Mike KirbyUniversity of UtahSchool of Computingkirby@cs.utah.edu

Dmitry BedrovUniversity of Utah

6 CS15 Abstracts

d.bedrov@utah.edu

CP5

Minimal Set of Mechanisms Controlling Type I In-terferon Differential Signaling

Type I interferon ligands differentially trigger a wide rangeof cellular responses through a common heterodimeric re-ceptor. We seek to identify minimal configurations of cel-lular mechanisms in interferon signaling that could repro-duce this observed behavior. We developed and applied aBayesian model selection method tailored for linear steadystate threshold models. The best models emphasize theimportance of the rate of endocytosis and receptor bindingdynamics within the endosome for interferon signaling.

Pencho YordanovETH Zurichpencho.yordanov@bsse.ethz.ch

Irene Otero-Muras, Joerg StellingDepartment of Biosystems Science and Engineering, ETHZurichirene.otero@bsse.ethz.ch, joerg.stelling@bsse.ethz.ch

CP5

Uncertainty Propagation Using Infinite Mixture ofGaussian Processes and Variational Bayesian Infer-ence

Uncertainty propagation (UP) is a very challenging mathe-matical and computational problem. Among other things,UPs difficulty is due to the limited number of model eval-uations, the curse of dimensionality, discontinuities, andmultivariate responses with non-trivial correlations. In or-der to deal with all these problems simultaneously, we de-velop an infinite mixture of multi-output Gaussian processmodel. We train the model using variational Bayesian in-ference and we obtain highly competing results in porousflow problems.

Peng Chen, Nicholas ZabarasCornell Universitypc423@cornell.edu, nzabaras@gmail.com

Ilias BilionisPurdue Universityebilionis@gmail.com

CP6

Data Based Regularization Methods

Often one is looking for preconditioners with special behav-ior on certain subspaces. So in Multigrid methods the pre-conditioner (smoother) should be defined to remove highfrequency error components while in regularization prob-lems the preconditioner (seminorm) should not recover thenoise. In this talk we will present different methods toobtain such preconditioners especially in connection withill-posed inverse problems by finding data dependent semi-norms.

Thomas K. HuckleInstitut fuer InformatikTechnische Universitaet Muenchen

huckle@in.tum.de

CP6

Preconditioner Scaling for Finite Element Modelsof Turbulent Air/Water Flow in Coastal and Hy-draulic Applications

While three-dimensional models of turbulent air/waterflow are seeing application in coastal and hydraulic engi-neering, the computing resources required for simulatingfield problems is a major barrier to widespread adoption ofthe overall approach. One route to scalable solvers is ex-ploiting the block structure of operators arising from dis-cretizations of multi-phase Navier-Stokes equations. Wepresent a study of recently developed approximate Schurcomplement factorizations to a stabilized finite elementcode for multi-phase flow.

Chris KeesU.S. Army Engineer Research and Development CenterCoastal and Hydraulics Laboratorychristopher.e.kees@usace.army.mil

Aron AhmadiaUS Army Engineer Research and Development Centeraron@ahmadia.net

Jed BrownMathematics and Computer Science DivisionArgonne National Laboratory and CU Boulderjed@jedbrown.org

Matthew FarthingUS Army Engineer Research and Development Centermatthew.w.farthing@usace.army.mil

Barry F. SmithArgonne National LabMCS Divisionbsmith@mcs.anl.gov

CP6

A Scalable Newton-Krylov-Schwarz Method forCoupled Fluid-Structure Interaction Problems

Fluid-structure interaction is a challenging multi-physicsproblem. The difficulties are due to the high nonlinearityderived from the convective term of fluid problems, the con-stitutive relationship of solid materials, the dependency ofthe solution on the displacement of the moving fluid mesh,and unbalanced message passings between different proces-sors resulting from the partition of unstructured meshesinto a large number of parts. To overcome the difficul-ties, we study an inexact Newton-Krylov algorithm witha Schwarz preconditioner to solve the monolithically cou-pled fluid-structure system. We show that the proposedalgorithm is scalable in terms of the iteration count andthe total compute time on a supercomputer with a largenumber of processors.

Fande Kong, Xiao-Chuan CaiDepartment of Computer ScienceUniversity of Colorado Boulderfande.kong@colorado.edu, cai@colorado.edu

CP6

A Parallel Linear Solver Exploiting the Physical

CS15 Abstracts 7

Properties of the Underlying Mechanical Problem

The iterative solution of large systems of equations maybenefit from parallel processing. However, using a straight-forward domain decomposition in ’layered’ geomechanicalfinite element models with significantly different stiffnessesmay lead to slow or non-converging solutions. Physics-based domain decomposition is the answer to such prob-lems, as explained in this paper and demonstrated on thebasis of a few examples. Together with a two-level pre-conditioner comprising an additive Schwarz preconditionerthat operates on the sub-domain level, an algebraic coarsegrid preconditioner that operates on the global level, andadditional load balancing measures, the described solverprovides an efficient and robust solution of large systemsof equations. Although the solver has been developed pri-marily for geomechanical problems, the ideas are applicableto the solution of other physical problems involving largedifferences in material properties.

Kees VuikDelft University of Technologyc.vuik@tudelft.nl

CP7

Parallel Graph Coloring for Scientific Computing

Graph coloring has many applications in scientific comput-ing, such as parallel scheduling, sparse matrix reordering,and automatic differentiation. Often the graph coloringitself must be computed in parallel. We describe new soft-ware for parallel graph coloring on multicore and manycorearchitectures. Our implementation is based on the Kokkoslibrary, which makes the code portable to many platforms,including Intel MIC and GPUs. We discuss algorithmicissues and show some preliminary results.

Erik G. BomanSandia National Labs, NMScalable Algorithms Dept.egboman@sandia.gov

CP7

Solving Sparse Linear Systems on GPUs Based onthe Biell Storage Format

Nowadays, the GPU has evolved into a highly parallelcoprocessor which is suited to compute-intensive, highlyparallel computation. Solving sparse linear systems isone of basic task for scientific and engineering comput-ing. Achieving high performance of this task on GPUsis relatively challenging, especially when the matrix has nospecific structure. For the general sparse matrices, we haveproposed a new data structure based on the BiELL (bisec-tion ELLPACK) format, which is designed to realize theload balance better and thus improve the performance ofthe SpMV (sparse matrix-vector multiplication) on GPUs.Now, we use this new format in iterative methods and pre-conditioning techniques for solving sparse linear systems.Numerical results on various matrices show that GMRES,CG and some preconditioning techniques using this newformat have higher performance than that of using otherformats on GPUs and their CPU counterparts.

Tongxiang GuComputer Network Information Center,Chinese Academy of Sciencegu tx@sina.com

Cong ZhengGraduate School of Chinese Academy of EngineeringPhysicszhengcong55@126.com

Shou GuUniversity of Electronic Science and Technology of China294258779@qq.com

Xingping LiuInstitute of Applied Physics and ComputationalMathematicslxp@iapcm.ac.cn

CP7

Spectral Methods in PDE Solving: a Multi-GPUFramework

Spectral methods offer unconditionally stable time-stepping schemes for solving PDEs numerically. Althougha parallel spectral scheme necessitates the parallelizationof the FFT, all other operations can be executed asyn-chronously. We present a framework utilizing the benefitsof multi-GPU hardwares and demonstrate the advantagesand disadvantages of the method on the results obtainedfor surfactant assisted liquid phase separation in the wa-ter/CO2/hydrocarbon system, which is of high industrialimportance nowadays on the field of improved recovery.

Gyula I. TothWignes Research Centre for PhysicsBudapest, HungaryGyula.Toth@ift.uib.no

Tatjana Kuztensova, Bjorn KvammeDepartment of Physics and TechnologyUniversity of Bergentatyana.kuznetsova@ift.uib.no, bjorn.kvamme@ift.uib.no

CP7

Direct Hierarchical Schur Method for Nested Dis-section Reordered Linear Systems on Multi-GPUs

We propose a direct hierarchical Schur complement methodto solve sparse symmetric positive-definite linear systemson multinode GPU clusters. By exploring the structures ofthe reordered coefficient matrices and developing a schemeto distribute data and schedule tasks, we can solve theproblem efficiently. Our method solves the diagonal blockand Schur subproblems by GPU-based Cholesky factoriza-tion to gain accelerated performance. Numerical resultssuggest the method is scalable for GPU-clusters with dif-ferent node numbers.

Cheming ChuDepartment of Mathematics, National Taiwan Universityr00221036@ntu.edu.tw

Pochuan WangInstitute of Applied Mathematical Sciences, NationalTaiwanUniversityr02246011@ntu.edu.tw

Weichung WangInstitute of Applied Mathematical SciencesNational Taiwan University

8 CS15 Abstracts

wwang@ntu.edu.tw

CP7

Optimizing Structured Grid Numerical Simula-tions for Numa-Multicore Systems

NUMA-multicore systems are now ubiquitous. Optimaldata placement and data move are crucial to fully utilizethese systems. In this talk, we share our experience inoptimizing JASMIN framework for these systems. Firstly,we developed an efficient NUMA-aware heap manager toenforce data locality. Secondly, we designed a scalableNUMA-aware algorithm for structured grid data communi-cations. These technologies are then integrated into JAS-MIN framework and numerical results shows that our ap-proach improves significantly the performance of real-wordapplications on typical NUMA-multicore systems with 10KCPU cores.

Zhang YangInstitute of Applied Physics and ComputationalMathematicsChina Academy of Engineering Physicsyang zhang@iapcm.ac.cn

Aiqing ZhangInstitute of Applied Physics and ComputationalMathematicszhang aiqing@iapcm.ac.cn

Zeyao MoLaboratory of Computational Physics, IAPCMP.O. Box 8009, Beijing 100088, P.R. Chinazeyao mo@iapcm.ac.cn

CP8

Scalable Alternative to Domain Decomposition

We present a novel algorithm based on decomposing therange of a PDE instead of the error. The method allowsefficient use of W and full multigrid cycles in a parallelsetting. A performance model predicts extreme weak scal-ability of the algorithm and numerical tests up to 1000cores confirm the predicted scalability.

David A. AppelhansUniversity of Colorado, Boulderdappelha@gmail.com

Thomas ManteuffelUniversity of Coloradotmanteuf@colorado.edu

Steve McCormickDepartment of Applied MathCU-Boulderstevem@colorado.edu

John RugeUniversity of Coloradojruge@colorado.edu

CP8

Reducing Communication Costs for Sparse MatrixMultiplication within Algebraic Multigrid

We consider the sequence of sparse matrix-matrix mul-

tiplications performed during the setup phase of alge-braic multigrid. In particular, we show that the mostcommonly used parallel algorithm is often not the mostcommunication-efficient one for all of the matrix-matrixmultiplications involved. By using an alternative algo-rithm, we show that the communication costs are reduced(in theory and practice), and we demonstrate the perfor-mance benefit for both model and real problems on large-scale distributed-memory parallel systems.

Grey BallardSandia National Laboratoriesgmballa@sandia.gov

Jonathan J. HuSandia National LaboratoriesLivermore, CA 94551jhu@sandia.gov

Christopher SiefertSandia National Laboratoriescsiefer@sandia.gov

CP8

Avoiding Communication and Synchronization inKrylov Eigensolvers

Solving sparse eigenproblems is an important task in manyengineering problems; Krylov subspace methods, e.g. IR-LAN, TRLAN, are frequent solvers of choice. Krylov sub-space eigensolvers have well-known difficulties scaling be-yond 10,000 processors. This bottleneck is due to commu-nication from dot products at each iteration rather thanmatrix-vector products. When matrix-vector productsscale well, judiciously-applied preconditioners reduce to-tal iterations; they shift work from globally-communicatingdot products to locally-communicating matrix-vector prod-ucts, and we witness improvements in scalability.

Alexander Breuer, Claire Eisner, Jaroslaw Knap, KennethLeiterU.S. Army Research Laboratoryalexander.m.breuer.civ@mail.mil,claire.g.eisner.ctr@mail.mil, jaroslaw.knap.civ@mail.mil,kenneth.w.leiter2.civ@mail.mil

CP8

αSetup-Amg: An Adaptive Setup Based AmgSolver for Large-Scale Simulations with Long Time-Stepping

Coarse-level visiting is the main reason that causes loss ofscalability for AMG solver on massive parallel computer.In our presented adaptive setup strategy, coarsening is per-formed based on the smoothing behavior on each level, in-stead of constructing via an independent setup phase intraditional procedure. As a results, doing relaxations onfiner-levels as much as possible, while the required coarse-levels as less as possible. Realistic simulations on O(104)cores show the improved scalability.

Xiaowen XuInstitute of Applied Physics and ComputationalMathematicsxwxu@iapcm.ac.cn

CP9

A Multiscale Finite Volume with Oversampling

CS15 Abstracts 9

Method to Simulate Low-Frequency Electromag-netic Geophysical Responses

In Geophysics, simulation of low-frequency Electromag-netic (EM) fields in highly heterogeneous, anisotropic me-dia is computationally expensive. One reason being themultiple length scales that coexist in a given realistic set-ting. Discrete models require very fine meshes leading tosolve large linear systems of equations. Here, we develop amultiscale finite-volume method with oversampling to re-duce the size of the system of equations to be solved whileretaining a good level of accuracy in the solution.

Luz Angelica A. Caudillo MataEarth, Ocean and Atmospherical Sciences DepartmentUniversity of British Columbialcaudill@eos.ubc.ca

Eldad HaberDepartment of MathematicsThe University of British Columbiahaber@math.ubc.ca

Lars RuthottoDepartment of Mathematics and Computer ScienceEmory Universitylruthotto@emory.edu

Christoph SchwarzbachUniversity of British Columbiacschwarz@eos.ubc.ca

CP9

A Computational Shock-Tube for ReproducibleComputational Experiments in Traumatic BrainInjury

We developed a computational shock tube with conser-vative finite volume methods and interface-shock interac-tion to complement experiments in traumatic brain in-jury(TBI). The 3D model was implemented using com-pressible Euler equations coupled with a Tammann-EOS.An experimental setup was simulated and yielded insightsnot available by experimental means, emphasizing the im-portance of geometry and yielding cavitation as a possibledamage mechanism. The code is open-source to promotereproducible research.

Mauricio J. Del RazoUniversity of Washingtonmauricio delrazo@yahoo.com

Randall LeVequeUniversity of WashingtonApplied Mathrjl@uw.edu

David CookVA Hospitaldgcook@u.washington.edu

CP9

Universal Meshes for Problems with MovingBoundaries

We develop a framework for the design of high-order finiteelement methods for moving-boundary problems using auniversal mesh: a stationary background mesh contain-

ing the domain of interest for all times that adapts to thegeometry of the immersed domain by adjusting a smallnumber of mesh elements in the neighborhood of the mov-ing boundary. We illustrate the approach and compareit with conventional arbitrary Lagrangian Eulerian (ALE)schemes via numerical examples involving fluid-structureinteraction.

Evan S. GawlikStanford UniversityInstitute for Computational and MathematicalEngineeringegawlik@stanford.edu

Adrian LewStanford UniversityMechanical Engineeringlewa@stanford.edu

CP9

Numerical Simulations of Biological Invasions

Biological invasions occur when there is a road on which anepidemic propagates faster than in the outlying fields adja-cent to the roads. These types of invasions can be modeledusing reaction-diffusion equations with varying parameterson the roads and in the outlying areas with coupling be-tween the two. We will present a numerical method tostudy this problem. Comparisons with previous analyti-cal work with a straight road will be presented, as well asnumerical simulations of more complex road shapes.

Shilpa KhatriDepartment of MathematicsUniversity of North Carolina at Chapel Hillskhatri3@ucmerced.edu

Anna-Karin TornbergKTHakto@kth.se

CP9

Asymptotic-Preserving Space-Time DiscontinuousGalerkin Schemes for a Class of Relaxation Systems

We consider in this work a class of singularly perturbedhyperbolic balance laws that admit a diffusive limit. Suchsystems arise naturally in radiative transport applicationsif one starts with a Boltzmann description and expands thedistribution function in spherical harmonics (i.e., the Pn

approximation). One key difficulty in solving such systemsis that standard numerical schemes have maximum time-step restrictions that vanish in the singular limit. Sev-eral approaches have been proposed in the literature toovercome this difficulty, many of which are based on split-ting the equation into stiff and non-stiff pieces and usingappropriate semi-implicit time-stepping methods. In thiswork we employ a different strategy in order to achieveasymptotic-preservation. We develop a scheme using aspace-time discontinuous Galerkin approach. Several nu-merical test cases are used to validate the proposed scheme.

Anna LischkeIowa State Universityalischke@iastate.edu

James A. RossmanithIowa State University

10 CS15 Abstracts

Deparment of Mathematicsrossmani@iastate.edu

CP10

Finite-Difference Frequency-Domain Analysis ofPhotonic Devices with Periodic Structures Basedon Domain Decomposition

We present an efficient algorithm and implementation of3D finite-difference frequency-domain simulation of pho-tonic devices. By proposing a new matrix-reorderingscheme in the domain decomposition framework, ourmethod exploits the homogeneous and periodic structuresin photonic devices with Yee’s mesh and achieves com-puting resources saving in memory usage and total run-time. The linear system solver is capable of solving the ill-conditioned problems and suitable for parallel computationvia high-performance computers with GPU or many-coreaccelerators.

Cheng-Han DuDepartment of Mathematics, National Taiwan Universityb92006@csie.ntu.edu.tw

Pochuan WangInstitute of Applied Mathematical Sciences, NationalTaiwanUniversityr02246011@ntu.edu.tw

Weichung WangInstitute of Applied Mathematical SciencesNational Taiwan Universitywwang@ntu.edu.tw

CP10

High Order Schemes Based on Operator Splittingand Deferred Corrections for Stiff Time DependentPdes

We consider quadrature formulas of high order in timebased on Radau–type, L–stable implicit Runge–Kuttaschemes to solve time dependent stiff PDEs. Instead ofsolving a large nonlinear system of equations, we developa method that performs iterative deferred corrections tocompute the solution at the collocation nodes. The numeri-cal stability is guaranteed by a dedicated operator splittingtechnique that efficiently handles the stiffness of the PDEsand provides initial and intermediate solutions to the iter-ative scheme.

Max DuarteCenter for Computational Sciences and EngineeringLawrence Berkeley National LaboratoryMDGonzalez@lbl.gov

Matthew EmmettLawrence Berkeley National LaboratoryCenter for Computational Sciences and Engineeringmwemmett@lbl.gov

CP10

Monolithic Multi-Time-Step Coupling Methods forTransient Systems

We shall present new multi-time-step coupling methodsfor first- and second-order transient systems. The pro-posed methods are based on dual Schur domain decompo-

sition, and employ techniques from differential/algebraicequations. We shall also provide a systematic theoreticalstudy of these methods. Several numerical examples will beshown to illustrate the theoretical findings and the salientfeatures of the proposed methods.

Saeid KarimiUniversity of Houstonskarimi@central.uh.edu

Kalyana NakshatralaUniversity Of Houston - Main Campusknakshatrala@uh.edu

CP11

A Parallel Fast Sweeping Method for Quadtreesand Octrees

We present a hybrid shared memory and message pass-ing algorithm for the fast sweeping method on tree basedadaptive grids. We utilize graph theory to decompose thetree into clusters of nodes that can be updated simulta-neously via a shared memory parallelization model. Largescale parallelization is accomplished by domain decompo-sition with a message passing model. We present scalingresults on a number of time-independent Hamilton Jacobiequations.

Miles L. DetrixheUniversity of California Santa Barbaramdetrixhe@engineering.ucsb.edu

CP11

A Communication Algorithm for the Patch-BasedMultiblock Structured Mesh Applications

Multiblock structured mesh allows to handle complexconfigurations which are widely existed in computationalphysics applications. A Patch-based data structure is al-ways used in applications with multiblock structured meshto get satisfying parallel performance. However, suchPatch-based data structure seriously challenges the blockto block data communications. This talk presents an algo-rithm for such communication and introduces its integra-tion to JASMIN infrastructure to support the peta-scalesimulations while tens of thousands of processors are used.Performance results show its robustness.

Hong GuoInstitute of Applied Physics and ComputationalMathematicsguo hong@iapcm.ac.cn

CP11

Scalable Parallel Assembly for High-PerformanceComputing with Isogeometric and Higher-OrderFinite Elements

Isogeometric and higher-order finite element methods leadto system matrices whose parallel assembly requires exten-sive communication. We introduce a distributed-memorydomain decomposition strategy, which uniquely assignseach degree of freedom to one processor, therefore elimi-nating communication completely. We show that althoughcontributions from interface elements need to be computedseveral times on different processors, our approach leads toa scalable and efficient parallel assembly. Algorithmic de-tails and performance measurements for different examples

CS15 Abstracts 11

are presented.

Vasco VarduhnTechnische Universitat Munchenvvarduhn@umn.edu

Dominik SchillingerUniversity of Minnesotadominik@umn.edu

CP11

Exploring Communication Options with AdaptiveMesh Refinement

Finite difference and volume based codes comprise a signif-icant portion of the workload on modern high performancecomputers. Many of these codes use Adaptive Mesh Re-finement (AMR) as a computational strategy. We havedeveloped miniAMR, a miniapp in the Mantevo suite, toexplore AMR communication issues. We compare mini-AMR to CTH, a shock hydrodynamics code, and use mini-AMR to explore some communication strategies that maybe necessary as we move to future architectures.

Courtenay T. Vaughan, Richard BarrettSandia National Laboratoriesctvaugh@sandia.gov, rfbarre@sandia.gov

CP11

A Communication Staging Technique for a Hierar-chical Ocean Model

We study a communications staging technique applied toan algorithmically accelerated, free-surface, z-level oceanmodel. The ocean model is a hierarchical high-order /low-order model, which allows mapping to heterogeneousarchitectures and exploitation of advanced communicationalgorithms. We compare the benefit of communicationstaging between a current numerical method and a re-search method under development, within this high-order/ low-order framework. We provide numerical examples tosupport our study and compare to traditional implemen-tations.

Geoff Womeldorff, Chris Newman, Dana Knoll, LuisChaconLos Alamos National Laboratorywomeld@lanl.gov, cnewman@lanl.gov, nol@lanl.gov, cha-con@lanl.gov

CP12

Asymptotic-Preserving Scheme for the Fokker-Planck-Landau-Maxwell System in the Quasi-Neutral Regime

This work deals with the numerical resolution of theFokker-Planck-Maxwell system in the quasi-neutral regime.In this regime the stiffness of the stability constraints ofclassic schemes causes huge calculation times. That is why,we introduce a new stable numerical scheme consistentwith the transitional and limit models. Such schemes arecalled Asymptotic-Preserving schemes in literature. Thisnew scheme is able to handle the quasi-neutrality limitregime without any restrictions on time and space steps.Next, this approach can be easily applied to angular mo-ment models by using a moments extraction. Finally, theefficientcy of the scheme is validated on the Batishev test

case.

Stephane BrullInstitut de Mathematiques de Bordeaux UMR 5251Universite Bordeauxstephane.brull@math.u-bordeaux1.fr

Bruno Dubroca, d’Humiere Emmanuel, Guisset SebastienCELIAdubroca@math.u-bordeaux1.fr, dhumieres@celia.u-bordeaux1.fr, guisset@celia.u-bordeaux1.fr

CP12

Coarse Multiscale Timestepping for Problems inPlasma Physics with Equation-Free Projective In-tegration

Multiscale plasma problems are hard to simulate becausethe physics of micro and macro-scales are strongly linked.We propose a coarse-grained numerical scheme, based onequation-free projective integration, for a kinetic plasmasystem modelled by the Vlasov-Poisson equations, follow-ing the idea of [Shay, Drake, Dorland 2006]. A particle-in-cell (PIC) code is used to simulate the micro scale dynam-ics. As a first test case, we simulate the propagation andsteepening of a nonlinear ion acoustic wave.

Paul Cazeaux, Jan HesthavenEPFLpaulcazeaux@gmail.com, jan.hesthaven@epfl.ch

CP12

Semi-Lagrangian Discontinuous Galerkin Schemesfor the Relativistic Vlasov-Maxwell System

The Vlasov-Maxwell system describes the evolution of acollisionless plasma, represented through a probability den-sity function (PDF) that self-interacts via the electromag-netic force. One of the main difficulties in numerically solv-ing this system is the severe time-step restriction that arisesfrom parts of the PDF associated with moderate-to-largevelocities. The dominant approach in the plasma physicscommunity is the so-called particle-in-cell method. Thefocus of the current work is on semi-Lagrangian methods.In particular, we develop a method based on high-orderdiscontinuous Galerkin (DG) scheme in phase space, andan operator split, semi-Lagrangian method in time. Themethod is designed to be (1) high-order accurate, (2) massconservative, and (3) positivity-preserving. The resultingscheme is applied to laser-plasma acceleration problems.

Pierson GuthreyIowa State UniversityDepartment of Mathematicspguthrey@iastate.edu

James A. RossmanithIowa State UniversityDeparment of Mathematicsrossmani@iastate.edu

CP12

Discontinuous Galerkin Deterministic Solvers ofBoltzmann-Poisson Models of Hot ElectronicTransport Using Empirical Pseudopotential Meth-ods

We develop Discontinous Galerkin deterministic solvers of

12 CS15 Abstracts

Boltzmann-Poisson models of electronic transport, incor-porating numerical full energy bands obtained from Empir-ical Pseudopotential Methods (EPM), to improve the semi-conductor physical modeling related to energy bandstruc-ture, charge carrier group velocity and scatterings. We willpresent the DG schemes related to electronic transport inboth a conduction band and multi-band system. Simula-tions related to nano-devices such as n+ − n − n+ diodesand double gated MOSFETS will be presented.

Jose A. Morales EscalanteICES, The University of Texas at Austinjmorales@ices.utexas.edu

Irene M. GambaDepartment of Mathematics and ICESUniversity of Texasgamba@math.utexas.edu

Yingda ChengDepartment of MathematicsMichigan State Universityycheng@math.msu.edu

Armando MajoranaDipartimento di Matematica e InformaticaUniversity of Catania - Italymajorana@dmi.unict.it

Chi-Wang ShuBrown UniversityDiv of Applied Mathematicsshu@dam.brown.edu

James R. ChelikowskyInstitute for Computational Engineering and SciencesUniversity of Texas at AUstinjrc@utexas.edu

CP12

Vlasov-Poisson Simulations of Magnetized PlasmasUsing High-Order Continuum Methods

The Vlasov-Poisson equation system, which describes col-lisionless plasma dynamics, can be solved in conservation-law form using continuum methods. A fourth-order accu-rate finite volume method has been implemented using theChombo library to solve the governing equations in twospatial and two velocity dimensions. A new benchmarkbased on the Dory-Guest-Harris instability has been de-veloped for validating magnetized plasma simulations inhigher dimensional phase space. Extension of the methodto cylindrical coordinates is described.

Genia VogmanUniversity of California - Berkeleygeniav@berkeley.edu

Phillip ColellaLawrence Berkeley National LaboratoryPColella@lbl.gov

Uri ShumlakAerospace and Energetics Research ProgramUniversity of Washington

shumlak@uw.edu

CP13

Parallel Methods for Accelerated Multilevel MonteCarlo for Partial Differential Equations with Ran-dom Input

An improvement on previous work where MLMC for PDEsusing finite element iterative solvers was accelerated by im-proving the initial guess during sampling. Using informa-tion gathered at previous samples, the number of iterationsper Monte Carlo sample were greatly reduced. However,these methods did not allow for any parallel computation.In this work we propose alternate methods which can ben-efit from parallel processing.

Zane ColginMiddle Tennessee State Universityzac2g@mtmail.mtsu.edu

CP13

Topology Optimization under Manufacturing Un-certainties

The focus of this work is on incorporating manufacturinguncertainties in the topology optimization of micro andnano devices. The considered microfabrication process isphotolithography, which transfers a mask pattern onto asubstrate. Deviations between the print and the designoccur due to light diffraction and process variations andthese can change severely the design performance. Robustsolutions can be obtained by including uncertainties in thedesign process. The modification increases significantly thecomputational cost and different strategies for its reductionare discussed.

Boyan S. LazarovDepartment of Mechanical EngineeringTechnical University of Denmarkbsl@mek.dtu.dk

CP13

Reducing Dimensionality Through Active Sub-spaces, and the Effect of Gradient Approximationson the Associated Eigenpairs

Uncertainty quantification studies struggle in high dimen-sions; active subspaces are new tools for dimension reduc-tion. Finding active subspaces requires gradient informa-tion which in practice is often unknown. To work aroundthis problem, we can approximate gradients by fitting mod-els to the data and computing the gradients associated withthe models. We illustrate this principle using Local LinearRegressions, and investigate how approximation errors inthe gradients affect the estimates of the eigenpairs. Exam-ples are shown for selected test functions

Uno B. VaalandNorwegian University of Science and Technology, Norwayubvaaland@gmail.com

Paul ConstantineColorado School of MinesApplied Mathematics and Statistics

CS15 Abstracts 13

pconstan@mines.edu

CP13

A Multi-Model Approach for Uncertainty Propaga-tion and Model Calibration in CFD Applications

Monte Carlo-based uncertainty propagations are computa-tionally expensive or even impractical for complex systemssuch as turbulent flows. Efforts to reduce sampling errorsand modeling errors often compete for limited computa-tional resources. Here we propose a multi-model MonteCarlo method that combines models of multiple fidelitiesto propagate uncertainties. A Gaussian process is used toconstruct the model discrepancy between high- and low-fidelity models to improve the results.

Jianxun Wang, Heng XiaoDept. of Aerospace and Ocean Engineering, Virginia Techvtwjx@vt.edu, hengxiao@vt.edu

CP13

Detecting Discontinuities and Localized FeaturesUsing Gaussian Processes

Constructing surrogates of physical models can be ex-tremely difficult, especially when they exhibit sharp, oreven discontinuous, variations. Iteratively-built tree-decompositions, or two-stage classification-regression ap-proaches, have been able to partially deal with this prob-lem. However, virtually all such techniques rely on intuitiveideas. Here, we develop a two-level-deep, potentially infi-nite mixture of Gaussian processes that can automaticallydetect local features with no ad hoc assumptions.

Ilias BilionisPurdue Universityebilionis@gmail.com

Nicholas ZabarasCornell Universitynzabaras@gmail.com

CP14

Optimal Control of Level Sets

We present two level set approaches for numerical simula-tion of evolving interfaces, each based on PDE-constrainedoptimization problems. In the first one the optimal controlprocedure constrains the level set function so as to satisfya conservation law and thus produces a mass conservativenumerical solution. The second approach is designed topreserve the signed distance function property of the levelset function by incorporating the residual of the Eikonalequation into the cost functional and prescribing a bilinearstate equation. Both approaches are evaluated numerically.

Christopher Basting, Dmitri KuzminDortmund University of Technologychristopher.basting@math.tu-dortmund.de,kuzmin@math.uni- dortmund.de

CP14

Fractional Powers of Finite Element Approxima-tion for An Parabolic Optimal Control Problems

In this paper, a numerical theory based on fractional fi-nite element approximations for an optimal control prob-lem with pointwise control constraints is presented and an-

alyzed. The state and co-state variables are approximatedby the piecewise linear functions and the control is ap-proximated by piecewise constant functions. We derive, apriori error estimates for both the control variable and thestate variables. We illustrate with a numerical example toconfirm our theoretical results.

Manickam KandasamyPeriyar University, Salem 636011, INDIAkkmmanickam@gmail.com

Periasamy PrakashDepartment of Mathematics,Periyar UniversitySalem, INDIIAkkmmanickam@gmail.com

CP14

Optimal Order Multigrid Preconditioners for Lin-ear Systems Arising in the Semismooth NewtonMethod Solution Process of a Class of Control-Constrained Problems

In this work we discuss multigrid preconditioners forcontrol-constrained optimal control problems constrainedby semilinear elliptic PDEs. Building upon the existingwork from linear-quadratic case, we study preconditonersfor the submatrices of the reduced Hessian arising in thesemismooth Newton solution process. The control is dis-cretized using piecewise constant finite elements. It is ob-served that the resulting preconditioner is of optimal orderwith respect to the discretization. Analytical and numeri-cal results are presented.

Jyoti SaraswatThomas More Collegesaraswj@thomasmore.edu

Andrei DraganescuDepartment of Mathematics and Statistics, UMBCUniversity of Maryland, Baltimore Countydraga@umbc.edu

CP14

Multigrid Preconditioners for Stochastic OptimalControl Problems with Elliptic Spde Constraints

We consider an optimal control problem constrained by anelliptic SPDE, with a stochastic cost functional of trackingtype. We use a sparse grid stochastic collocation approachto discretize in the probability space and finite elementsto discretize in the physical space. To accelerate the solu-tion process, we propose a deterministic multigrid precon-ditioner for the stochastic reduced KKT system, similar tothe preconditioners introduced by Draganescu and Dupontfor the deterministic PDE constrained problem.

Ana Maria SoaneTowson UniversityDepartment of Mathematicsasoane@umbc.edu

CP14

Numerical Realization of the Open Pit Mine Plan-ning Problem

By reformulating a model for open pit mine planning due to[F. Alvarez et al., 2011], we obtain an optimization problemsubject to viscosity solutions of an underlying Hamilton-

14 CS15 Abstracts

Jacobi PDE. We apply a monotone discretization scheme,which yields an optimal control problem of a system ofODEs. We present the algorithmic treatment and numeri-cal results of this problem under consideration of the effortconstraint, which is of non-incremetal type.

Nikolai StrogiesHumbold Universitat zu BerlinMatheon Mathematics for key technologiesstrogies@mathematik.hu-berlin.de

Andreas GriewankHU Berlin, Germanygriewank@math.hu-berlin.de

CP15

Fast Supercomputing Algorithms for Power Sys-tem Operation and Control

We have developed new supercomputing algorithms formulticore architectures for the state estimation and powerflow problems that present a step towards the real timepower grid optimization and control. We have also devel-oped allocation algorithms for Phasor Measurement Units(PMUs) for estimating the state of a nonlinear power sys-tem in real time. These algorithms involve partitioning oflarge power systems into several sub-systems, and multi-threaded solving with PMU data constraints.

Eugene A. FeinbergStony Brook Universityeugene.feinberg@stonybrook.edu

Bruce FardaneshNew York Power Authoritybruce.fardanesh@nypa.gov

Muqi Li, Roman SamulyakStony Brook Universitymuqi.li@stonybrook.edu,roman.samulyak@stonybrook.edu

George StefopoulosNew York Power Authoritygeorge.stefopoulos@nypa.gov

Gaurish TelangStony Brook Universitygtelang@ams.sunysb.edu

CP15

Simulation-based Current Estimation in Magneto-hydrodynamic Generators

Direct power generation via magnetohydrodynamic princi-pals offers an increase in efficiency over traditional turbo-machinery systems but commercialization is impeded byhigh lifecycle costs. The generators electrodes are dam-aged by the formation of high current density arcs. How-ever, these arcs induce magnetic fields which are measur-able nearby. The development of sensors to detect thesearcs is critical in controlling the phenomenon. We producesimulations using the Mimetic Finite Differences and per-form inversion by simulation-based parameter estimation.

Duncan A. McgregorOregon State UniversityDepartment of Mathematics

mcgregod@math.oregonstate.edu

Vrushali Bokil, Nathan L. GibsonOregon State Universitybokilv@math.oregonstate.du,gibsonn@math.oregonstate.edu

Charles WoodsideNational Energy Technology Laboratoryrigel.woodside@netl.doe.gov

CP16

Data-Driven Uncertainty Quantification withAdaptive Sparse Grids in Subsurface Flow Simu-lations

We present a novel data-driven approach to propagate un-certainty through an expensive subsurface flow simulation.We remove the gap between the subjective approximationof the input’s uncertainty and the unknown real distri-bution by applying sparse grid density estimation. Welink the estimation to the adaptive sparse grid collocationmethod to propagate the uncertainty and obtain new re-finement criteria. Our approach excels by speed, flexibilityand thus can be applied in many fields from environmentalto financial sciences.

Fabian FranzelinUniversitat Stuttgartfabian.franzelin@ipvs.uni-stuttgart.de

Sergey OldayshkinUniversity of Stuttgartsergey.oladyshkin@iws.uni-stuttgart.de

Benjamin PeherstorferACDL, Department of Aeronautics & AstronauticsMassachusetts Institute of Technologypehersto@mit.edu

Dirk PflugerUniversity of StuttgartDirk.Pflueger@ipvs.uni-stuttgart.de

CP16

HPC and Model Reduction Algorithms for Large-Scale Simulation of Stochastic Wave PropagationModels

We discuss a new class of efficient iterative high-orderhigh performance computing (HPC) model reduction algo-rithm for simulating wave propagation exterior to stochas-tic configurations containing very large numbers of parti-cles. Such simulations are crucial in important medical ap-plications such as in vivo and in vitro blood measurementsusing light scattering of blood cells, and topical climatescience applications such as light scattering and absorptionby atmospheric aerosols. Even simulation for a single de-terministic configuration with a large number of particlesis a large-scale computational challenge. The stochasticnature of the configuration leads to a larger dimensionalmodel involving three spatial and several stochastic vari-ables. Our approach provides a practically feasible HPCframework to compute highly accurate statistical momentsto quantify uncertainties in stochastic configurations.

Mahadevan GaneshColorado School of Mines

CS15 Abstracts 15

mganesh@mines.edu

CP16

Quantification of Structural Uncertainty in a LandSurface Model

This study identifies and quantifies model structural un-certainty in the Community Land Model, by fully explor-ing the high-dimensional model parameter space with ef-ficient sampling and then evaluating the discrepancies be-tween the corresponding numerical simulations and obser-vations using wavelet decomposition and other spatiotem-poral analysis approaches. The power spectra, dominanttemporal scales and energy, and characteristic phase shift,are summarized to help quantify model structural uncer-tainty and identify the major processes contributing tosuch uncertainty.

Zhangshuan Hou, Maoyi HuangPacific Northwest National Labzhangshuan.hou@pnnl.gov, maoyi.huang@pnnl.gov

Jaideep RaySandia National Laboratories, Livermore, CAjairay@sandia.gov

Laura SwilerSandia National LaboratoriesAlbuquerque, New Mexico 87185lpswile@sandia.gov

CP16

PDE-Constrained Optimization Applied to CoreFlooding from Reservoir Engineering

This talk explores the impact of PDE-constrained opti-mization on the core flooding problem to determine rock-fluid parameters essential to effective reservoir simulation.Current core flooding technologies are time-consuming andinvolve manual inversion for parameters of interest on sim-plified physical models of fluid flow. We demonstrate, onsimple model problems, that PDE-constrained optimiza-tion can automate the process and do so in a robust waythat incorporates more realistic physical fluid flow model-ing.

Caleb C. MagruderRice University, Computational and Applied Mathematicscm47@rice.edu

Jeremy Brandman, Shivakumar KameswaranExxonMobil Corporate Strategic Researchjeremy.s.brandman@exxonmobil.com, shivaku-mar.kameswaran@exxonmobil.com

CP16

Integration of Geophysical Fluid Dynamics andFully 3D Fluid Dynamics to Simulate MultiphysicsCoastal Ocean Flows

An integration of geophysical fluid dynamics and fully 3Dfluid dynamics models is proposed to simulate multiphysicscoastal ocean flows. This integration is the first of its kindand able to capture flow phenomena at spatial scales O(1) m – O (10,000) km. The approachs methodology andsoftware development are discussed, and its unprecedentedcapabilities will be demonstrated in its applications to cru-cially important problems that are beyond the reach of

other existing models.

Hansong Tang, Ke QuDept. of Civil Eng., City College of NewYork, CUNYhtang@ccny.cuny.edu, kqu00@citymail.cuny.edu

CP17

An Efficient, Pressure Projection Method for Re-acting Low-Mach Flow Simulations

A new explicit variable-density pressure projection methodis proposed with a focus on transient low-Mach-number re-acting flows. This method introduces a new form of thepressure Poisson equation suitable for use with an explicitalgorithm. The density, assumed to be a function of anarbitrary set of transported scalars, is determined by solv-ing a non-linear system of equations at each point in thedomain. The proposed method is evaluated using severaltime-varying, variable-density test cases as well as an an-nular jet flow.

Amir BiglariThe Institute for Clean and Secure EnergyDepartment of Chemical Engineering, University of Utahamir.biglari@utah.edu

Tony SaadInstitute for Clean and Secure EnergyUniversity of Utahsaadtony@gmail.com

James C. SutherlandDepartment of Chemical EngineeringThe University of Utahjames.sutherland@chemeng.utah.edu

CP17

Energy-Stable Open Boundary Conditions forTwo-Phase Flows

We present an effective open boundary condition, andan associated numerical algorithm, within the phase fieldframework for dealing with two-phase outflows or openboundaries. Two-phase outflows refer to situations wherethe interface between two immiscible incompressible flu-ids passes through open portions of the domain boundary.The proposed open boundary conditions ensure the energystability of the two-phase system, even in situations wherestrong backflows or vortices occur at the two-phase out-flow boundaries. Numerical examples involving two-phaseinflows/outflows will be presented to demonstrate the ef-fectiveness of the method when large density ratios andlarge viscosity ratios are involved and when strong back-flows occur at the two-phase outflow boundaries.

Suchuan DongPurdue Universitysdong@math.purdue.edu

CP17

A Low Mach Number Model for Moist Atmo-spheric Flows

We introduce a low Mach number model for moist atmo-spheric flows that accurately incorporates reversible moistprocesses in flows whose features of interest occur on ad-vective rather than acoustic time scales. We numericallyassess the validity of the more computationally efficient low

16 CS15 Abstracts

Mach number approximation for moist atmospheric flowsby contrasting the low Mach number solution to referencesolutions computed with a fully compressible formulationfor a variety of test problems.

Max DuarteCenter for Computational Sciences and EngineeringLawrence Berkeley National LaboratoryMDGonzalez@lbl.gov

Ann S. AlmgrenLawrence Berkeley National Laboratoryasalmgren@lbl.gov

John B. BellCCSELawrence Berkeley Laboratoryjbbell@lbl.gov

CP17

A Stable Projection Method for the IncompressibleNavier-Stokes Equations on Arbitrary Geometriesand Adaptive Quad/oc-Trees

We present a novel stable projection method for the incom-pressible Navier-Stokes equations on non-graded adaptivequad/oc-trees with arbitrary geometries. The viscosity istreated implicitly through a finite volume approach basedon Voronoi partitions and the convective term is discretizedwith a semi-Lagrangian scheme, thus relaxing the time steprestrictions.

Arthur GuittetUCSBarthur.guittet@gmail.com

CP18

Dual-Mixed Finite Element Methods for theBrinkman Problem

We develop a dual-mixed finite element method for theBrinkman problem of viscous flow in porous media. Theprimary unknowns are the fluid velocity, the fluid stress,and the deviatoric part of the velocity gradient. Themethod is stable and accurate for a wide range of problemparameters, including both the Stokes and Darcy limitingcases.

Jason HowellCollege of Charlestonhowelljs@cofc.edu

Noel J. WalkingtonDepartment of Mathematical SciencesCarnegie Mellon Universitynoelw@andrew.cmu.edu

CP18

Numerical Modeling of Non-Associated FlowModel by Successive Convex Optimization: Appli-cation in Incompressible Porous Media

In this study, we propose a numerical method to solve thePDEs of incompressible saturated porous media under dy-namic condition and material nonlinearity. Two parallelschemes are implemented to handle the incompressibilitycondition and the non associated flow material model. Theapproach couples the Raviart-Thomas mixed and Galerkin

finite elements to reach to a stable space based on the inf-sup condition. In the meanwhile, we cast the computationfor material state update as a successive convex optimiza-tion problem.

Zahra S. Lotfian, Mettupalayam SivaselvanSUNY at Buffalozahrasad@buffalo.edu, mvs@buffalo.edu

CP18

Physically Motivated and Certified Approximationof Large Elastic Structures in Real-Time

We introduce a physically motivated, certified model re-duction approach for the simulation of large component-based elastic structures as bridges. We build the systemfrom a library of interoperable, parametrized componentsand apply a domain decomposition method. We computethe displacement field in real-time at a high FEA by usinga reduced basis approximation within the component andphysical modes on the interfaces/ports. The approxima-tion is certified by error bounds based on local, component-wise error indicators.

Kathrin SmetanaDepartment of Mechanical EngineeringMassachusetts Institute of Technologyksmetana@mit.edu

Phuong Huynh, David KnezevicAkselosphuong.huynh@akselos.com, david.knezevic@akselos.com

Anthony T. PateraMassachusetts Institute of TechnologyDepartment of Mechanical Engineeringpatera@mit.edu

CP18

A Variational Multi-Scale Approach Using LinearSimplicial Finite Elements for Transient Viscoelas-tic Solid Mechanics

We present a variational multi-scale (VMS) approach forlinear and nonlinear transient viscoelastic solid mechanics.The method is stable and second-order accurate on linearsimplicial finite elements (including in the incompressiblelimit), with only one additional equation for pressure. Us-ing a VMS decomposition, we model the fine-scale variablesby residual-consistent formulations to maintain the accu-racy. We assess the performance of the method by usingmanufactured solutions, and test it on 3D problems withcomplex geometries.

Xianyi Zeng, Guglielmo ScovazziDuke Universityxy.zeng@duke.edu, guglielmo.scovazzi@duke.edu

CP18

High-Order Mixed Finite Elements for a PressurePoisson Equation Reformulation of the Navier-Stokes Equations with Electric Boundary Condi-tions

Pressure Poisson equation (PPE) reformulations for theNavier-Stokes equations represent a class of methods thatreplace the incompressibility constraint by a Poisson equa-tion for the pressure, with a suitable choice of the bound-

CS15 Abstracts 17

ary conditions so that the incompressibility is maintained.In this talk we present a mixed finite element methods forthe Shirokoff-Rosales PPE reformulation, and demonstratethat this approach allows for arbitrary order of accuracyboth in space and in time.

Dong ZhouTemple Universitydong.zhou@temple.edu

David ShirokoffNew Jersey Institute of Technologydavid.g.shirokoff@njit.edu

Benjamin SeiboldTemple Universityseibold@temple.edu

Rodolfo R. RosalesMassachusetts Inst of TechDepartment of Mathematicsrrr@math.mit.edu

Prince ChidyagwaiLoyola University MarylandDepartment of Mathematics and Statisticspchidyagwai@loyola.edu

CP19

Hierarchical Hpk-Adaptivity for IsogeometricAnalysis

Input your abstract, including TeX commands, here. Hier-archical h-adaptivity has since been implemented for ten-sor product B-splines, NURBS, and T-splines in the con-text of isogeometric analysis. We have implemented hpk-adaptivity in the hierarchical unstructured regime. Wepresent several benchmark examples, which highlight theadvantages of local hierarchical refinement, the necessityof multiple types of refinement, and the power of mixedrefinement types. We present convergence results for hier-archical hpk-refinements, as well as efficient algorithms forhandling hierarchical hpk-adaptivity.

Emily EvansMathematics DepartmentBrigham Young Universityejevans@math.byu.edu

Kevin TewBrigham Young Universitykevin tew@byu.edu

CP19

A Stencil Based Finite Element Method

A Stencil based FEM approach will be introduced whichemploys tensor-product grids with FEM discretizations.This approach eliminates costly FEM assembly, allows forstencil based computations which further reduces the needfor sparse matrix storage and indirect memory access, andmoreover is highly suitable for efficient geometric multigridsolvers. Complex boundaries and immersed (and moving)interfaces are treated locally with a new macro grid align-ment technique. Examples and computational results willbe presented to show the computational effectiveness of the

approach.

Johan S. HysingTokto Inst. of TechnologyAoki Laboratoryjohan@sim.gsic.titech.ac.jp

CP19

An Anchored Analysis of Variance Petrov-GalerkinProjection Scheme for a Class of High DimensionalElliptic Partial Differential Equations

High dimensional operator equations from state space es-timation, molecular dynamics, and mathematical financepresent an interesting numerical challenge because theirdimensionality necessitates schemes beyond classical meshbased methods. In this work, we propose a novel anchoredseparation of variables function decomposition in conjuc-tion with a Petrov-Galerkin projection scheme to overcomethis “curse of dimensionality’. A class of model high dimen-sional elliptic partial differential equations are consideredand numerical results using this nonlinear approximationare presented.

Matthew T. LiUniversity of Toronto Institute for Aerospace Studiesmatt.li@mail.utoronto.ca

Christophe AudouzeUniversity of TorontoInstitute for Aerospace Studiesc.audouze@utoronto.ca

Prasanth B. NairUniversity of Torontopbn@utias.utoronto.ca

CP20

Ground States and Dynamics of Spin-Orbit-Coupled Bose-Einstein Condensates

We study analytically and asymptotically as well as numer-ically ground states and dynamics of two-component spin-orbit-coupled Bose-Einstein condensates (BECs) modeledby the coupled Gross-Pitaevskii equations (CGPEs). Infact, due to the appearance of the spin-orbit (SO) couplingin the two-component BEC with a Raman coupling, theground state structures and dynamical properties becomevery rich and complicated.

Yongyong CaiUniversity of Wisconsin-Madisonyongyong.cai@gmail.com

Weizhu BaoDept. of Mathematics and Center for ComputationalScience anmatbaowz@nus.edu.sg

CP20

Fast Ewald Summation for Mixed Periodic Bound-ary Conditions Based on the Nonuniform Fft

We introduce a generalization of the NFFT based fastEwald summation to mixed periodic boundary conditions.In our approach, we combine the corresponding Ewald for-mulas with the NFFT based fast summation. The newalgorithms can be tuned to high accuracy and the perfor-

18 CS15 Abstracts

mance can be compared to those of well established meth-ods for the fully periodic case (P3M, P2NFFT). In our talkwe will present the main ideas and show numerical results.

Franziska Nestler, Michael PippigChemnitz University of TechnologyDepartment of Mathematicsfranziska.nestler@mathematik.tu-chemnitz.de,michael.pippig@mathematik.tu-chemnitz.de

CP20

Parallel Replica Dynamics with Spatial Paralleliza-tion for a Driven System

We explore the parallel efficiency and speedup for paral-lel replica dynamics (PRD) with spatial parallelization. Intraditional PRD, each replica is assigned to an individualprocessor, which extends the time domain for the simula-tion. By adding spatial parallelization of replicas, we areable to simulate larger systems over the same extendedtime domain. Numerical results on a driven system indi-cate that this approach can lead to more efficient solutionsfor realistic physical systems.

Michael T. Stobb, Juan MezaUniversity of California, Mercedmstobb@ucmerced.edu, jcmeza@ucmerced.edu

Ashlie MartiniUniversity of CaliforniaMercedamartini@ucmerced.edu

CP21

Simulating Non-Dilute Transport in Porous MediaUsing a Tcat-Based Model

Predicting the transport of non-dilute species in fluids ofvariable density in porous media is a challenging problem.We use a thermodynamically constrained averaging theory(TCAT)-based model, which consists of a flow equation,a species transport equation, and closure relations. Werewrite the model as a system of two partial differential-algebraic equations. We use a stiff temporal integrator toperform 1D simulations. The model is nonlinear and non-smooth. We will discuss results and numerical difficulties.

Deena H. GiffenNorth Carolina State Universitydhannou@ncsu.edu

CP21

Hierarchical Model Reduction of the Navier-StokesEquations for Incompressible Flows in Pipes

Hierarchical Model Reduction is a novel technique designedfor reducing computational costs when solving incompress-ible flows in networks of pipes. It consists of a separatediscretization of the axial and the transversal componentsof the flow. The former is approximated by finite elements,the latter by spectral methods. The local accuracy of thetransversal discretization can be adaptively modulated. Inthis talk we present analysis and numerical results, havinghemodynamics as reference application.

Sofia GuzzettiEmory UniversityDepartment of Mathematics and Computer Science

sofia.guzzetti@emory.edu

Simona PerottoMOX - Modeling and Scientific ComputingDipartimento di Matematicasimona.perotto@polimi.it

Alessandro VenezianiMathCS, Emory University, Atlanta, GAale@mathcs.emory.edu

CP21

Interaction Between Toroidal Swimmers in StokesFlow

The focus of this research has been devoted to study the in-teraction between two or more self-propelled toroidal swim-mers in Stokes flow by applying the method of regularizedStokeslets. In the study of the interaction between twoor more toroidal swimmers, we interpret these as three-dimensional, zero Reynolds number analogues of finite vor-tex dipoles in an ideal fluid. Then, we examine the stabil-ity of relative equilibria that can form for these swimmerswhen they are initially placed in tandem or abreast.

Jianjun HuangWorcester Polytechnic Institutejhuang@wpi.edu

Lisa J. FauciTulane UniversityDepartment of Mathematicsfauci@tulane.edu

CP21

Brownian and Hydrodynamic Motion of ComplexShaped Particles in Straight and Branching BloodVessels

We develop a computational methodology for the study ofthe motion of complex shaped nanoparticles within straightand branching vessels subject to thermal fluctuations. Aframework based on Markovian fluctuating hydrodynamicsof the fluid together with a non-Markovian Langevin dy-namics perturbing motion of the particle is adopted. Animportant application of the method is the transport ofnanocarriers within a blood vessel for targeted drug deliv-ery. Supported by NIH through grant U01-B016027.

Yaohong WangDepartment of MathematicsUCSByaohong@seas.upenn.edu

David EckmannDepartment of Anesthesiology and Critical CareUniversity of Pennsylvaniadavid.eckmann@uphs.upenn.edu

Ravi RadhakrishDepartment of BioengineeringUniversity of Pennsylvaniarradhak@seas.upenn.edu

Helena Vitoshki, Portonovo AyyaswamyDepartment of Mechanical Engineering and AppliedMechanicsUniversity of Pennsylvania

CS15 Abstracts 19

elenavit@seas.upenn.edu, ayya@seas.upenn.edu

CP21

An ALE-Phase-Field Method for Dynamic Wettingof Moving Particles

A hybrid method that uses an arbitrary Lagrangian-Eulerian technique to track solid particles and a phase-fieldmethod to capture fluid interfaces as well as moving con-tact lines is developed. The Navier-Stokes and the Cahn-Hilliard equations are are solved by a mixed finite elementmethod on an adaptive triangular moving mesh. Numer-ical results on the interactions between floating particles,also known as the cheerio effect, and the effect of dynamicwetting in water-entry problems will be presented.

Pengtao YueVirginia Polytechnic Institute and State Universityptyue@math.vt.edu

CP22

Anchored ANOVA Petrov-Galerkin (AAPG) Pro-jection Schemes for Parabolic Stochastic PartialDifferential Equations

We present an intrusive method based on the combina-tion of Hoeffding functional ANOVA decomposition withstochastic Galerkin projection for solving a class of high-dimensional parabolic stochastic PDEs. Enforcing thecomponent functions of the approximate solution to be or-thogonal with respect to an appropriate measure and usingadapted test functions, the stochastic weak formulation isdecoupled into independent low-dimensional subproblems.An a priori error analysis and numerical studies for stochas-tic diffusion models are provided.

Christophe AudouzeUniversity of TorontoInstitute for Aerospace Studiesc.audouze@utoronto.ca

Prasanth B. NairUniversity of Torontopbn@utias.utoronto.ca

CP22

Stochastic Low-Dimensional Modeling of NaturalConvection Using Dynamically Orthogonal Decom-position

An efficient numerical method for studying the effect ofstochastic parameters on natural convection is presented.In this methodology, the solution is approximated by a gen-eralized Karhunen-Loeve expansion. The elements of thebasis remain orthogonal for all times and they evolve ac-cording to the system dynamics to capture the energeticallydominant stochastic subspace. The stochasticity can be in-troduced at the boundary conditions and source terms, aproblem setup that includes a wide range of engineeringproblems.

Hessameddin BabaeeMITbabaee@mit.edu

CP22

Local Polynomial Chaos Expansion for Linear Dif-

ferential Equations with High Dimensional Ran-dom Inputs

We present a localized PC expansion for PDEs withrandom inputs, where most existing methods incur pro-hibitively high simulation cost. The local polynomial chaosmethod employs a domain decomposition technique to ap-proximate the stochastic solution locally in a much lowerdimensional random space. Our method applies the cou-pling conditions at the interfaces of the subdomains alongwith accurate samples to ensure both accuracy and high ef-ficiency. We present the general mathematical frameworkof our methodology.

Yi ChenPurdue Universitychen411@purdue.edu

Dongbin XiuUniversity of Utahdongbin.xiu@utah.edu

John D. JakemanSandia National Labsjdjakem@sandia.gov

claude gittelsonETH Zurichclaude.gittelson@sam.math.ethz.ch

CP22

Variance Reduction in the Simulation of StochasticDifferential Equations

Variance reduction techniques are commonly used to en-hance the efficiency of Monte Carlo simulations. This talkfocuses on variance reduction for single and coupled sys-tems of stochastic ordinary differential equations. Variancereduction techniques such as antithetic variates and controlvariates will be described and results presented.

David J. HorntropDept of Mathematical Sciences, Center for Applied MathNew Jersey Institute of Technologydavid.horntrop@njit.edu

CP22

Fully Implicit Runge-Kutta Methods for Multi-Channel Stiff Stochastic Differential Systems withJumps

We discuss systems of ordinary SDEs with non-commutative multi-channel noise including jump-diffusionprocesses. Such systems arise in biochemical networks thatinvolve reactions at different time scales. They are in-herently stiff, both in deterministic and stochastic compo-nents, and change their stiffness with uncertainty. To re-solve this issue we consider fully implicit split-step stochas-tic balanced Runge-Kutta methods and investigate theirconvergence, stability and positivity preserving properties.Numerical examples are provided to show the effectivenessof these methods.

Viktor Reshniak, Abdul KhaliqMiddle Tennessee State Universityvr2m@mtmail.mtsu.edu, abdul.khaliq@mtsu.edu

Guannan ZhangOak Ridge National Laboratory

20 CS15 Abstracts

zhangg@ornl.gov

David A. VossWestern Illinois Universityd-voss1@wiu.edu

CP23

Space-Time Adaptive Multiresolution Simulationsof the Compressible Euler Equations

Fully space-time adaptive multiresolution simulations ofthe compressible Euler equations applied to 2d and 3d Rie-mann problems will be presented. A new higher order localtime stepping strategy is also proposed. The computa-tional efficieny in terms of CPU time and memory com-pression will be assessed. The accuracy of the adaptivesimulations with respect to fine grid computations will bestudied.

Margarete O. Domingues

Instituto Nacional de Pesquisas Espaciais (INPE)margarete.oliveira.domingues@gmail.com

Muller Lopes, Odim MendesINPE, Sao Jose dos Campos, Brazilmullermslopes@gmail.com, odim.mendes@inpe.br

Kai SchneiderUniversite de Provence, Aix-MarseilleCentre de Mathematiques et Informatiquekschneid@cmi.univ-mrs.fr

CP23

Cubic B-Spline Quasi-Interpolation Based Numer-ical Scheme for Hyperbolic Conservation Laws

The present work analyzes the Cubic B-Spline Quasi-Interpolation (CBSQI) based explicit numerical schemesfor hyperbolic conservation laws. To improve the stabilityof the proposed numerical scheme, we modify the CBSQIscheme by adding an artificial diffusion to the numericalscheme through a diffusion parameter b. We derive a rela-tion between the CFL condition and b, which ensures themonotonicity of the proposed numerical scheme. Further,the L∞-error and the TVD property of the modified BSQIscheme are established.

Rakesh KumarIIT Bombayrakeshk@math.iitb.ac.in

Sambandam BaskarIndian Institute of Technology Bombaybaskar@math.iitb.ac.in

CP23

A Space-Time Finite Volume Differencing Methodfor Robust Higher Order Schemes for TransportEquations

A space-time discretization method is applied to constructrobust higher-order schemes for transport equations. Aunified space-time error for integral formulations are con-structed using general weighted quadratures for flux inte-grals. Efficient quadrature approximations of sources arethen sought to account for local space-time fluxes through aconstrained minimization of error. Residual errors are then

utilized to guide right time-steps to ensure error diminish-ing discretizations. Results for 1D heat and hyperbolicconservation laws will be demonstrated.

Yaw KyeiNorth Carolina A&T State UniversityGreensboro, NC 27401ykyei@ncat.edu

CP23

A Runge-Kutta Discontinuous Galerkin Methodfor Modeling Storm-Water Flow in Networks ofDrainage Channels

A unique hybrid 1D/2D approach is presented to modelwater flow in networks of channels that naturally exist incoastal areas. The governing 1D and 2D shallow waterequations are discretized using an RKDGmethod. Flows inindividual channel branches are treated as 1D flows. Thesebranches are conservatively coupled together at junctionsusing 2D elements. The accuracy of the model is estab-lished by comparing the simulation results to experimentaldata and other numerical models.

Prapti NeupaneInstitute for Computation, Engineering and ScienceUniversity of Texas at Austinprapti@ices.utexas.edu

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu

CP23

Lagrangian Particle Method for Complex Flows

A new Lagrangian particle method improving the smoothparticle hydrodynamics (SPH) has been developed forequations of compressible flows. The method eliminatestwo major deficiencies of SPH: the dependence on parame-ter called the smoothening length and the presence of largelinear errors of SPH differential operators. Particle-basedstable, high order upwinding schemes have been developedusing moving weighted least squares. Rigorous verificationtests and applications to complex free surface flows will bediscussed.

Roman Samulyak, Hsin-Chiang Chen, Wei LiStony Brook Universityrosamu@ams.sunysb.edu, hcchen@ams.sunysb.edu,wli@ams.sunysb.edu

CP24

Quantifying Scale Coupling and Energy Pathwaysin the Ocean

The oceans display energetic dynamics across a wide rangeof spatial scales, and researchers have long worked to bet-ter understand the energy coupling between these variousscales. While there have been previous attempts to under-stand energy pathways, assumptions of homogeneity andisotropy have presented a limitation upon the applicabilityof the analyses. Here we present a more general technique,unrestricted by the usual assumptions of homogeneity orisotropy, which allows one to simultaneously probe the dy-namics in both space and time. We makes use of a novelcoarse-graining framework, which accounts for the spheri-

CS15 Abstracts 21

cal geometry of the problem, to directly analyze the cou-pling between scales. We apply this technique to stronglyeddying high-resolution simulations using LANLs Paral-lel Ocean Program. We examine the extent to which thetraditional paradigm for such pathways is valid at variouslocations such as in western boundary currents, near theequator, and in the deep ocean.

Hussein Aluie, Matthew HechtLos Alamos National Laboratoryhussein@rochester.edu, mhecht@lanl.gov

Geoffrey VallisUniversity of Exeterg.vallis@exeter.ac.uk

CP24

A Numerical Simulation of the Sediment Dynamicsin a Three Dimensional Fluid Flow

In this study we use NaSt3D as fluid solver for incom-pressible two-phase flow problems in three dimensions. Weapply this fluid solver to the problem of sediment transportprocesses. The main parts in sediment transport are bedload and suspension load. Both parts are calculated fromthe fluid velocities and are used to compute the transportof sediment masses. Single phase examples like dunes andripples as well as two-phase phenomena like scouring at anobstacle can be reproduced by this model.

Markus BurkowInstitute for Numerical SimulationUniversity Bonnburkow@ins.uni-bonn.de

Michael GriebelUniversitat BonnInst fur Angewandte Mathematikgriebel@ins.uni-bonn.de

CP24

Openfoam Implementation of a New Subgrid-ScaleModel for Large Eddy Simulation

We have recently proposed a novel subgrid scale modelbased on random vortex structures for large eddy simula-tion of the ocean. It is developed for homogeneous and in-compressible flows. In this study, we validate the model bynumerical simulations and compare with well-known sub-grid scale models and direct numerical simulation. Tur-bulent channel flow is solved at different Reynolds num-bers using OpenFOAM software. The results indicate thestrengths of our model and the directions for improvement.

Rukiye KaraDepartment of MathematicsMimar Sinan Fine Arts Universityrukiye.kara@msgsu.edu.tr

Mine CaglarDepartment of MathematicsKoc University

mcaglar@ku.edu.tr

CP24

Free Surface Waves on a Horizontal Shear Flow

Free surface waves on a non-uniform mean flow are con-sidered. The mean flow U(y) varies with the transversecoordinate y but not the vertical. The domain is boundedon one side by a flat rigid vertical wall and unboundedon the other side. The mean flows considered are nonzeronear the vertical wall and approach zero far from the wall,e.g. U = ey. For large y where the mean flow is near-zero the waves are merely irrotational Stokes’ waves. Nearthe wall the mean flow and the waves are rotational butstill inviscid. Solutions are obtained using a nonuniformcoordinate transformation that converts the free surfaceboundary condition into a modified Bessel equation. Thesolution for linear waves that are periodic along the wall isan expansion in Bessel of imaginary argument and imagi-nary order. Eigenvalues are found numerically.

John P. MchughUniversity of New Hampshirejohn.mchugh@unh.edu

Gary LaphamMaine Maritime Academygary.lapham@mma.edu

CP24

Three-Dimensional Wavelet-Based Adaptive MeshRefinement Algorithm for Numerical Simulation ofAtmospheric Global Chemical Transport

Accurate numerical modeling of multi-scale Global Chem-ical Transport Models (GCTMs) is a challenging task.Here we present Wavelet-based Adaptive Mesh Refinement(WAMR) method that allows efficient numerical simulationof the GCTMs by permitting two-three orders of magni-tude finer local resolution than static-grid GCTMs for thesame number of grid points. Therefore, WAMR provides arealistic opportunity to model efficiently challenging multi-scale GCTMs on existing computers by producing accurateresults at a relatively low computational cost. Supportedby NSF grant HRD-1036563

Artem N. Semakin, Yevgenii RastigejevNorth Carolina A&T State Universityarte-semaki@yandex.ru, ye rast@yahoo.com

CP25

Tensor Rank Prediction via Cross Validation

The use of higher order tensors in machine learning hasbecome increasingly popular in recent years. Traditionaltechniques like clustering and principle component analy-sis can be extended to N-way data through the CanonicalPolyadic (CP) tensor decomposition, but only if the rankis known ahead of time. Although computing the rank isNP-hard, we approximate it using cross validation, a sta-tistical technique used to choose model complexity. Wepresent results for dense, normally distributed data.

Woody N. AustinUniversity of Texas - Austinaustinwn@cs.utexas.edu

Tamara G. Kolda, Todd Plantenga

22 CS15 Abstracts

Sandia National Laboratoriestgkolda@sandia.gov, tplante@sandia.gov

CP25

Lu and Partial Orthogonalization Precondition-ing for Conjugate Gradient Solution of Overdeter-mined Sparse Least Squares Problems

Let PLU = AQ be a decomposition of a sparse rank nmatrix A with m rows and n columns, m > n. Conju-gate gradient iteration on the system LTL can be used tofind x minimizing ||Ax − b||2. We compare LU and par-tial orthogonalization preconditionings and also a hybridscheme using both techniques. Automated conversion toC++ from Matlab and Octave scripts is explored.

Gary W. HowellNorth Carolina State Universitygary howell@ncsu.edu

Marc BaboulinUniversity of Paris-Sud/INRIAmarc.baboulin@inria.fr

CP25

On a priori and a posteriori Eigenvalue/eigenvectorError Estimates for Nonlinear Eigenvalue Prob-lems

In this talk we present the recent results in finite elementapproximations for nonlinear eigenvalue problems, withnonlinearity in the spectral parameter. New a priori anda posteriori eigenvalue/eigenvector error estimates are in-troduced and verified using the Residual Inverse IterationMethod (RINVIT) for nonlinear eigenvalue problems. Var-ious numerical examples arising from applications in struc-tural mechanics and electromagnetics are discussed to dis-play the performance of our approach. This is a joint workwith Daniel Kressner (EPF Lausanne).

Agnieszka MiedlarTU Berlinmiedlar@math.tu-berlin.de

Daniel KressnerEPFL LausanneMathicsedaniel.kressner@epfl.ch

CP25

Efficient Low-Rank Solutions of Generalized Lya-punov Equations

An iterative method for the low-rank approximate solu-tion of a class of generalized Lyapunov equations is stud-ied. At each iteration, a standard Lyapunov is solved us-ing Galerkin projection with an extended Krylov subspacemethod. This Lyapunov equation is solved inexactly, thusproducing a nonstationary iteration. The inexactness cri-teria for convergence is provided by a new theorem. Thesetools, together with others presented, comprise an effi-cient algorithm. Numerical experiments indicate that thismethod is competitive vis-a-vis the current state-of-the-artmethods, both in terms of computational times and storageneeds.

Daniel B. SzyldTemple University

Department of Mathematicsszyld@temple.edu

Setephen ShankMassachussets Instittute of Technologysshank@mit.edu

Valeria SimonciniUniversita’ di Bolognavaleria.simoncini@unibo.it

CP25

An Implementation and Analysis of the RefinedProjection Method For (Jacobi-)Davidson TypeMethods

The computation of interior eigenvalues of large sparse ma-trices remains a challenging problem. Compared to theRayleigh-Ritz projection, the refined projection methodis a more effective way to extract Ritz pairs and achievemonotonic convergence but with a much higher compu-tational cost. We analyze four different implementationsof refined projection and present a new efficient approachto compute interior eigenvalues accurately for (Jacobi-)Davidson type methods. Numerical experiments demon-strate the effectiveness and accuracy of the presentedmethod.

Lingfei WuDepartment of Computer ScienceCollege of William & Marylfwu@cs.wm.edu

Andreas StathopoulosCollege of William & MaryDepartment of Computer Scienceandreas@cs.wm.edu

CP26

Updating and Downdating Techniques for Net-works

The total communicability of a network is the sum of theentries in the exponential of its adjacency matrix. Thisquantity offers a good measure of connectivity and can beuseful in the design of networks having certain desirableproperties. I will discuss algorithms that can be used toconstruct networks that are sparse and have a large totalcommunicability. Computational results will be provided.

Francesca ArrigoUniversita degli Studi dell’Insubriafarrigo87@gmail.com

Michele BenziDepartment of Mathematics and Computer ScienceEmory Universitybenzi@mathcs.emory.edu

CP26

Dynamic Causal Modelling of Brain-Behaviour Re-lationships

Dynamic Causal Modelling (DCM) of neuroimaging datahas become a standard tool for identifying the structureand plasticity of brain networks that respond to the ex-perimental manipulation (e.g., sensory stimuli or task de-

CS15 Abstracts 23

mands). DCM, however, does not explain how distributedbrain responses are causally involved in the production ofbehaviour. Here, we propose a generic extension of DCMthat captures how experimental manipulations are trans-formed, through large-scale brain networks, into behaviour(e.g. choices, reaction times).

Jean Daunizeau, Lionel RigouxICMjean.daunizeau@gmail.com, lionel.rigoux@gmail.com

CP26

Using Space Filling Curves to Find An ElementThat Contains a Given Point

Many techniques used in computational science and engi-neering use a 2D triangulation or 3D tesselation of givenregion, for example finite element analysis or computergraphics. Often one needs to locate a triangle or tetrahe-dron that contains a given point. For example, to evalute afinite element solution at an arbitrary point, a containingelement must be located. We present a new fast algorithmfor this operation which is based on space filling curves.

William F. MitchellNIST, Gaithersburg, MDwilliam.mitchell@nist.gov

CP26

Topology Backs Holistic Medicine

The holistic concept in alternative medical practice up-holds that “all of people’s needs should be taken into ac-count.” In other words, the body is seen as a whole. Theholistic point of view can be scientifically validated by de-termining whether different bodily variables are related toone another. In this study we provide strong evidence sup-porting this claim. We establish the existence of at leastone fully non-linear relationship involving two bodily vari-ables.

Fernando SchwartzDepartment of MathematicsUniversity of Tennesseefernando@math.utk.edu

Louis XiangThe Chinese University of Hong Konglouisxiang1994@gmail.com

Kwai L. WongJoint Institute for Computational ScienceUniversity of Tennessee/ORNLkwong@utk.edu

MS1

Local Methods in Network Science

Local methods for methods for network analysis return aproperty of the network without looking even at the entirenetwork. Thus, their runtimes are typically sublinear inthe size of the input network. I’ll discuss recent work onusing local methods to compute centrality vectors such asthe PageRank vector and the heat kernel vector. Theseinvolve approximately solving linear systems and approxi-mate matrix exponentials, respectively. We’ll also see howthese primitives give highly scalable algorithms for com-

munity detection.

David F. GleichPurdue Universitydgleich@purdue.edu

MS1

Identifying the Largest Entries in Matrix Multipli-cation

Consider matrices A and B of size m × p and p × n. Wewish to determine the indices of the largest entries in them × n product matrix C = AB without explicitly calcu-lating C. For instance, if A represents an adjacency net-work of social connections, then C = AA′ (i.e., B = A′)represents the number of common neighbors for any pairof nodes. The largest entries correspond to those pairswith the most common neighbors. Alternatively, it maybe the case that A and B are latent variables in a predic-tion task, and the largest entries in C = AB correspondto the most likely pairings. The matrices A and B may bedense with p � m,n or general sparse matrices (in whichcase C may or may not be dense). We propose a sampling-based method to efficiently identify the largest entries inC. Each sample produces a pair (i, j), and the pairs thatare sampled most frequently correspond to the largest en-tries in C in expectation. Specifically, the probability ofchoosing pair (i, j) is proportional to c2ij . The number ofsamples for a given confidence level is independent of thesize of the matrices, and in practice s � mn. The cost ofthe method is O(nnz(A) + nnz(B)) for preprocessing andO(log(nnz(A)) + log(m) + log(n)) per sample.

Grey Ballard, Tamara G. KoldaSandia National Laboratoriesgmballa@sandia.gov, tgkolda@sandia.gov

Ali PinarSandia National Labsapinar@sandia.gov

C. SeshadhriUniv. California Santa Cruzcsesha@gmail.com

MS1

Mining Uncertain Networks

Abstract not available at time of publication.

Evamaria TerziBoston Universityevimaria@cs.bu.edu

MS1

Network Science of Brain Networks

Abstract not available at time of publication.

Zoltan ToroczkaiUniversity of Notre-Dametoro@nd.edu

MS2

Convex Biclustering

In the biclustering problem, we seek to simultaneouslygroup observations and features. We present a convex

24 CS15 Abstracts

formulation of the biclustering problem that possesses aunique global minimizer and an iterative algorithm, CO-BRA, that is guaranteed to identify it. The key contri-butions of our work are its simplicity, interpretability, andalgorithmic guarantees. We demonstrate the advantagesof our approach, which includes stably and reproduciblyidentifying biclusterings, on simulated and real microarraydata.

Eric ChiRice Universityechi@rice.edu

Richard G. BaraniukRice UniversityElectrical and Computer Engineering Departmentrichb@rice.edu

Genevera AllenRice Universitytba@rice.edu

Ronald CoifmanYale UniversityDepartment of Computer Sciencecoifman@math.yale.edu

MS2

Cluster-based Reduced-order Modelling: FromShear Flows to Engine Tumble Motion

We propose a cluster-based ROM strategy to distil nonlin-ear mechanisms in an unsupervised manner. This strat-egy uses cluster analysis to partition snapshot data into asmall number of representative states in the state space.The transitions between the states are dynamically mod-elled as Markov process. CROM has potential applicationsfor the systematic identification of physical mechanisms ofcomplex dynamics, for the identification of precursors todesirable and undesirable events, and for flow control de-sign exploiting nonlinearities.

Eurika KaiserInstitute PPRIME, CNRSeurika.kaiser@univ-poitiers.fr

Bernd R. NoackInstitut PPRIME, CNRSbernd.noack@univ-poitiers.fr

Laurent Cordier, Laurent CordierInstitute PPRIME, CNRSlaurent.cordier@univ-poitiers.fr,laurent.cordier@univ-poitiers.fr

Andreas SpohnInstitute PPRIME, ENSMAandreas.spohn@ensma.fr

Marc Segond, Markus W AbelAmbrosys GmbHmarc.segond@ambrosys.de, markus.abel@ambrosys.de

Guillaume DavillerCERFACS, Francedaviller@cerfacs.fr

Jan sth, Sinisa Krajnovic

Chalmers University of Technologyjan.osth@chalmers.se, sinisa@chalmers.se

Yujun CaoInstitute PPRIME, ENSMARENAULT, Franceyujun.cao@ensma.fr

Jacques BoreeInstitute PPRIME, ENSMAjacques.boree@ensma.fr

Robert K. NivenUNSW/ADFA, Australiar.niven@iinet.net.au

Louis N. CattafestaFCAAP, Florida State University, USAcattafes@gmail.com

MS2

Self-Tuning Complex Systems

Abstract not available at time of publication.

J. Nathan KutzUniversity of WashingtonDept of Applied Mathematicskutz@uw.edu

MS2

The Impact of L1 optimization in Nonlinear PDE

At this time almost everyone interested in finding sparsesolutions to discrete equations is aware that l1 optimiza-tion plays a key role. However that fact that L1 optimiza-tion, using the techniques developed for l1, is a very pow-erful tool in nonlinear PDE and numerical analysis is lesswidely known. H. Brezis, in 1974, showed that adding anL1 type penalty to calculus of variations problems whichlead to elliptic equations plus a signum type terms givessolutions with compact support. I will discuss this, numer-ical aspects, applications to Schrodinger equations, obsta-cle problems, numerical homogenization and certain highdimensional PDE’s.

Stanley J. OsherUniversity of CaliforniaDepartment of Mathematicssjo@math.ucla.edu

MS3

Modulus of Families of Walks on Graphs

The modulus of a family of paths in a continuum providesa quantitative assessment of the “richness’ of the family:large families of short paths have larger modulus than smallfamilies of long paths. In the discrete setting, the conceptof modulus can be linked to several graph-theoretic quan-tities including shortest path, minimum cut, and effectiveresistance. This talk will cover connections among theseconcepts, some applications, and a numerical algorithm forcomputing the modulus.

Nathan AlbinKansas State University

CS15 Abstracts 25

albin@math.ksu.edu

MS3

Graph Directed Topic Modeling

Recent advancements in dictionary learning or topic mod-eling algorithms find data representations using sparse cod-ing techniques such as L1 or non-parametric Bayesian reg-ularizations. Concurrently, the graph community has de-veloped algorithms to segment data into clusters using sim-ilarity measures. In this work, we integrate the graphicalmodels and dictionary learning concepts to infer represen-tations directed by a graphical structure, enforcing priorcorrelations among documents. The utility of this tech-nique is demonstrated on text and image data.

Arjuna FlennerNaval Air Weapons Stationaflenner@mac.com

Cristina Garcia-CardonaLos Alamos National Laboratorycgarciac@lanl.gov

MS3

Building Graphs to Analyze Big Data

There has been increasing demand to understand the dataaround us. The flood of social media requires new math-ematics, methodologies and procedures to extract knowl-edge from massive datasets. Spectral methods are graphbased techniques that uses eigenfunctions of a graph toextract the underlying global structure of a dataset. Theconstruction of these, application dependent, graphs re-quire new mathematical ideas that extend data represen-tation, distance, topic modeling and sparsity. The productis often massive matrices that push the limits of matrixcomputation. This talk looks at applications to analyzingtext, images, Twitter microblogs and content based search.

Blake HunterUCLA Mathematics Departmentbhunter@cmc.edu

MS3

An Incremental Reseeding Strategy for Clustering

In this work we propose a simple and easily parallelizablealgorithm for multiway graph partitioning. The algorithmalternates between three basic components: diffusing seedvertices over the graph, thresholding the diffused seeds,and then randomly reseeding the thresholded clusters. Wedemonstrate experimentally that the proper combinationof these ingredients leads to an algorithm that achievesstate-of-the-art performance in terms of cluster purity onstandard benchmarks datasets. Moreover, the algorithmruns an order of magnitude faster than the other algorithmsthat achieve comparable results in terms of accuracy. Thisa joint work with X. Bresson, H. Hu, A. Szlam and J. vonBrecht.

Thomas LaurentLoyola Marymount Universitythomas.laurent@lmu.edu

MS4

Adaptive h-refinement for Reduced-order Models

via Basis Splitting

This talk discusses a method to adaptively refine reduced-order models a posteriori without requiring additional full-order-model solves. The technique is analogous to mesh-adaptive h-refinement: it enriches the reduced-basis spaceonline by ‘splitting’ a given basis vector into several vec-tors with disjoint support. The splitting scheme is de-fined by a tree structure constructed offline via recursivek-means clustering of the state variables using snapshotdata. The method identifies the vectors to split onlineusing a dual-weighted-residual approach that aims to re-duce error in an output quantity of interest. The resultingmethod generates a hierarchy of subspaces online withoutrequiring large-scale operations or full-order-model solves.Further, it enables the reduced-order model to satisfy anyprescribed error tolerance regardless of its original fidelity,as a completely refined reduced-order model is mathemat-ically equivalent to the original full-order model.

Kevin T. CarlbergSandia National Laboratoriesktcarlb@sandia.gov

MS4

Online-Adaptive Reduced Bases for ParametricProblems

We address the topic of projection-based model order re-duction for parametric systems. If the solution manifoldunder varying parameters or time is complex, single re-duced projection spaces are not sufficient to achieve globalaccurate approximation. Locality with respect to param-eter or time for generating submodels in the offline phaseis a solution but may be misleading or yield redundantmodels. Therefore, we propose to generate reduced mod-els by online-greedy procedures from dictionaries of basiselements.

Bernard HaasdonkUniversity of Stuttgarthaasdonk@mathematik.uni-stuttgart.de

MS4

A Nonlinear Trust Region Framework for PDE-Constrained Optimization Using Progressively-Constructed Reduced-Order Models

The large computational cost associated with high-fidelitysimulations has limited their use in many-query scenarios(optimization and UQ). A nonlinear trust-region frame-work using Reduced-Order Models (ROMs) is introducedas a means to accelerate PDE-constrained optimization. Aprogressive approach is employed to construct a ROM dur-ing the optimization procedure. On problems from aero-dynamic shape optimization, the framework reduces thenumber of queries to the high-dimensional model by a fac-tor of 4 with no loss in accuracy.

Matthew J. ZahrStanford UniversityUniversity of California, Berkeleymzahr@stanford.edu

Charbel FarhatStanford University

26 CS15 Abstracts

CFarhat@stanford.edu

MS5

A Bound-Plus-Equality Constrained QuadraticMinimization Algorithm for Inverse Problems

Solutions of inverse problems are often obtained by solvinga quadratic minimization problem, e.g., the least squaressolution in linear cases. Prior information can be in-corporated into such problems by adding constraints tothe quadratic minimization. Moreover, L1 regularizationmethods, such as total variation and wavelet-based regu-larization, can be implemented by solving a constrainedquadratic minimization problem. In this talk, we presentan algorithm for solving bound-plus-equality constrainedquadratic minimization problems, with applications inimaging.

Johnathan M. BardsleyUniversity of Montanabardsleyj@mso.umt.edu

Marylesa HowardNational Security Technologies, LLChowardmm@nv.doe.gov

MS5

Statistically Motivated Preconditioners and Stop-ping Criteria for Biomedical Inverse Problems

The solution of large-scale, ill-posed, possibly underdeter-mined linear systems of equation arises in many applica-tion to linear and nonlinear biomedical inverse problems.In this talk we show how statistical a-priori expectationabout the solution and statistical description of the noisein the right-hand side can be exploited to improve the res-olution of the linear system and design solid stopping rulesfor Krylov-type iterative methods.

Daniela CalvettiCase Western Reserve UnivDepartment of Mathematicsdxc57@case.edu

Erkki SomersaloCase Western Reserve Universityejs49@case.edu

MS5

Numerical Implementation of a New Class ofForward-Backward-Forward Diffusion Equationsfor Image Restoration

In this talk, we present the implementation and numer-ical experiments demonstrating new forward-backward-forward nonlinear diffusion equations for noise reductionand deblurring, developed in collaboration with PatrickGuidotti and Yunho Kim. The new models preserve andenhance the most desirable aspects of the closely-relatedPerona-Malik equation without allowing staircasing. Byusing a Krylov subspace spectral (KSS) method for time-stepping, the properties of the new models are preservedwithout sacrificing efficiency.

James V. LambersUniversity of Southern MississippiDepartment of MathematicsJames.Lambers@usm.edu

Patrick GuidottiUniversity of California at Irvinegpatrick@math.uci.edu

Yunho KimUlsan National Institute of Science and TechnologyDepartment of Mathematical Sciencesyunhokim@unist.ac.kr

MS5

Recycling Krylov Subspaces for Parametric LinearSystems Arising from Hyperspectral Diffuse Opti-cal Tomography

The imaging of chromophore concentrations using DiffuseOptical Tomography (DOT) data can be mathematicallydescribed as an ill-posed and non-linear inverse problem.The reconstruction algorithm for hyperspectral data evenusing a linearized Born model is prohibitively expensive,both in terms of computation and memory. We discussnovel computational strategies for reducing the computa-tional cost based on a recycling Krylov subspace approachfor a class of parameteric linear systems. We will demon-strate the resulting computational gains and the validity ofour approach by comparison with synthetic experiments.

Arvind SaibabaDepartment of Electrical and Computer EngineeringTufts Universityarvind.saibaba@tufts.edu

Misha E. Kilmer, Eric MillerTufts Universitymisha.kilmer@tufts.edu, elmiller@ece.tufts.edu

MS6

The Dirichlet-Neumann Iteration and UnsteadyThermal Fluid Structure Interaction

We consider unsteady thermal fluid structure interactionto model industrial gas quenching in steel forging, wheresteel is cooled using high pressured gas. The models arethe compressible Navier-Stokes equations and the nonlin-ear heat equation. In time, a previously developed efficientadaptive higher order time integration scheme with lin-ear extrapolation within a partitioned Dirichlet-Neumannframework for the coupling is considered. The iteration issurprisingly fast and we present some analysis that explainsthis phenomenon.

Philipp BirkenDepartment 10, Mathematics and Natural SciencesUniversity of Kassel, Germanyphilipp.birken@na.lu.se

Azahar Monge SanchezLund UniversityCentre for the Mathematical Sciencesazahar.monge@na.lu.se

MS6

Multi-level Acceleration of Strongly CoupledFluid-structure Interaction with Manifold Map-ping

Strongly coupled partitioned fluid-structure interactionproblems require multiple coupling iterations per time step.In order to reduce the number of coupling iterations, the

CS15 Abstracts 27

manifold mapping algorithm is applied, which originatesfrom multi-fidelity optimization. Preliminary computa-tions showed a gain of factor four in terms of the numberof coupling iterations with two grid levels. To gain a largerspeedup, the use of more than two levels is investigated fora three-dimensional engineering case, namely a hydrofoil.

David BlomDelft University of Technologyd.s.blom@tudelft.nl

Alexander H. van Zuijlen, Hester BijlFaculty Aerospace EngineeringDelft University of Technology, NLa.h.vanzuijlen@tudelft.nl, h.bijl@tudelft.nl

MS6

Multirate GARK Schemes

Multirate GARK schemes define a multirate extensionof GARK schemes, generalized additive Runge-Kuttaschemes. These allow for exploiting multirate behaviourin both the right-hand sides and in the components in arather general setting, and are thus especially useful forcoupled problems in a multiphysics setting. We discuss twotypes of MGARK schemes: IMEX methods, which makesfully use of the different dynamics and stability propertiesof the coupled system; and fully implicit schemes, which in-herit the stability properties from both underlying schemeswithout any coupling constraint.

Michael GuentherBergische Universitaet Wuppertalguenther@math.uni-wuppertal.de

Adrian SanduVirginia Polytechnic Institute andState Universitysandu@cs.vt.edu

MS6

Partitioned Fluid-Structure Interaction on Mas-sively Parallel Systems

Multi-physics applictions such as fluid-structure interac-tion (FSI) need massively parallel computations to resolveall relevant spatial and temporal scales. Yet, many classicalcoupling approaches limit the scalability of the overall sim-ulation. A partitioned approach allows to reuse highly scal-able single-physics codes. We discuss different milestonestowards massively parallel FSI, including inter-solver par-allelism, parallel communication, and parallel data map-ping. All methods are implemented in the coupling librarypreCICE. Test cases with different solvers are presented.

Florian Lindner, Miriam MehlUniversitat Stuttgartflorian.lindner@ipvs.uni-stuttgart.de,miriam.mehl@ipvs.uni-stuttgart.de

Benjamin UekermannTU Munichuekerman@in.tum.de

MS7

Envelopes: Subspace Methods for Efficient Estima-

tion in Multivariate Statistics

An envelope is a nascent construct for increasing efficiencyin multivariate statistics. Improvements in efficiency aremade possible by recognizing that the data may containextraneous variation that is immaterial to the purpose ofthe analysis. This leads to an active subspace – an enve-lope – for enveloping the material information and therebyreducing variation. Beginning with the multivariate lin-ear model, we will discuss various types envelopes and howthey act to improve efficiency.

Dennis CookUniversity of Minnesotadennis@stat.umn.edu

MS7

Active Subspaces in Theory and Practice

We review the theory of the active subspace method froma dimensionality reduction perspective. We describe howa space with lower dimension than the input space can beconstructed using gradient information for the quantitiesof interest. Bounds are constructed that relate the errorin reduced order models of the quantities of interest tothe SVD of the Covariance matrix of the input-output Ja-cobian. Applications from aerospace engineering and oilreservoir simulation will be presented.

Eric DowMassachusetts Institute of Technologyericdow@mit.edu

MS7

Mathematical Foundations of Subspace Selections

In this talk we present and analyze algorithms which al-low us to detect the relevant subspaces characterizing acertain nonlinear phenomenon, exclusively from randomcollections of relatively few data. We discuss the theoreti-cal guarantees given by these algorithms both for samplesdrawn at random according to specific clustering distribu-tions and for samples drawn without any specific cluster-ing. We show applications in determining regularizationparameters in image denoising, without need of knowingthe noise level a priori.

Massimo FornasierTechnical University Munichmassimo.fornasier@ma.tum.de

Valeriya NaumovaSimula Research Laboratoryvaleriya@simula.no

MS7

Order Determination for Dimension Reduction Us-ing An Alternating Pattern of Spectral Variability

Similar eigenvalues in random matrices leads to highly vari-able eigenvectors; otherwise, eigenvector variability tendsto be small. We exploit this phenomenon to estimate therank of a fixed, unknown matrix. The proposed methodcombines eigenvalue drops and eigenvector variability topinpoint the rank. Under general conditions, we establishthe consistency of the new estimator. We also compare theproposed method with other order-determination methods

28 CS15 Abstracts

by simulations and in an applied setting.

Bing LiDepartment of StatisticsPenn Statebing@stat.psu.edu

Wei LuoPenn State Universitywul132@psu.edu

MS8

Filtering Unstable Quadratic Dissipative Systems

Data assimilation refers to the combination of noisy mea-surements of a physical system with a model of the systemin order to infer the state and/or parameters. In the con-text of numerical weather prediction the underlying modelis typically an unstable dynamical system. Unstable dy-namical systems can be stabilized, and hence an estimateof the solution recovered from noisy data, provided twoconditions hold. First, observe enough of the system: inparticular, the unstable modes. Second, weight the ob-served data sufficiently over the model. This talk will il-lustrate this for the 3DVAR filter applied to three unstablequadratic dissipative dynamical systems of increasing di-mension: the Lorenz 1963 model, the Lorenz 1996 model,and the 2D Navier-Stokes equation.

Kody LawSRI UQ Center, CEMSE, KAUSTkodylaw@gmail.com

Andrew StuartMathematics Institute,University of Warwicka.m.stuart@warwick.ac.uk

Daniel Sanz-AlonsoUniversity of Warwickd.sanz-alonso@warwick.ac.uk

Abhishek ShuklaWarwicka.shukla@warwick.ac.uk

MS8

Conditions for Successful Data Assimilation inHigh Dimensions

We show that numerical data assimilation can be successfulonly if an effective dimension of the problem is not exces-sive. This effective dimension depends on the noise in themodel and the data, and can be moderate even when thenumber of variables is huge. We analyze several data as-similation algorithms, including particle filters, and showthat well-designed particle filters can solve most of thosedata assimilation problems that can be solved in principle.

Matthias MorzfeldDepartment of MathematicsLawrence Berkeley National Laboratorymmo@math.lbl.gov

Alexandre ChorinDepartment of MathematicsUniversity of California at Berkeley

chorin@math.berkeley.edu

MS8

High Dimensional Non-Gaussian Bayesian Infer-ence with Transport Maps

Characterizing high dimensional posterior distributions inthe context of nonlinear and non-Gaussian Bayesian in-verse problems is a well-known challenging task. A recentapproach to this problem seeks a deterministic transportmap from a reference distribution to the posterior. Thusposterior samples can easily be obtained by pushing for-ward reference samples through the map. In this talk, weaddress the computation of the transport map in high di-mensions. In particular, we propose a scalable adaptivealgorithm that exploits recent ideas in dimensionality re-duction for Bayesian inverse problems.

Alessio Spantini, Youssef M. MarzoukMassachusetts Institute of Technologyspantini@mit.edu, ymarz@mit.edu

MS8

Ensemble Methods for Large-Scale PDE-Constrained Bayesian Inverse Problems

Sampling techniques are important for large-scale high di-mensional Bayesian inferences. However, general-purposetechnique such as Markov chain Monte Carlo is intractable.We present an ensemble transform algorithm that is rootedfrom the optimal transportation theory. The method trans-forms the prior ensemble to posterior one via a sparse op-timization. We develop methods to accelerate the compu-tation of the transformation. Numerical results for large-scale Bayesian inverse problems governed by PDEs will bepresented.

Kainan WangTexas A&M Universitykainan@ices.utexas.edu

Tan Bui-ThanhThe University of Texas at Austintanbui@ices.utexas.edu

MS9

Matrix-Free Interior-Point Method for Large ScaleMachine Learning Problems

We present a general interior point method for piecewiselinear quadratic (PLQ) penalties. These penalties are ubiq-uitous in signal processing, inverse problems, and machinelearning applications; examples include the L2, L1, Huber,Vapnik, hinge loss, elastic net, and many others. We ex-ploit a conjugate representation of these penalties to designan interior point method for the entire class. The repre-sentation also gives rise to a calculus that makes it possibleto handle compositions, addition, and smoothing of PLQpenalties, as well as exploit specific problem structure. Themethod is available in an open source package called IP-solve. Future work focuses on matrix free implementationsof IPsolve. Joint work with James Burke, Gianluigi Pil-lonetto, and Dominique Orban.

Aleksandr AravkinIBM T.J. Watson Research Center

CS15 Abstracts 29

saravkin@us.ibm.com

MS9

Matrix Free Methods for Large-Scale NonlinearConstrained Optimization

We present two methods for solving exact penalty subprob-lems for nonlinear constrained optimization problems onproduct sets that arise when solving large-scale optimiza-tion problems. The first is a novel iterative re-weighting al-gorithm (IRWA) that iteratively minimizes quadratic mod-els of relaxed subproblems while automatically updating arelaxation vector. The second approach is based on alter-nating direction augmented Lagrangian (ADAL) technol-ogy applied to our setting. The main computational costsof each algorithm are the repeated minimizations of convexquadratic functions which can be performed matrix-free.Both algorithms are globally convergent under loose as-sumptions, and each requires at most O(1/ε2) iterations toreach epsilon-optimality of the objective function. Exper-iments exhibit the ability of both algorithms to efficientlyfind inexact solutions. However, in certain cases, these ex-periments indicate that IRWA can be significantly moreefficient than ADAL.

James V. BurkeUniversity of WashingtonDepartment of Mathematicsburke@math.washington.edu

MS9

Gauges, Duality, and Phase Retrieval

Gauge functions significantly generalize the notion of anorm, and gauge optimization is the class of problems forfinding the element of a convex set that is minimal withrespect to a gauge. These conceptually simple problemsappear in a remarkable array of applications. I illustratethese ideas in the context of the phase retrieval problem,and show how they lead to new algorithmic approaches forlarge problems.

Michael FriedlanderMathematics DepartmentUniversity of California, Davismpf@math.ucdavis.edu

MS9

Anatomy of a Matrix-Free Interior-Point Solver forConvex Optimization

Recent updates to PDCO (Saunders et al.) implementmultiple matrix-free and semi-matrix-free options, includ-ing CG with constraint preconditioner, a limited-memoryLDL factorization preconditioner, and several formulationsof the Newton equations as a system or least-squares prob-lem. Most take advantage of regularization. The newobject-oriented design lets users select a variant appropri-ate for their problem, and implement new system solvers.We illustrate the new solvers on large-scale problems.

Dominique OrbanGERAD and Dept. Mathematics and IndustrialEngineeringEcole Polytechnique de Montreal

dominique.orban@gerad.ca

MS10

Difference Potentials Method for Parabolic Modelsin Irregular Domains

The Difference Potentials Method (DPM) was originallydesigned as a computationally efficient framework for thenumerical approximation of the solutions to elliptic prob-lems in irregular domains in 2D and 3D. Additionally, DPMcan handle general boundary conditions with equal ease.Recently DPM was extended with high-order accuracy toparabolic models with variable coefficients and interfaces.I will discuss this extension and illustrate the performanceof the approach with several 1D and 2D examples.

Jason AlbrightUniversity of UtahMath Departmentalbright@math.utah.edu

Yekaterina EpshteynDepartment of mathematicsUniversity of Utahepshteyn@math.utah.edu

MS10

Multidimensional Embedded Finite DifferenceMethods which Satisfies Energy Estimates

Abstract not available at time of publication.

Adi DitkowskyDepartment of Applied MathematicsTel Aviv Universityadid@post.tau.ac.il

MS10

High Order Cut Finite Elements Methods

We will present recent work on high order finite elementmethods for cut and composite meshes. The commontheme is to use Nitsche’s method to enforce conditions onboundaries or interfaces, or to solve PDEs on surfaces. Theinstabilities that may occur can be resolved in various waysfor example using a mesh-based element-wise association orby adding stabilization terms to the variational form. Boththeoretical and numerical results will be shown.

August JohanssonSimula School of Research and Innovation SimulaResearch LabNorwayaugust@simula.no

Mats G. LarsonDepartment of MathematicsUmea Universitymats.larson@math.umu.se

MS10

High-Order Accurate Difference Potentials Meth-ods for the Stokes–Darcy Problem

The Stokes–Darcy problem is a multiphysics model cou-pling Stokes flow with flow in porous media. In my talkI will present an efficient, high-order accurate numerical

30 CS15 Abstracts

method for this problem. This method, based on the Dif-ference Potentials Method, uses uniform Cartesian gridswhich do not conform to boundaries or interfaces, and isuniformly high-order accurate. I will present numerical re-sults to test the new method. This talk is based on jointwork with Y. Epshteyn.

Yekaterina EpshteynDepartment of mathematicsUniversity of Utahepshteyn@math.utah.edu

Kyle R. SteffenUniversity of UtahDepartment of Mathematicssteffen@math.utah.edu

MS11

Finite Element Multigrid Framework for MimeticFinite Difference Discretizations

We are interested in the efficient multigrid method of lin-ear systems of equations discretized from the mimetic finitedifference (MFD) schemes which work on general unstruc-tured and irregular grids and result in discrete operatorsthat satisfy the exact sequence connecting grad, div andcurl operators on the continuous level. We derive suchMFD schemes from the standard finite element spaces.Using the finite element framework, we are able to ana-lyze the convergence of the MFD discretizations and con-struct efficient multigrid methods for the MFD discretiza-tions of elliptic partial differential equations based on thelocal Fourier analysis. Finally, we present several numer-ical tests to demonstrate the robustness and efficiency ofthe proposed multigrid methods.

Francisco Jose GasparUniversity of Zaragozafjgaspar@unizar.es

Xiaozhe HuThe Pennsylvania State Universityxiaozhe.hu@tufts.edu

Carmen RodrigoUniversity of Zaragozacarmenr@unizar.es

Ludmil ZikatanovDepartment of MathematicsThe Pennsylvania State Universityltz@math.psu.edu

MS11

New Multigrid Methods for Saddle Point Problems

We have developed new smoothers for the Stokes and linearelasticity problems. Using the multigrid Poisson solve, weprecondition the indefinite system from the finite elementdiscretization of these saddle point problems. We provethe resulting multigrid algorithms are contractions withthe contraction number depending on the regularity of thesolution but independent of the mesh level.

Susanne BrennerDepartment of MathematicsLouisiana State Universitybrenner@math.lsu.edu

Hengguang LiDepartment of MathematicsWayne State Universityhli@math.wayne.edu

Li-yeng SungDepartment of Mathematics and CCTLouisiana State Universitysung@math.lsu.edu

MS11

Adaptive Regularization Strategies for NonlinearPDE

We will discuss an adaptive regularization strategy for sta-bilizing Newton-like iterations on a coarse mesh, developedin the context of adaptive finite element methods for non-linear PDE. This methods allows the adaptive algorithmto start on a coarse mesh where the problem data is badlyresolved and the linearizations feature indefinite and ill-conditioned Jacobians. Stable configurations of the regu-larized coarse-mesh iterates are used to refine the mesh,leading to sufficient resolution of the data to accuratelyapproximate the PDE solution. We will discuss the useof a positive semidefinite penalty term which is adaptedwith both mesh refinements and iterations of the nonlinearsolver. Numerical examples demonstrate the effectivenessof the method and illustrate the distinct phases of the so-lution process.

Sara PollockTexas A&M Universitysnpolloc@math.tamu.edu

MS11

Robust Multilevel Preconditioners for EllipticProblems with Discontinuous Coefficients

We develop robust and efficient multilevel solvers for thelarge scale linear systems arising from finite element dis-cretizations of general second order elliptic equations inheterogeneous materials. In this talk, we will discuss theinfluence of the discontinuous (and possibly anisotropic)coefficients to the overall performance of the multilevel pre-conditioners.

Yunrong ZhuDepartment of MathematicsUniversity of California at San Diegozhuyunr@isu.edu

MS12

Efficient Eigensolver Algorithm on Accelerator-Based Architecture

The enormous gap between the high-performance capabil-ities of GPUs and the slow interconnect between themhas made the development of numerical software that isscalable across multiple GPUs extremely challenging. Wedescribe a successful methodology on how to address thechallenges –starting from our algorithm design, kernel opti-mization and tuning, to our programming model– in the de-velopment of a scalable high-performance symmetric eigen-value and singular value solver.

Azzam Haidar, Piotr LuszczekDepartment of Electrical Engineering and ComputerScience

CS15 Abstracts 31

University of Tennessee, Knoxvillehaidar@utk.edu, luszczek@eecs.utk.edu

Stanimire TomovInnovative Computing Laboratory, Computer ScienceDeptUniversity of Tennessee, Knoxvilletomov@eecs.utk.edu

MS12

GPGPU Acceleration of the Ams Eigensolver Us-ing Magma

The automatic multilevel substructuring (AMS) technol-ogy is a state-of-the-art eigensolver for large-scale eigen-value problems and has been frequently used to speed upthe eigensolution process for finite element models, es-pecially for noise and vibration (N&V) analysis in theautomotive industry. To further accelerate the eigenso-lution process using the AMS technology, it is essentialto take advantage of high performance GPGPU accelera-tors. MAGMA project by University of Tennessee providesvarious numerical linear algebra subroutines on GPGPUand those subroutines have been facilitating the adop-tion of GPGPU acceleration to this technology. Recently,MAGMA team developed a new high-performance algo-rithm for symmetric dense eigenproblems, which has beena performance bottleneck for more than a decade on multi-core architectures. By adopting this new high-performancealgorithm, the performance of the AMS technology can besignificantly accelerated. In this paper/talk, we will intro-duce the new high-performance MAGMA algorithm anddemonstrate the AMS performance benefits using thoseeigensolution routines.

Mintae KimSIMULIA Dassault Systemesmintae.kim@3ds.com

Luis Crivelli, Michael Wood, Cristian Ianculescu,Vladimir BelskySIMULIA-Dassaults systemesluis.crivelli@3ds.com, michael.wood@3ds.com, cris-tian.ianculescu@3ds.com, vladimir.belsky@3ds.com

MS12

High-Performance Computation of Pseudospectra

This talk introduces several high-performance variationsof Van Loan’s triangularization followed by inverse itera-tion algorithm which involve parallel reduction to (quasi-)triangular or Hessenberg form followed by interleaved Im-plicitly Restarted Arnoldi iterations driven by multi-shift(quasi-)triangular or Hessenberg solves with many right-hand sides. Since multi-shift (quasi-)triangular solves canachieve a very high percentage of peak performance on bothsequential and parallel architectures, such an approachboth improves the eigenvaluesciency of sequential pseu-dospectral computations and provides a high-performancedistributed-memory scheme. Results from recent imple-mentations within Elemental (P. et al.) will be pre-sented for a variety of large dense matrices and practicalconvergence-monitoring schemes will be discussed

Jack L. PoulsonComputational Science and EngineeringGeorgia Institute of Technology

jack.poulson@gmail.com

MS12

Towards Materials Design with Extreme-ScaleQuantum Simulations

With ever improving accuracy of ab initio electronic struc-ture methods, quantum simulations have now become apredictive tool that can be used to search for new mate-rials with desired properties. For simulations tools to berelevant for such searchers, calculations for individual com-pounds have to be very reliable and optimized to minimizethe machine and energy footprint, as they have to be re-peated automatically tens or hundreds thousands of times.Today, this can be accomplished with clusters that havehybrid CPU-GPU nodes. We will discuss the algorithmicdevelopments that were necessary to run modern electronicstructure codes on such systems.

Thomas C. SchulthessSwiss National Supercomputing Centerschulthess@cscs.ch

Anton KozhevnikovETH ZurichInstitut f. Theoretische Physikantonk@ethz.ch

Solca RaffaeleETHEidgenossische Technische Hochschule Zurichrasolca@student.ethz.ch

MS14

Opportunities and Challenges in First PrinciplesModels of Materials

First principles models based on quantum mechanics haveprovided a significant insight into materials and moleculesin recent years, and hold the promise of an ability to de-sign new materials properties one atom at a time. However,these models also raise a number of important challenges.First, many involve rather ad hoc approximations to theSchrodinger’s equation. For example, the mathematicalbasis of widely used exchange and correlation functionalsof density functional theory is unclear. Second, many ofthese models are extremely computationally demanding,thereby limiting their applicability to relatively small com-putational cells. However, interesting properties of mate-rials require calculations that are orders of magnitude be-yond what is currently possible. This talk will give a briefoverview of state of the art first principle methods, and pro-vide opinions on opportunities and challenges where math-ematics and computational sciences can lead to significantimpact.

Kaushik BhattacharyaHowell N. Tyson Sr. Professor of MechanicsCalifornia Institute of Technologybhatta@caltech.edu

MS14

New Liquid-Crystal Based Models and Technolo-gies

Research on liquid-crystal based suspensions is rapidly ad-vancing motivated by applications in materials science aswell as in biological systems. From proposals for new

32 CS15 Abstracts

display technologies and nanofluidic devices to more fun-damental questions about the mechanisms of clusteringand de-clustering in systems of particles, new experimentalfindings call for new modeling and analysis efforts. Efficientengineering of these systems requires advances to currentunderstanding of isotropic fluid colloids, in that the exis-tence of structure in the liquid matrix affords new opportu-nities for flow control, processing, and suspension stability.One of the newly observed phenomena is the quadratic de-pendence of the drift velocity of particles moving in anionic liquid crystal matrix, on the direction transverse tothe applied electric field. This property may allow for sig-nificant technological applications such as the developmentof AC- electrophoresis. I will present a survey of the cur-rent research status on liquid crystal colloids pointing tochallenging mathematical and computational issues, suchas in the case of particles of typical size above 50nm. An-other line of research involving liquid crystal elastomersis the modeling and development of microdevices, such aspumps and valves. A basic mechanism is the ability ofthe anisotropic elastomer to control the evolution of liquidcrystal defects. Devices made of liquid crystal elastomers,in addition to exhibiting excellent shape memory, hardlyrequire any micromachining processes. I will outline someof the main mathematical issues and their research status.

Carme CaldererUniversity of Minnesotacalde014@umn.edu

MS14

Opportunities in Computational Science:Genomes, Mesoscale and Closing the Loop

Strategies for advancing computational science will bedrawn from three concepts now in their infancy: theMaterials Genome(1) mesoscale science(2), and closing theloop among computation, synthesis, characterization andtargeted materials outcomes(3). Each of these strategiesaddresses the fundamental challenge of materials science:capturing and controlling increasingly complex andfunctional materials behavior. Examples will be drawnfrom battery science, composite materials and biology. 1.http://www.sciencedirect.com/science/article/pii/S13590286140000602. http://science.energy.gov//media/bes/pdf/reports/files/OFMS rpt.pdf3. http://www.nsf.gov/mps/advisory/mpsac other reports/materials instrumentation-final from subcommittee.pdf

George CrabtreeArgonne National Laboratorycrabtree@anl.gov

MS14

Problems in Pattern Formation, Geometry and De-sign of Materials

We propose to study some mathematical problems, com-bining geometry and analysis, that arise from practicalquestions of materials design. Manipulating the micro-structure of a material can radically change its mechan-ical responses. For example, the basic engineering designgoal of actuation of nematic glass sheets is to determineimprinted director distributions in the flat sheet, in orderto achieve particular actuated shapes on exposure to ap-propriate stimuli. Another rich source of related analyticalquestions is provided by the heterogeneous incompatibili-ties of strains, present in bulk and in thin structures, asso-ciated with growth, swelling or shrinkage, plasticity, etc. Inthis vein, one class of mathematical problems we will dis-

cuss is related to wrinkling of thin films and the symmetrybreaking in the prestress-to-wrinkle-to-crumple transition,where some insight may be gained by simplifying a com-plex system in terms of a reduced set of coordinates. Thesecond class of problems concerns the actuation of thin ne-matic glass sheets. Yet another class of problems relates tothe interaction of nonlinear pdes and mechanics of materi-als in the prediction of static and dynamic microstructurepatterns.

Marta LewickaDepartment of MathematicsUniversity of Pittsburghlewicka@pitt.edu

MS15

High Order Semi-Lagrangian DiscontinuousGalerkin Schemes for First and Second OrderPDEs

High order semi-lagrangian DG schemes are proposed forsome linear first and second order multi-dimensional time-dependant PDEs, based on splitting techniques and one-dimensional gaussian quadrature formula. Stability andconvergence is proved for the splitting and for variable co-efficients. Extention to some non-linear PDEs will be alsodiscussed.

Olivier BokanowskiUniversite Paris-Diderotboka@math.jussieu.fr

MS15

High-order Discontinuous Galerkin Methods forSome Kinetic Models

In this talk, I will present our recent progress in developinghigh-order discontinuous Galerkin methods for simulatingsome kinetic models, such as Vlasov-Maxwell equations,some discrete-velocity models in the diffusive limit, andthe BGK model. Theoretical results will be discussed interms of conservation, stability, accuracy, and asymptoticpreserving property, together with some numerical exam-ples.

Fengyan LiRensselaer Polytechnic Institutelif@rpi.edu

MS15

Convergence of Semi-Discrete Stationary WignerEquation with Inflow Boundary Conditions

Making use of the Whittaker-Shannon interpolation for-mula with shifted sampling points, we propose in this papera well-posed semi-discretization of the stationary Wignerequation with inflow boundary conditions. The conver-gence of the solutions of the discrete problem to the contin-uous problem is then analyzed, providing certain regularityof the solution of the continuous problem.

Tiao LuPeking Universitytlu@math.pku.edu.cn

Ruo LiSchool of Mathematical SciencePeking Universityrli@math.pku.edu.cn

CS15 Abstracts 33

Zhangpeng SunPeking Universitysunzhangpeng@pku.edu.cn

MS15

Self-Organized Hydrodynamics in An Annular Do-main: Modal Analysis and Nonlinear Effects

The self-organized hydrodynamics model of collective be-havior is studied on an annular domain. A modal analysisof the linearized model around a perfectly polarized steady-state is conducted. It shows that the model has only pureimaginary modes in countable number and is hence stable.Numerical computations of the low-order modes are pro-vided. The fully non-linear model is numerically solved andnonlinear mode-coupling is then analyzed. Finally, the effi-ciency of the modal decomposition to analyze the complexfeatures of the nonlinear model is demonstrated.

Hui YuUniversite de Toulouse; UPS, INSA, UT1, UTM ;h.yu@imperial.ac.uk

MS16

The Role of Intraclot Transport in the Dynamics ofPlatelet Deposition and Coagulation Under Flow

We present a spatial-temporal continuum model of bloodclot formation in response to vascular injury that incor-porates platelet activation, adhesion, and cohesion, treatscoagulation reactions comprehensively, and includes the in-fluence of flow and thrombus growth on one another. Wefocus on transport of platelets and proteins within the clotitself and how it influences the progression of the coagula-tion reactions and thus has profound effects on the growthand ultimate structure of the thrombus.

Aaron L. FogelsonUniversity of Utahfogelson@math.utah.edu

Karin LeidermanApplied MathematicsUC Mercedkleiderman@ucmerced.edu

MS16

Modeling Cardiac Electro-Fluid-Mechanical Inter-action

Integrative models of the heart that account for the cou-pling between cardiac mecahnics, fluid dynamics, and elec-trophysiology promise to serve as powerful platforms forunderstanding cardiac diseases and for treatment planningand optimization. This talk will describe progress towardsthe development of such electro-fluid-mechanical models ofthe heart using the framework of the immersed boundary(IB) method, with a focus on new image-based model ofthe heart and work to develop validated high-resolutionmodels of cardiac fluid dynamics.

Boyce GriffithUniversity of North Carolina at Chapel Hillboyceg@email.unc.edu

MS16

An Integrative Model of Lamprey Locomotion Us-

ing the Immersed Boundary Method

The lamprey is considered a model organism for neuro-physiology and locomotion studies. Here we present a 2D,integrative, multi-scale model of the lamprey’s anguilliform(eel-like) swimming driven by neural activation and mus-cle kinematics coupled to body interactions with fluid sur-roundings and implemented using the immersed boundarymethod. Effects on swimming speed and cost (metabolicwork) at each scale as well as the role of feedback on per-formance are presented.

Christina HamletTulane UniversityDepartment of Mathematicschamlet@tulane.edu

Eric TytellTufts UniversityDepartment of Biologyeric-tytell@tufts.edu

Lisa J. FauciTulane UniversityDepartment of Mathematicsfauci@tulane.edu

MS16

Modeling Escherichia Coli Chemotaxis in a Fluid

The hydrodynamics of Escherichia coli is modeled by cou-pling the chemotaxis equations of a simplified phosphory-lation cascade with the method of regularized Stokeslets ofthe fluid motion. For a slow enough diffusion rate of the at-tractant gradient, simulations have consistently resulted ina biased random walk of the majority of cells towards thehighest concentration of attractant, chemotactic behavior.The results demonstrate how the phosphorylation affectsthe run and tumble mechanism of swimming bacteria.

Hoa NguyenTrinity Universityhnguyen5@trinity.edu

MS17

On First Experiments for Nuclear Engineering Ap-plications on Intel Xeon Phi

Next generation of supercomputers integrate many corecomputational units and will involve multilevel of paral-lelism such as Intel Xeon Phi. For nuclear engineering, nu-merical simulation is based on verified and validated largesimulation codes. Moving to these new computing architec-tures, will imply deep modifications and all existing codeswill not be adapted easily. The subject of this talk is topresent first experiments on porting existing CEA appli-cations for nuclear engineering on Xeon Phi architecture.

Christophe Calvin

CEA-Saclay/DEN/DANS/DM2Schristophe.calvin@cea.fr

MS17

Opportunities and Challenges in Developing andUsing Scientific Libraries on Emerging Architec-

34 CS15 Abstracts

tures

Scalable manycore and accelerator based systems are be-coming the norm, and will soon be the dominant platformsfor very high end systems. In the development of new al-gorithms and libraries for these systems, common themeshave emerged that, if appreciated and adopted by applica-tion and library developers, will improve portability, per-formance and resilience in the future. In this presentation,we give an overview of some of these themes, and discussstrategies for application development efforts today thatwill have lasting value in the future.

Michael HerouxSandia National Laboratoriesmaherou@sandia.gov

MS17

Managing Portability for ASC Applications

Large production-quality multi-physics software containstens of thousands of inner-loop kernels that must run ef-fectively on multiple processor architectures and a varietyof memory subsystems. We have identified a set of fourkey encapsulation idioms that allow us to manage porta-bility in legacy applications while imposing minimal re-strictions on the way developers write software. We willdiscuss our experience integrating these idioms into largesoftware projects, and present performance behavior forselect applications.

Jeff KeaslerLawrence Livermore National Laboratorykeasler1@llnl.gov

Richard HornungLawrence Livermore National Labhornung@llnl.gov

MS17

ppOpen-APPL/HEXA: A Framework for Develop-ment of Parallel FEM/FVM Applications on IntelXeon Phi

ppOpen-HPC is an open source infrastructure for devel-opment and execution of large-scale scientific applicationson post-peta-scale supercomputers with automatic tuning(AT). ppOpen-APPL/HEXA is a part of ppOpen-HPC anda special framework for development of parallel FEM/FVMcodes with voxel-type hexahedral meshes. In this talk,outline of development, optimization and utilization ofppOpen-APPL/HEXA is described. Moreover, details ofoptimization of preconditioned iterative solvers, and ma-trix assembling procedures for Intel Xeon Phi processorsare presented.

Kengo NakajimaThe University of TokyoInformation Technology Centernakajima@cc.u-tokyo.ac.jp

MS18

Fast Solvers for Wave Propagation and Scatteringby General Structures

We present fast spectral solvers for Partial DifferentialEquations that address some of the main difficulties as-sociated with simulation of realistic problems of propaga-tion and scattering in the frequency domain. Based on

fast high-order methods for evaluation of integral operatorsthese algorithms can solve, with high-order accuracy, prob-lems of electromagnetic and acoustic scattering for largeand complex three-dimensional geometries. A variety ofapplications will be presented which demonstrate the sig-nificant improvements the new algorithms can provide overthe accuracy and speed resulting from other approaches.

Oscar P. BrunoCalifornia Institute of Technologyobruno@caltech.edu

MS18

Scalable Algorithms for Density Matrix Calcula-tions of Cavity Quantum Electrodynamic Systems

If a coupled quantum systems shows some level of entangle-ment, that system can not simply be described by a singlestate. They exist in mixed states. Furthermore, real quan-tum systems exhibit dephasing and decoherence, which re-quires a statistical description of the system. This is donethrough the density matrix formulation. Density matricesdescribe the system as a statistical ensemble of several purequantum states.The time dynamics of the density matrixare governed by the Lindblad master equation, which hasinvolves operator multiplication from both the right andleft of the density matrix. We study the time dynamicsof a system consisting of quantum dots coupled to a sin-gle plasmon mode. The size of the density matrix growsquickly; a physically reasonable system of 16 quantum dotsrequires a matrix dimension of 50 ∗ 216. At this size, ex-treme scale computing must be utilized. Aside from thenovel physics applications, we are currently studying howbest to treat this system, through different time steppingschemes (RK and exponential time integrator) and differ-ent parallelization algorithms.

Matthew OttenDepartment of PhysicsCornell Universitymjo98@cornell.edu

MS18

Electromagnetic Power Absorption and PlasmonResonances on Rough Conducting Surfaces

In this talk we present high-order integral equation meth-ods for the evaluation of electromagnetic wave scatteringand absorption by dielectric/conducting bumps and cav-ities on penetrable half-planes. The numerical far- andnear-fields exhibit excellent convergence as discretizationsare refined –even at and around points where singular fieldsand infinite currents exist. The methods presented in thistalk are applied to study the absorption of electromagneticpower that results from the presence of defects on flat con-ducting surfaces. The performance of the integral equationsolvers herein discussed allows for the accurate evaluationof electromagnetic fields at and around the surface of theconducting material where relevant physical phenomena,such as skin-depth effects, occur. Finally we discuss theapplication of the high-order integral equation methods tothe evaluation electromagnetic fields resulting from excita-tion of plamon resonances on rough conducting surfaces.

Carlos A. Perez-ArancibiaComputing and Mathematical SciencesCalifornia Institute of Technologycperezar@caltech.edu

CS15 Abstracts 35

Oscar P. BrunoCalifornia Institute of Technologyobruno@caltech.edu

MS18

Generalized Combined Sources Integral Equationsfor Helmholtz Transmission Problems

We present a new class of well conditioned integral equa-tions for the solution of two and three dimensional scatter-ing problems by homogeneous penetrable scatterers. Ournovel boundary integral equations result from representa-tions of the fields inside and outside the scatterer as com-binations of single and double layer potentials acting onsuitably defined regularizing operators. The regularizingoperators are constructed to be approximations of the ad-mittance operators that map the transmission boundaryconditions to the exterior and respectively interior Cauchydata on the interface between the media. The latter op-erators can be expressed in terms of Dirichlet-to-Neumannoperators. We refer to these regularized boundary inte-gral equations as Generalized Combined Source IntegralEquations (GCSIE). The ensuing GCSIE are shown to beintegral equations of the second kind in the case when theinterface of material discontinuity is a smooth curve in twodimensions and a smooth surface in three dimensions.

Catalin TurcDepartment of Mathematical SciencesNew Jersey Institute of Technologycatalin.c.turc@njit.edu

MS19

Generalized Radiative Transfer: Accounting Accu-rately for Unresolved Variabilities at No Compu-tational Cost, Yet Without Homogenization

Generalized Radiative Transfer (GRT) is formalized asthe integral 1D radiative transfer equation in a uniformmedium, but where the exponential functions in the prop-agation kernel are replaced with two closely related powerlaws. An adapted Markov chain numerical solution wasdeveloped. GRT theory applies to challenging transportproblems with highly variable optical properties over abroad range of scales. Another application is to the effi-cient and yet accurate computation of broadband spectralresponses.

Anthony B. Davis, Feng XuJet Propulsion LaboratoryCalifornia Institute of Technologyanthony.b.davis@jpl.nasa.gov, feng.zu@jpl.nasa.gov

MS19

Quadrature-Based Moment Methods for RadiationTransport

Radiation transport can be described by a kinetic equa-tion with free transport and scattering operators. The highdimensionality of the density function makes the numeri-cal solution very challenging. Available strategies rangefrom Monte-Carlo approaches, to collocation such as dis-crete ordinate methods, to moment methods. An impor-tant aspect of radiation solvers is related to how they rep-resent the phase-space dependence of the density function,which can lead to so-called ray effects where radiation trav-els along fixed directions in physical space. To overcomethese effects, moment methods can use a delta-function

representation with adaptive quadrature nodes, or a con-tinuous representation. In general, the positivity of thereconstructed density function is not guaranteed with tra-ditional moment methods, and positivity constraints orfiltering are required. Here we explore quadrature-basedmoment methods that reconstruct the density function onthe unit sphere. The transported moment set is com-posed of the trigonometric moments of the spherical an-gles. Compared to quadrature-based reconstruction on theunit square, the additional constraint of periodicity on theunit sphere requires special considerations. Here we em-ploy Szego quadrature and an extension of CQMOM onthe unit circle. The density function is reconstructed usingthe extended quadrature method of moments (EQMOM)with a von Mises kernel density function. Special attentionis paid to the hyperbolicity of the moment transport equa-tions, and to the numerical algorithms to handle realizablespatial fluxes, scattering and the diffusion limit.

Rodney O. FoxIowa State UniversityDepartment of Chemical and Biological Engr.rofox@iastate.edu

Cory HauckOak Ridge National Laboratoryhauckc@ornl.gov

Ming Tse P. LaiuDepartment of Electrical and Computer EngineeringUniversity of Maryland - College Parkmtlaiu@umd.edu

Frederique LaurentLaboratoire EM2C - CNRS UPR 288Ecole Centrale Parisfrederique.laurent@em2c.ecp.fr

Marc MassotLaboratoire EM2C - UPR CNRS 288Ecole Centrale Parismarc.massot@em2c.ecp.fr

MS19

Stability of PN Approximations for the RadiativeTransfer Equation in the Free Streaming Limit

Based on a mixed variational framework we will investi-gate solvability of the radiative transfer equation in thefree streaming limit. Using this framework we will discussthe classical PN approximations and related stability is-sues. As an alternative we present an equivalent stabilizedvariational method.

Matthias SchlottbomFachbereich MathematikAG Numerik und Wissenschaftliches Rechnenschlottbom@uni-muenster.de

Herbert EggerNumerical Analysis and Scientific ComputingDarmstadt University of Technologyegger@mathematik.tu-darmstadt.de

MS19

On Combining Moment Methods and Discrete-Velocity-Schemes for Solving the Boltzmann Equa-

36 CS15 Abstracts

tion

Varius methods exit to solve the Boltzmann Equation de-terministically. Moment methods and discrete-velocity-schemes are two possibilities both using very different ap-proaches and serving very different purposes. Momentmethods focus on physical variables and come with build-inconservation properties, Galilean invariance, easy couplingto CFD, etc. Discrete velocity schemes can approximatevery complex distribution functions and are relatively easyto implement. This talk will discuss the similarities ofboth approaches and possible combinations, like the useof physically-adaptive velocity grids.

Manuel TorrilhonSchinkelstrasse 2RWTH Aachen Universitytorrilhon@rwth-aachen.de

MS20

ODTLES: A Multiscale Approach for Highly Tur-bulent Flows

ODTLES combines the ability of ODT to resolve moleculareffects with the ability of Large Eddy Simulations (LES)to describe 3D large scale flows. ODTLES is based on anextended LES scale separation ansatz wherein moleculareffects and the turbulent cascade are simulated by ODTwhile a standard 3D numerical approach time advancesthe 3D large scale flow. Simulation results for highly tur-bulent flows reveal the model and numerical properties ofODTLES.

Christoph GlaweBTU Cottbusglawechr@tu-cottbus.de

Heiko SchmidtBTU CottbusMechanical Engineeringschmidth@tu-cottbus.de

Alan KersteinConsultantalan.kerstein@gmail.com

MS20

Particle-Scalar Field Interactions in One-Dimensional Turbulence

The development of Lagrangian particle models in the con-text of one-dimensional turbulence (ODT) allows the studyof the interactions of particles with various scalar fields ina novel sense. We describe finite Stokes-number effects ofthe relative dispersion of scalars and particles. We alsoshow the wide range of interaction time scales associatedwith particle slip across scalar gradients and with scalar-field diffusion possible with full ODT resolution of scalarfields.

John C. HewsonSandia National Laboratoriesjchewso@sandia.gov

Guangyuan Sun, David O. LignellBrigham Young University

gysungrad@gmail.com, davidlignell@byu.edu

MS20

One-dimensional Turbulence Simulation: Overviewand Application to Soot Formation in Non-premixed Flames

An overview of one-dimensional turbulence (ODT) simula-tion of turbulent flows is presented along with recent ad-vances and application to soot formation in nonpremixedflames. ODT is a computationally affordable stochasticmodel that resolves a full range of scales and can be ap-plied to flow regimes not available to direct numerical simu-lation. Soot formation, radiation, and flame emission is animportant and challenging multiphysics problem to whichwe apply ODT for fundamental insight and model valida-tion.

David O. Lignell, Victoria LansingerBrigham Young Universitydavidlignell@byu.edu, vlansinger@gmail.com

John C. HewsonSandia National Laboratoriesjchewso@sandia.gov

MS20

Multiphase Turbulent Reacting Flow SimulationsUsing ODT

Abstract Results for application of the One-DimensionalTurbulence model to multiphase turbulent combustion ofcoal is considered. Results are compared to a pilot-scalereactor and the ability of the model to capture ignition de-lay in this situation is evaluated. Because of its low costrelative to DNS and LES, ODT can be used to explorehigh-fidelity thermochemistry models. We explore severalmodels for heterogeneous and homogeneous reactions andevaluate their ability to reproduce the observed experimen-tal data.

James C. SutherlandDepartment of Chemical EngineeringThe University of Utahjames.sutherland@chemeng.utah.edu

Babak GoshayeshiUniversity of Utahb.goshayeshi@gmail.com

MS21

The most current list of partic-ipating companies is available atwww.siam.org/meetings/cse15/career.php.

For the most recent list of participating companies visithttp://www.siam.org/meetings/cse15/career.php

Bill KolataSIAMkolata@siam.org

MS22

Cilia Beating Patterns are not HydrodynamicallyOptimal

We examine the hydrodynamic performance of two cilia

CS15 Abstracts 37

beating patterns reconstructed from experimental data.In their respective natural systems, the two beating pat-terns correspond to: (A) pumping-specialized cilia, and(B) swimming-specialized cilia. We compare the perfor-mance of these two cilia beating patterns as a function ofthe metachronal coordination in the context of two modelsystems: the swimming of a ciliated cylinder and the fluidpumping by a ciliated carpet. Three performance mea-sures are used for this comparison: (i) average swimmingspeed/pumping flow rate; (ii) maximum internal momentsgenerated by the cilia; and (iii) swimming/pumping effi-ciencies. We found that, in both models, pattern (B) out-performs pattern (A) in almost all three measures, includ-ing hydrodynamic efficiency. These results challenge thenotion that hydrodynamic efficiency dictates the cilia beat-ing kinematics, and suggest that other biological functionsand constraints play a role in explaining the wide varietyof cilia beating patterns observed in biological systems.

Hanliang GuoAerospace and Mechanical EngineeringUniversity of Southern Californiaguohanliang@gmail.com

Janna C. NawrothHarvard School of Engineeringjnawroth@gmail.com

Yang DingBeijing Computational Science Research Centerdingyang@csrc.ac.cn

Eva KansoUniversity of Southern Californiakanso@usc.edu

MS22

A Numerical Method for Doubly-Periodic StokesFlow Near a Wall

We present a numerical method for computing doubly-periodic Stokes flow in the presence of a wall. By findingfundamental solutions to Stokes equation in Fourier spaceexactly, in practice only an inverse FFT has to be com-puted. Our algorithm can be used to effectively modelarrays of pulmonary or nodal cilia. We match theoretical,numerical and experimental results.

Franz M. HoffmannMathematics DepartmentTulane Universityfhoffma@tulane.edu

MS22

Computation of the Regularized Image Systems forDoubly-Periodic Brinkman Flow in the Presence ofa Wall

A fast summation method of Ewald type is developed forBrinkman flow due to doubly-periodic arrays of regularizedforces near a plane wall. Method of images is applied tofind the Brinkman flow due to one regularized force; thenPoisson summation formula is applied to arrive at the finalformula for the doubly-periodic flow. Initial simulation re-sults for fluid-cilia interaction problems are also presented.

Hoang-Ngan NguyenUniversity of California, Mercedzhoangngan@gmail.com

Karin LeidermanApplied MathematicsUC Mercedkleiderman@ucmerced.edu

MS22

Accelerated Boundary Integral Simulations forFluid-Structure Interactions in Periodic StokesFlow

Boundary integral formulations for Stokes flow involvesthe periodic summation of Green’s functions. The Ewaldsummation formula for the Stokeslet under triply pe-riod boundary conditions is well known (Hasimoto, 1959).Based on this formula, we have developed a spectrally ac-curate FFT based method to speed up the computations.Such methods are also needed for the Stresslet, and forsystems that are only quasi-periodic. Ewald summationformulas and corresponding FFT based Spectral Ewaldmethods for such cases will be discussed. Boundary inte-gral formulations and simulation results for fluid-structureproblems employing Spectral Ewald methods will also bepresented.

Anna-Karin TornbergKTHakto@kth.se

MS23

Symmetry-Preserving Conservative LagrangianScheme for Compressible Euler Equations in Two-Dimensional Cylindrical Coordinates

In applications such as astrophysics and inertial confine-ment fusion, there are many three-dimensional cylindrical-symmetric multi-material problems which are usually simu-lated by Lagrangian schemes in the two-dimensional cylin-drical coordinates. For this type of simulation, a criticalissue for the schemes is to keep spherical symmetry in thecylindrical coordinate system if the original physical prob-lem has this symmetry. In the past decades, several La-grangian schemes with such symmetry property have beendeveloped, but all of them are only first order accurate.In this talk, we develop a second order cell-centered La-grangian scheme for solving compressible Euler equationsin cylindrical coordinates, based on the control volume dis-cretizations, which is designed to have uniformly secondorder accuracy and capability to preserve one-dimensionalspherical symmetry in a two-dimensional cylindrical geom-etry when computed on an equal-angle-zoned initial grid.The scheme maintains several good properties such as con-servation for mass, momentum and total energy, and thegeometric conservation law. Several two-dimensional nu-merical examples in cylindrical coordinates are presentedto demonstrate the good performance of the scheme interms of accuracy, symmetry, non-oscillation and robust-ness. This is a joint work with Chi-Wang Shu.

Juan ChengInstitute of Applied Physics and ComputationalMathematicsBeijing, Chinacheng juan@iapcm.ac.cn

MS23

Superconvergent HDG Methods for Third-Order

38 CS15 Abstracts

Equations in One-Space Dimension

We design and analyze the first hybridizable discontinuousGalerkin methods for third-order linear equations in one-space dimension. The methods are defined as discrete ver-sions of characterizations of the exact solution in terms oflocal problems and transmission conditions. They provideapproximations to the exact solution u and its derivativesq := u′ and p := u′ which are piecewise-polynomials of de-gree ku, kq and kp, respectively. We consider the methodsfor which the difference between these polynomial degreesis at most two. We prove that all these methods have su-perconvergence properties which allows us to prove thattheir numerical traces converge at the nodes of the parti-tion with order at least 2 k + 1, where k is the minimumof ku, kq , kp. This allows us to use an element-by-elementpost-processing to obtain new approximations for u, q andp converging with order at least 2k + 1 uniformly.

Bo DongUniversity of Massachusetts Dartmouthbdong@umassd.edu

Yanlai ChenDepartment of MathematicsUniversity of Massachusetts Dartmouthyanlai.chen@umassd.edu

Bernardo CockburnSchool of MathematicsUniversity of Minnesotacockburn@math.umn.edu

MS23

A Local Discontinuous Galerkin Scheme for thePatlak-Keller-Segel Chemotaxis Model

In this talk, a new local discontinuous Galerkin method isdesigned for solving the Patlak-Keller-Segel (PKS) equa-tion. We give the error analysis and also prove the positive-preserving property for the scheme on 1D and 2D struc-tured meshes. Numerical simulations will be presentedwhich confirm the predicted convergence rate.

Yang YangMichigan Technological Universityyyang7@mtu.edu

Xingjie LiBrown Universityxingjie li@brown.edu

Chi-Wang ShuBrown UniversityDiv of Applied Mathematicsshu@dam.brown.edu

MS23

Optimal Error Estimates for DiscontinuousGalerkin Methods Based on Upwind BiasedFluxes for Linear Hyperbolic Equations

We analyze discontinuous Galerkin methods using upwind-biased numerical fluxes for time-dependent linear conser-vation laws. In one dimension, optimal a priori error esti-mates of order k + 1 are obtained when piecewise polyno-mials of degree at most k (k ≥ 0) are used. We extend theanalysis to the multidimensional case on Cartesian mesheswhen piecewise tensor product polynomials are used. Nu-

merical experiments are shown to demonstrate the theo-retical results.

Xiong Mengharbin institute of technologyUniversity of East Angliaxiongmeng@hit.edu.cn

MS24

A Novel Elliptic Solver Based on RBF-Finite Dif-ferences for Understanding the Earth’s ElectricSystem

The Global Electric Circuit (GEC) represents the Earth’selectric link between solar, upper and lower atmosphereprocesses, and cloud system dynamics. It is modeled byan elliptic PDE in 3D spherical-like geometry with highlyvariable coefficients. Due to the several computationalchallenges that it presents, a novel radial basis function-generated finite differences (RBF-FD) solver has been de-veloped. Several features of RBF-FD have proven to bevery beneficial. Among all, the ability to easily handle ir-regular boundaries such as the Earths topography standsout. In this talk, we present this novel RBF-FD ellipticsolver and the new techniques for handling irregular ge-ometries that was motivated by it.

Victor Bayona

National Center for Atmospheric Research (NCAR)vbayona@ucar.edu

Natasha FlyerNational Center for Atmospheric ResearchInstitute for Mathematics Applied to Geosciencesflyer@ucar.edu

MS24

Guidelines to Modeling the Navier-Stokes and Eu-ler Equations with RBF-FD

In applications of radial basis functions (RBFs) for fluidmodeling, infinitely smooth RBFs have traditionally beenused due to the spectral convergence properties. However,fluid flows in nature can exhibit complex features such thatspectral accuracy cannot be realized on resolutions thatare observable or practical. A novel approach for mod-eling with RBF-generated finite differences (RBF-FD) ispresented by using polyharmonic spline RBFs (PHS RBF)together with higher-order polynomials. The approach istested on nonhydrostatic compressible atmospheric flowsin limited area domains. Test cases include flows exhibit-ing Kelvin-Helmholtz instabilities, turbulence, and bubbleupdrafts, simulating cloud entrainment. General guidelinesare given as to how to choose the parameters involved, suchas the degree of the PHS RBF, the order of the polynomi-als, stencil size, node layout, etc.

Natasha FlyerNational Center for Atmospheric ResearchInstitute for Mathematics Applied to Geosciencesflyer@ucar.edu

Louis WickerNOAA, NSSLlouis.wicker@noaa.gov

Gregory BarnettDepartment of Applied MathematicsUniversity of Colorado, Boulder

CS15 Abstracts 39

gregory.barnett@colorado.edu

MS24

A High-Order RBF-Based Leray ProjectionMethod for the Incompressible Stokes and Navier-Stokes Equations

We present a novel pressure-free Leray projection methodfor the solution of the incompressible Stokes and Navier-Stokes equations in two dimensions. The discrete Lerayprojector is constructed via generalized interpolation withdivergence-free Radial Basis Functions (RBFs). This RBF-based Leray projection method does not require that onespecify boundary conditions for the pressure. Resultsdemonstrate that the RBF-based Leray projection methoddemonstrates high orders of convergence in both time andspace.

Edward FuselierHigh Point UniversityDepartment of Mathematics and Computer Scienceefuselie@highpoint.edu

Varun ShankarSchool of ComputingUniversity of Utahvshankar@math.utah.edu

Grady B. WrightDepartment of MathematicsBoise State University, Boise IDgradywright@boisestate.edu

MS25

Distributed Contraction of Tensors

Unlike distributed matrix multiplication, which has beenextensively studied, limited work has been done incharacterizing distributed tensor contractions. In thistalk, a characterization is presented for a family ofcommunication-optimal distributed tensor contraction al-gorithms on torus networks. The framework usesthree fundamental communication operators to generatecommunication-efficient algorithms for arbitrary tensorcontractions. Trade-off involving use of additional mem-ory for reduced inter-processor communication is also ad-dressed. Experimental results on a BlueGene/Q systemdemonstrate good scalability on 256K cores.

P Sadayappan, Samyam RajbhandariOhio State Universitypsaday@gmail.com, samyamrb@gmail.com

Sriram KrishnamoorthyPacific Northwest National Laboratorysriram@pnnl.gov

Pai-Wei LaiOhio State Universitylaip@cse.ohio-state.edu

MS25

A Framework for Distributed Tensor Computa-tions

Branches of scientific computing, express data as a tensorwhich can be viewed as a multi-dimensional analog of amatrix. For instance, chemical methods heavily rely on

the tensor contraction operation, which can be viewed as ageneralization of matrix-matrix multiplication. The alge-bra associated with tensors in these applications is referredto as multi-linear algebra, the multi-dimensional analogof linear algebra. Problems in this area of research fre-quently require the use of distributed-memory computingarchitectures to compute the desired method or operation.One common approach to computing multi-linear opera-tions acting on tensors on such architectures is to cast theoperation in terms of linear operations acting on matri-ces and utilize high-performance linear algebra libraries tocompute the result. Unfortunately, the underlying linearalgebra library may incur higher network communicationcosts than is necessary as some structure of the multi-linearobjects is lost when cast to linear objects. In this work,we introduce a notation for describing distributions of ten-sor data on processing grids, relate redistributions of datato well-studied collective communications, and describe amethod to systematically derive and analyze algorithms forthe tensor contraction operation.

Martin D. SchatzDepartment of Computer SciencesThe University of Texas at Austinmartin.schatz@utexas.edu

Tamara G. KoldaSandia National Laboratoriestgkolda@sandia.gov

Robert A. van de GeijnThe University of Texas at AustinDepartment of Computer Sciencervdg@cs.utexas.edu

MS25

Tensor Computation for Chemistry and MaterialScience

Tensors are ubiquitous in many-body quantum physics thatsupports chemistry and materials science. We will dis-cuss the types of tensor structures that arise in numer-ical simulation of many-body physics and the resultingcomputational challenges. We will also discuss TiledAr-ray, a modern C++ library for block-sparse tensor com-putation and how it addresses some of these challenges.(see github.com/ValeevGroup/tiledarray for more informa-tion).

Justus CalvinVirginia Techjustusc@vt.edu

Edward F. ValeevVirginia Polytechnic Institute and State Universityefv@vt.edu

MS25

Exploiting Multiple Tensor Symmetries thoughBlock Diagonalization

Suppose an order-6 tensor A has the property that thevalue in entry A(i1, i2, i3, j1, j2, j3) does not change if thei-indices are permuted, or if the j-indices are permuted, orif the i-indices as a group are swapped with the j-indicesas a group. Such a tensor has multiple symmetries andif it is smartly unfolded into a matrix A, then A itself hasinteresting structure above and beyond ordinary symmetry.In the case of the given example, there are permutation

40 CS15 Abstracts

matrices Γ1 and Γ2 (both involving Kronecker productsand perfect shuffles) such that both Γ1AΓ

T1 and Γ2AΓ

T2

equal A. We show how to compute a structure-preserving,low-rank approximation to A using LDLT with diagonalpivoting together with a very cheap block diagonalizationthat is performed at the start. The full exploitation ofstructure has ramifications for efficiency and applications.

Charles Van LoanCornell UniversityDepartment of Computer Sciencecv@cs.cornell.edu

Joseph VoktCornell Universityjoseph.vokt@gatech.edu

MS26

The Role of Microdomains and Ephaptic Couplingin Cardiac Action Potential Propagation

Much of our theoretical understanding of cardiac propaga-tion is built on the premise that gap junctional couplingbetween cells is the primary means of electrical coupling.In this talk, I will describe some of the newly discoveredfeatures of propagation that result from consideration ofmicrodomains and spatially inhomogeneous extracellularpotential and in doing so, provide new, indirect evidencefor the importance of ephaptic, or field effect, coupling.

James P. KeenerUniversity of Utahkeener@math.utah.edu

MS26

Strongly Scalable Numerical Approaches for Mod-eling Cardiac Electromechanics at High Spatiotem-poral Resolution

This study explores the feasibility of high resolution modelsof bidirectionally coupled cardiac electro-mechanics whichresolve cardiac anatomy at a para-cellular resolution. Anovel algebraic multigrid method is presented, custom-tailored for non-linear mechanics, which is shown to bestrongly scalable up to 4k cores when using a human wholeheart model. Benchmark results demonstrate that a singleheart beat can be simulated in about 15 minutes at fullanatomical and biophysical detail.

Christoph AugustinMedical University of GrazInstitute of Biophysicschristoph.augustin@medunigraz.at

Aurel NeicUniversity of Graz, Institute for MathematicsGraz, Austriaaurel.neic@uni-graz.at

Manfred Liebmann, Gundolf HaaseUniversity of Grazmanfred.liebmann@uni-graz.at, gundolf.haase@uni-graz.at

Gernot PlankInstitute of BiophysicsMedical University of Graz, Austria

gernot.plank@medunigraz.at

MS26

Towards Multidomain Modeling of Cardiac Elec-trophysiology

Mathematical models are established tools for studies ofcardiac tissue physiology and disease. Previously, we intro-duced an approach for multidomain mathematical model-ing of tissue electrophysiology (Sachse et al, Ann BiomedEng. 2009;37(5):874-89), which allows us to describe tis-sues as a mixture of cells with variable electrophysiologicalproperties and intercellular electrical coupling. Here, weprovide insights into our methodology to establish a micro-structural basis for this and other types of models. The ap-proach is based on high-resolution three-dimensional con-focal microscopy and image quantification.

Frank B. SachseCardiovascular Research and TrainingInstitute and Bioengineering Departmentfrank.sachse@utah.edu

Thomas SeidelCardiovascular Research and Training InstituteUniversity of Utahthomas.seidel@utah.edu

Jan Christoph EdelmannCardiovascular Research and Training InstituteUniversity ofUniversity of Utahedelmann@cvrti.utah.edu

Gunnar SeemannKarlsruhe Institute of TechnologyGermanygunnar.seemann@kit.edu

MS26

Multi-Scale Modeling of the Failing Heart: fromMolecule to Patient

Heart failure results in remodeling of the heart at themolecular, cellular, tissue, organ and organ system scales.Here we describe a new cellular model of the cardiac my-ocyte and the changes that occur in genetically engineeredmouse models of heart failure. We then extend the analysisto multi-scale models of arrhythmia and finally apply theseapproaches to patient-specific models of atrial fibrillationand heart failure.

Andrew D. McCullochDepartment of BioengineeringUniversity of California San Diegoamcculloch@ucsd.edu

Christopher Villongco, Adarsh KrishnamurthyUC San Diegoctvillongco@gmail.com, adarsh@ucsd.edu

David KrummenUC San DiegoVA San Diego Medical Centerdkrummen@ucsd.edu

Kevin VincentUCSD

CS15 Abstracts 41

vincent@ucsd.edu

MS27

Overview of the Field and the Community of FastMultipole Methods

At the last SIAM CSE conference, at least four mini sym-posia were devoted to fast algorithms for integral equa-tions, and I am sure there will be as much interest inthe topic at this conference, or more. It’s been almost30 years since the fast multipole method (FMM) was in-vented, but the activity in the field is getting hot. Thelandscape of computer hardware has contributed to this,with multi-core and then many-core architectures placingsevere constraints on communication bandwidth. FMMhas a uniquely favorable communications pattern, makingit more attractive as an alternative for various applications.This talk will overview the state of the art and of the com-munity, as the algorithm matures.

Lorena A. BarbaDepartment of Mechanical and Aerospace EngineeringGeorge Washington Universitylabarba@gwu.edu

MS27

N-body Methods in Computational Science andEngineering

N-body methods find numerous applications in science andengineering. In this talk, I will outline the evolution ofthe methods since the early methods and the adoption oftheir use in fields ranging from gravitational simulations tomachine learning.

George BirosUniversity of Texas at Austinbiros@ices.utexas.edu

MS27

Computer Science Aspects of Fast Multipole Meth-ods

Abstract not available at time of publication.

Richard VuducGeorgia Institute of Technologyrichie@cc.gatech. edu

MS27

The Geometry of the Fast Multipole Methods

An overview of the geometric aspect of the different kindsof fast multipole methods.

Lexing YingStanfordlexing@math.stanford.edu

MS28

Low-Complexity Stochastic Modeling of TurbulentFlows

Abstract not available at time of publication.

Mihailo R. JovanovicElectrical and Computer Engineering

University of Minnesotamihailo@umn.edu

MS28

Data Mining and Coarse Graining for NetworkEvolution Problems

In dynamic problems where what evolves is the struc-ture/connectivity of a complex network, coarse grainingrequires the identification of a small set of macroscopic ob-servables (variables) that hopefully suffice to characterizethe evolutionary dynamics. Data mining tools (and, inparticular, diffusion maps) can be used to provide such aparametrization of the dynamics, using graph metrics toprovide the pairwise similarities between ”nearby” graphs.We illustrate this approach in data sets from different(static as well as dynamically evolving) families of graphsand use the resulting variables to enhance dynamic mod-eling.

Yannis KevrikidisPrinceton Universityyannis@princeton.edu

MS28

Data-Driven Modeling of Complex Systems withControl

Analysis of large-scale datasets generated from complexsystems with external control is becoming increasingly im-portant for the engineering, applied, and biological sci-ences. Here, the development of a new method, whichextends Dynamic Mode Decomposition (DMD), incorpo-rates the effect of control to extract low-order models fromhigh-dimensional, complex systems. The method, calledDynamic Mode Decomposition with control (DMDc), wasdeveloped for the purpose of studying infectious diseasespread and designing intervention campaigns.

Joshua L. ProctorIntellectual VenturesJoshLProctor@gmail.com

MS28

A Deim Induced Cur Factorization

Abstract not available at time of publication.

Danny C. SorensenRice Universitysorensen@rice.edu

MS29

Geometric Methods in Image Processing, Net-works, and Machine Learning

We present new methods for segmentation of large datasetswith graph based structure. The method combines ideasfrom classical nonlinear PDE-based image segmentationwith fast and accessible linear algebra methods for com-puting information about the spectrum of the graph Lapla-cian. The goal of the algorithms is to solve semi-supervisedand unsupervised graph cut optimization problems. I willpresent results for image processing applications such asimage labeling and hyperspectral video segmentation, andresults from machine learning and community detection insocial networks, including modularity optimization posed

42 CS15 Abstracts

as a graph total variation minimization problem.

Andrea L. BertozziUCLA Department of Mathematicsbertozzi@math.ucla.edu

MS29

Sampling of Dynamic Graphs and Recovery of theSpectral Properties

Massive networks have become ubiquitous today. To mon-itor such very large networks, one must resort to samplingthese networks: a succinct subset of nodes and associatededges are extracted from the original network. In thispaper, we present an algorithm to recover the dominanteigenvectors of a very large graph using different realisticsampling strategies. We evaluate the performance of thealgorithm on realistic synthetic datasets and real networks.

Nathan D. MonnigDepartment Applied MathematicsUniversity of Colorado Bouldernathan.monnig@colorado.edu

Conrad HougenUniversity of Colorado at Boulderconrad.hougen@gmail.com

Francois G. MeyerUniversity of Colorado at BoulderUSAfmeyer@colorado.edu

MS29

Consistency of Variational Partitioning of PointClouds

I will discuss variational problems arising in machine learn-ing and their consistency as the number of data pointsgoes to infinity. Consider point clouds obtained as randomsamples of a measure on a Euclidean domain. Graph repre-senting the point cloud is obtained by assigning weights toedges based on the distance between the points. Manymachine learning algorithms are based on minimizing afunctional on this graph. Among them are balanced cutsand spectral methods for clustering. We will discuss underwhat conditions do the minimizers of graph based func-tionals converge to a well defined limit.

Nicolas Garcia Trillos, Dejan SlepcevCarnegie Mellon Universityngarciat@andrew.cmu.edu, slepcev@math.cmu.edu

James von BrechtUniversity of California, Los Angelesjub@math.ucla.edu

Thomas LaurentLoyola Marymount Universitythomas.laurent@lmu.edu

Xavier BressonSwiss Federal Institute of Technology (EPFL)Institute of Electrical Engineering

xavier.bresson@epfl.ch

MS29

A Panoply of Graph-ported PDEs and Processes

In fields such as image processing, data analysis and com-munity detection, the data sets are often modeled as agraph in which the nodes represent the data points andthe edges encode some relationship between the nodes,relevant to the task at hand. In recent years, peoplehave studied classical continuum partial differential equa-tions PDE models from image analysis, but formulated ongraphs to be applicable to data analysis problems. Thesestudies show interesting connections between continuumresults and the analogous problems on graphs. In this talkwe will explore some of these PDE type problems formu-lated on graphs and their connections with both contin-uum results and notions from graph theory. Examples in-clude threshold dynamics, modularity optimization, Ohta-Kawasaki minimization, and their relation to graph cuts,mean curvature flow, and bootstrap percolation.

Yves van GennipNottingham Universityy.vangennip@nottingham.ac.uk

MS30

Symplectic Model Reduction for Hamiltonian Sys-tems

Proper symplectic decomposition (PSD) is introduced asa symplectic model reduction technique using the sym-plectic Galerkin projection. Our aim is two-folded. First,to achieve computational savings for large-scale Hamilto-nian systems. Second, to preserve the symplectic struc-ture of the original system. As an analogy to the classicalPOD-Galerkin approach, the PSD is designed to build asymplectic subspace to fit empirical data, while the sym-plectic Galerkin projection constructs a low-order Hamil-tonian system on the symplectic subspace. The proposedtechnique can preserve system energy, volume of flow, andstability. Therefore, it can be better suited for model re-duction of hyperbolic PDEs as compared to the classicalPOD-Galerkin approach. The stability, accuracy, and ef-ficiency of the proposed technique are illustrated throughnumerical simulations of several linear and nonlinear waveequations.

Kamran MohseniUniversity of Florida, Gainesville, FLmohseni@ufl.edu

Liqian PengUniversity of Floridaliqianpeng@ufl.edu

MS30

An Adaptive and Efficient Greedy Procedure forthe Optimal Training of Parametric Reduced-Order Models

An adaptive and efficient approach for constructing para-metrically robust reduced-order models is developed. Theapproach is based on a greedy sampling of the underlyinghigh-dimensional model along with a fast and efficient sur-rogate based procedure for exploring the parametric spaceto identify parameters for which the error is likely to behigh. The procedure is illustrated on several cases, in-

CS15 Abstracts 43

cluding the realistic prediction of the response of a V-hullvehicle to underbody blasts.

Arthur Paul-Dubois-TaineStanfordartpdt@stanford.edu

David AmsallemStanford Universityamsallem@stanford.edu

MS30

Error Estimation for Hyper-Reduced Elastovis-coplastic Models

We propose an a posteriori error indicator related to hyper-reduced predictions of simulation outputs. We restrict ourattention to elastoviscoplastic materials having an incre-mental variational formulation of the constitutive equa-tions, when the outputs are extracted by a continuous func-tion of the displacements. We obtain an upper bound ofthe approximation error due to the hyper-reduced formu-lation. We show numerical results on oligocyclic fatigue.Computational speed-ups are preserved while errors are es-timated.

David RyckelynckMINES ParistechDavid.Ryckelynck@mines-paristech.fr

MS30

Geometric Methods in Adaptive Model Order Re-duction

The first part of this presentation addresses an originalmanifold learning approach to nonlinear flow problems,where geometric information is used to choose adaptivelylocal prediction neighborhoods for each ROM approxima-tion. The method provides a sensible tool for detectinggaps in the design of experiment and thus for adaptive re-finement. The second part deals with adaptive projection-based ROMs. We propose a method for adjusting a projec-tion subspace to a given parameter condition by optimizinga suitable goal function on the Grassmann manifold.

Ralf ZimmermannDLR Braunschweig, Germanyralf.zimmermann@tu-bs.de

Thomas FranzInstitute of Aerodynamics and Flow TechnologyDLR, German Aerospace Centerthomas.franz@dlr.de

MS31

Flexible Krylov Subspace Methods for Shifted Sys-tems with Multiple Right Hand Sides

Several PDE-based inverse problems require repeated so-lution to large-scale shifted systems of the form (K +zjM)xj,k = bk for j = . . . , nz and k = 1, . . . , ns. We pro-pose a flexible Krylov subspace method that uses multiplepreconditioners of the form K+τM and discuss extensionsto multiple right hand sides using both recycling and blockmethods. Numerical experiments using synthetic examplesfrom a model inverse problem, Hydraulic Tomography, will

demonstrate the performance of our algorithms.

Tania BakhosInstitute for Computational and MathematicalEngineeringStanford Universitytaniab@stanford.edu

Arvind SaibabaDepartment of Electrical and Computer EngineeringTufts Universityarvind.saibaba@tufts.edu

Peter K. KitanidisDept. of Civil and Environmental EngineeringStanford Universitypeterk@stanford.edu

MS31

An Iterative Algorithm for Large-Scale TikhonovRegularization

In this talk, we describe a hybrid iterative approach forcomputing solutions to large scale inverse problems viaTikhonov regularization. We consider a hybrid LSMR ap-proach, where Tikhonov regularization is used to solve thesubproblem of the LSMR approach. One of the benefits ofthe hybrid approach is that semiconvergence behavior canbe avoided. In addition, since the regularization parametercan be estimated during the iterative process, the regular-ization parameter does not need to be estimated a priori,making this approach attractive for large scale problems.We consider various methods for selecting regularizationparameters in the hybrid LSMR framework and discussstopping criteria for the iterative method. Numerical ex-amples from image processing illustrate the benefits andpotential of the new approach.

Julianne ChungVirginia Techjmchung@vt.edu

Katrina PalmerDepartment of Mathematical SciencesAppalachian State Universitypalmerk@appstate.edu

MS31

The Arnoldi-Tikhonov Framework: Choice of Reg-ularization Parameters and Matrices

Iterative Krylov subspace methods play a central role in theregularization of large-scale inverse problems. We describesome new regularization parameter choice techniques for anArnoldi-Tikhonov method. In addition, we describe howto adaptively choose a regularization matrix by exploitingthe previous approximations, and we introduce two newstrategies to approximate regularization terms weighted ina generic norm. The first strategy is exploits adaptive pre-conditioning, and the second strategy is based on a restart-ing procedure.

Silvia GazzolaUniversity of Padovagazzola@math.unipd.it

James G. NagyEmory UniversityDepartment of Math and Computer Science

44 CS15 Abstracts

nagy@mathcs.emory.edu

Paolo NovattiUniversity of Padovanovati@math.unipd.it

MS31

Unbiased Predictive Risk and Discrepancy Princi-ples Applied for LSQR Solutions of Ill-posed LeastSquares

Numerous methods exist for finding regularization param-eters when solving ill-posed linear inverse problems usingfull expansion methods such as the singular value decompo-sition (generalized SVD). Interpreting the propagation ofnoise through the Krylov subspace has limited developmentof robust parameter estimators for iterative solutions. Wedemonstrate the use of unbiased predictive risk estimatorsand discrepancy principles applied at the subspace level.The work is illustrated for a large scale three dimensionalinversion of gravity data.

Rosemary A. RenautArizona State UniversitySchool of Mathematical and Statistical Sciencesrenaut@asu.edu

MS32

Half-Imex Time Integrators for Large Scale Simu-lations of Turbulent Incompressible Flows

We develop high order time integrators for the incompress-ible Navier-Stokes equations. This system is an index 2differential-algebraic problem. For the velocity, we consideran explicit treatment of the nonsymmetric convective term,keeping the stiff viscous term implicit. At every stage, apressure Poisson problem has to be solved. We combinethe time integration with scalable domain decompositionsolvers, and show the efficiency of this approach for largecore counts (orders of hundreds of thousands).

Santiago BadiaInternational Center for Numerical Methods inEngineeringUniversitat Politecnica de Catalunya, Barcelona, Spainsbadia@cimne.upc.edu

Oriol ColomesInternational Center for Numerical Methods inEngineeringocolomes@cimne.upc.edu

MS32

Overview of Added-Mass Partitioned Algorithmsfor FSI Simulations

In recent work we have developed some partitioned algo-rithms for fluid-structure interaction (FSI) problems thatcouple various combinations of compressible and incom-pressible fluids with compressible bulk solids, rigid solidsand structural beams. These algorithms overcome theadded-mass instability for light solids that has plagued thetraditional partitioned approach. This talk will give anoverview of these new added-mass-partitioned (AMP) al-gorithms along with their implementation using deformingoverlapping grids.

William Henshaw

Rensselaer Polytechnic Institutehenshw@rpi.edu

MS32

Overcoming the Added Mass Instability for Cou-pling Incompressible Flows and Elastic Beams

A new partitioned algorithm for coupling incompressibleflows with elastic beams is described that overcomes theadded-mass instability for light solids. The algorithm re-quires no sub-iterations and is fully second-order accurate.The new scheme is shown to be stable, even for very lightbeams, through the analysis of a model problem. The ap-proach is then applied to the simulation of FSI problemsinvolving beams undergoing large deformations using de-forming composite grids.

Longfei LiDepartment of Mathematical SciencesUniversity of Delawarelongfei@udel.edu

MS32

Partitioned Algorithms for FSI Problems InvolvingElastic Solids Coupled to Compressible and Incom-pressible Fluids

New partitioned algorithms for the simulation of elasticsolids coupled to compressible and incompressible fluidsare described. For the compressible case, the coupling usesa interface project based on the solution of a fluid-solid Rie-mann problem, while Robin-Robin coupling conditions arederived for the incompressible case. Both coupling meth-ods result in stable schemes, without sub-iterations, evenfor FSI problems with large added-mass effects. Numeri-cal results are presented which verify the accuracy of thesenew added-mass partitioned (AMP) algorithms.

Donald W. SchwendemanRensselaer Polytechnic InstituteDepartment of Mathematical Sciencesschwed@rpi.edu

MS33

An Approach to Big Data in Inverse Problems

We develop innovative approaches to address the big datachallenge in large-scale inverse problems and UQ governedby expensive PDEs. Various numerical results will be pre-sented to demonstrate the effectiveness of our approaches.

Ellen B. LeUT Austinellenle@ices.utexas.edu

Aaron MyersUT Austin, ICESaaron@ices.utexas.edu

Tan Bui-ThanhThe University of Texas at Austintanbui@ices.utexas.edu

MS33

Active Subspaces for the Design of Supersonic Low-

CS15 Abstracts 45

Boom Aircraft

We apply the active subspace method to a realisticsimulation-based design problem: the Lockheed N+2 low-boom supersonic passenger jet. The method discovered alow-dimensional linear subspace of inputs that explaineda majority of the variability in drag, lift, and sonic-boom.We exploited this subspace to find an optimal design at re-duced computational cost, as well as automatically gener-ate deformation modes that yield intuitive interpretationssuch as twist and camber.

Trent W. LukaczykStanford Universitytwl26@stanford.edu

Juan J. AlonsoDepartment of Aeronautics and AstronauticsStanford Universityjjalonso@stanford.edu

Francisco PalaciosStanford Universityfpalacios@stanford.edu

MS33

Parameter Selection Techniques for Disease Models

We discuss parameter selection techniques for nonlinearlyparameterized, dynamic, disease models. The objective isto develop techniques to determine the sets of identifiableor influential parameters for these models. We compare theperformance of Morris screening, Sobol analysis employinganalysis of variance, Bayesian analysis, and active subspacetechniques utilizing singular value decompositions (SVD)and QR factorizations for models with both single and mul-tiple responses. We also detail the necessity of employingsuch parameter selection techniques before Bayesian modelcalibration and uncertainty propagation for models havinga large number of inputs.

Jared CookAsbury Universityjared.cook@asbury.edu

Nicholas MyersUniversity of Wisconsin-Milwaukeenjmyers@uwm.edu

Nina NingGeorge Washington Universityning9386@gwmail.gwu.edu

Mami WentworthNC Statemtonoe@ncsu.edu

Ralph C. SmithNorth Carolina State UnivDept of Mathematics, CRSCrsmith@ncsu.edu

MS33

Likelihood-Informed Dimension Reduction forBayesian Inverse Problems

The intrinsic dimensionality of an inverse problem is af-fected by prior information, the observations, and the prop-

erties of the forward operator. In many problems, changesfrom the prior to the posterior can be confined to a rel-atively low-dimensional subspace. We define and identifysuch a subspace, called the likelihood-informed subspace(LIS). We show that significant computational savings canbe achieved by using this subspace to approximate the pos-terior distribution.

Tiangang CuiMassachusetts Institute of Technologytcui@mit.edu

James R. MartinUniversity of Texas at AustinInstitute for Computational Engineering and Sciencesjmartin@ices.utexas.edu

Youssef M. MarzoukMassachusetts Institute of Technologyymarz@mit.edu

Antti SolonenLappeenranta University of TechnologyDepartment of Mathematics and Physicsantti.solonen@gmail.com

Alessio SpantiniMassachusetts Institute of Technologyspantini@mit.edu

Luis TenorioColorado School of Minesltenorio@mines.edu

MS34

Sparse Grid and Reduced Basis Approximation ofBayesian Inverse Problems

We present a computational reduction framework for effi-cient and accurate solution of Bayesian inverse problems onhigh- or infinite-dimensional parameter spaces that com-monly face the curse of dimensionality and large-scale com-putation. For the approximation of high or infinite di-mensional integration, we take advantage of sparsity inthe parametric solution maps in novel dimension-adaptivesparse grid interpolation and quadrature algorithms. Forlarge scale problems, we also exploit intrinsic sparsity inthe solution map and the high-fidelity approximation andpropose a novel, goal-oriented reduced basis method.

Peng ChenETH Zurichpeng.chen@sam.math.ethz.ch

Christoph SchwabETH ZuerichSAMchristoph.schwab@sam.math.ethz.ch

MS34

Goal-Oriented Model Adaptivity for Inference

We present a goal-oriented adaptive method for inverseproblems based on the use of multiple models. Previouswork has addressed the use of goal-oriented grid adaptationin inverse problems, but has been restricted to the singlemodel paradigm. Our method develops estimates for theerror in the prediction quantity of interest due to the use

46 CS15 Abstracts

of a lower fidelity model in the inference process. We alsopresent numerical experiments illustrating the efficiency ofthe method.

Vikram GargICES, U Texas, Austinvikram.v.garg@gmail.com

Harriet LiMITkameeko@mit.edu

Karen E. WillcoxMassachusetts Institute of Technologykwillcox@MIT.EDU

MS34

An Empirical Objective Bayes Method for LargeInverse Problems

The Geostatistical Approach is a general, flexible, and com-prehensive formalism for solving underdetermined param-eter estimation problems (inverse problems). The methodis increasingly used for problems with many unknowns andobservations. I will review some of the tools, all of whichexploit the problem structure, to make this approach com-putationally tractable for large problems, including Hierar-chical Matrices and Fast Multipole Method for fast matrixvector products, compression methods for dimensionalityreduction, and iterative methods.

Peter K. KitanidisDept. of Civil and Environmental EngineeringStanford Universitypeterk@stanford.edu

MS34

Applying UQ Approaches to Random OrdinaryDifferential Equations

Random Ordinary Differential Equations (RODEs) can of-fer an alternative concept for Stochastic Differential Equa-tions via path-wise solutions of ODEs, avoiding Ito calculusand frequently using coloured noise instead of white noiseprocesses for the underlying random effects. We focus onthe numerical solution of RODEs and their connection toUQ techniques to improve computational performance forapplications such as earthquake-induced motion of wire-frame buildings.

Tobias NeckelTechnische Universitat Munchenneckel@in.tum.de

Hans-Joachim BungartzTechnische Universitat Munchen, Department ofInformaticsChair of Scientific Computing in Computer Sciencebungartz@in.tum.de

Alfredo ParraTechnische Universitat Munchenalfredo.parra@tum.de

MS35

Matrix-Free Solvers for Robust PCA and Distance

Matrix Completion

The problem of (stable) robust PCA is to separate a datamatrix into low-rank, sparse and noise components. Due tothe cost of standard algorithms, which require full or par-tial SVDs at every step, the problem is extremely compu-tationally difficult for large-scale applications. We presenta new method that incorporates more information than atraditional first-order method, but without increased costper iteration, and show very favorable results comparedto other recent solvers. We also present variants of thisalgorithm. Lastly, we discuss the specific challenges of avariant of distance matrix completion that is applicable forlocating sites on chromosomes.

Stephen BeckerUC Boulderstephen.becker@colorado.edu

Aleksandr AravkinIBM T.J. Watson Research Centersaravkin@us.ibm.com

Aurelie LozanoIBM ResearchT. J. Watson Research Centeraclozano@us.ibm.com

MS35

Matrix Free Quadratic-penalty Methods for PDE-constrained Optimization

The large scale of seismic waveform inversion makes ma-trix free implementations essential. We show how to ex-ploit the quadratic penalty structure to construct ma-trix free reduced-space and full-space algorithms, whichhave some advantages over the commonly used Lagrangianbased methods for PDE-constrained optimization. This in-cludes the construction of effective and sparse Hessian ap-proximations and reduced sensitivity to the initial guess. Acomputational bottleneck is the need to solve a large leastsquares problem with a PDE block. When direct solversare not available, we propose a fast matrix free iterativeapproach with reasonable memory requirements. It takesadvantage of the structure of the least squares problemwith a combination of preconditioning, low rank decompo-sition and deflation.

Bas PetersUBCbpeters@eos.ubc.ca

Felix J. HerrmannSeismic Laboratory for Imaging and ModelingThe University of British Columbiafherrmann@eos.ubc.ca

MS35

Compressing Clustered Data using Sparse NMF

We propose a method for storing clustered data compactly,where each cluster is a collection of many similar datasetsin matrix form (such as a set of related images). We firstcompute basis elements for each cluster using low-rankSNMF via PDCO. We then use the preprocessing approachof Gillis (2012) to sparsify the full set of (already sparse)basis elements, without significant loss of quality.

Michael A. Saunders

CS15 Abstracts 47

Systems Optimization Laboratory (SOL)Dept of Management Sci and Eng, Stanfordsaunders@stanford.edu

San KimICME, Stanford Universitysankim@stanford.edu

MS35

Dimensionality Reduction and Uncertainty Quan-tification for Inverse Problems

Many inverse problems in science and engineering involvemulti-experiment data and thus require a large numberof forward simulations. Dimensionality reduction tech-niques aim at reducing the number of forward solves by(randomly) subsampling the data. In the special case ofnon-linear least-squares estimation, we can interpret thiscompression of the data as a (low-rank) approximation ofthe noise covariance matrix. We shoe that this leads todifferent design criteria for the subsampling process. Fur-thermore, the resulting low-rank structure can be exploitedwhen designing matrix-free methods for estimating (prop-erties of) the posterior covariance matrix. Finally, we dis-cuss the possibility of estimating the noise covariance ma-trix itself.

Tristan van LeeuwenMathematical InstituteUtrecht Universityt.vanleeuwen@uu.nl

MS36

A Fourth Order Accurate Embedded BoundaryMethod for the Wave Equation in Second OrderForm

A fourth-order accurate embedded boundary method forthe scalar wave equation with Dirichlet or Neumannboundary conditions is described. The method is based ona compact Pade-type discretization of spatial derivativestogether with a Taylor series method (modified equation)in time. A novel approach for enforcing boundary con-ditions is introduced which uses interior boundary pointsinstead of exterior ghost points. This technique removesthe small-cell stiffness problem for both Dirichlet and Neu-mann boundary conditions, is more accurate and robustthan previous methods based on exterior ghost points, andguarantees that the solution is single-valued when slenderbodies are treated. Numerical experiments are presented toillustrate the stability and accuracy of the method as wellas its application to problems with complex geometries.

Daniel AppeloUniversity of New Mexicoappelo@unm.edu

MS36

High-Order Numerical Methods for Elliptic Inter-face Problems

In our talk we consider elliptic equations with piecewisesmooth coefficients in irregular domains separated by arbi-trary shaped interfaces. Our numerical approach for theseproblems is based on generalized Calderon’s operators andthe Difference Potentials Method. The developed algo-rithm easily handles curvilinear boundaries, variable co-efficients and general boundary conditions. High-order ac-

curacy is achieved efficiently since only simple Cartesiangrids used regardless of the interface shape or boundary.The performance of the numerical method is illustrated inseveral numerical examples in 2D.

Michael MedvinskyUniversity of UtahDepartment of Mathematicsmedvinsky.michael@gmail.com

Yekaterina EpshteynDepartment of mathematicsUniversity of Utahepshteyn@math.utah.edu

Semyon V. TsynkovDepartment of MathematicsNorth Carolina State Universitytsynkov@math.ncsu.edu

Eli TurkelTel-Aviv Universityeliturkel@gmail.com

MS36

A Nitsche Stabilized Fictitious Domain Finite Ele-ment Method for the Wave Equation

We give a weak formulation for solving the wave equation(u = ∇2u + f) on a 2-dimensional fictitious domain. Inthe spatial finite element discretization, boundaries do notconform to element boundaries. Boundary conditions areenforced weakly by Nitsche’s method. Additional penaltyterms ensure a non-stiff temporal system. We give opti-mal a priori error estimates: second order for u − uh andu − uh and first order for ∇(u − uh), for linear elementsin L2-norm. Numerical experiments verify the theory. Ex-tensions to higher orders are discussed.

Simon StickoUppsala UniversityDepartment of Information Technologysimon.sticko@it.uu.se

Gunilla KreissDivision of Scientific ComputingUppsala Universitygunilla.kreiss@it.uu.se

MS37

Cascadic Multilevel for Saddle Point Least-SquaresMethods

We present a cascadic multilevel method for approximat-ing variational formulations of symmetric saddle point sys-tems. The discretization algorithm is based on the avail-ability of families of stable finite element pairs and on fastand accurate solvers for symmetric positive definite sys-tems. On each fixed level an efficient solver such as thegradient or the conjugate gradient algorithm for invertinga Schur complement is implemented. As a main applicationof our approach we define the “saddle point least-squares’method for solving first order systems of PDEs and relateit with the Bramble-Pasciak’s least-squares approach. Weapply our saddle point least-squares method to discretizingthe time harmonic Maxwell equations. The variable of in-terest for the Maxwell equations, the magnetic and electricvector fields, become the constrained variable in the saddle

48 CS15 Abstracts

point least-squares formulation, and bases or stiffness ma-trices associated with these variables are not needed. Thecascadic saddle point least-squares iterative discretizationwe build does not involve edge elements or spaces of bubblefunctions, and is suitable for preconditioning.

Constantin BacutaUniversity of DelawareDepartment of Mathematicsbacuta@math.udel.edu

MS37

Multigrid Method for Linear Elasticity withWeakly Imposed Symmetry

We present a new abstract framework for the convergenceanalysis of the subspace correction methods applied to thesystem of linear algebraic equations associated to the dif-ferential operator arising from the finite element-based dis-crete systems of the linear elasticity with weakly imposedsymmetry. The method is proven to be convergent uni-formly with respect to the mesh size and parameters thatappear in the equations. A special case of our theory canprovide a transparent and improved analysis for the multi-grid methods developed for the pseudo-stress formulationsof Stokes equation. Some sample numerical experimentsfor two dimensional cases are provided to illustrate the the-ory.

Young Ju LeeDepartment of MathematicsRutgers Universityyjlee@txstate.edu

MS37

Solver for Structure-Preserving Discretization ofIncompressible MHD Equations

A uniform solver for a stable structure-preserving finite el-ement discretization of incompressible MHD equation willbe introduced. Numerical results are provided to verifythe structure-preserving property and demonstrate the ef-fectiveness of the solver.

Yicong MaDepartment of MathematicsThe Pennsylvania State Universityma y@math.psu.edu

Xiaozhe HuThe Pennsylvania State Universityxiaozhe.hu@tufts.edu

Jinchao XuPennsylvania State Universityxu@math.psu.edu

MS37

Modeling and Numerical Studies for Fluid-Structure Interactions

In this talk, I will present our recent study on a dynamicfluid-structure interaction (FSI) problem involving witha rotational and elastic structure by using the arbitraryLagrangian-Eulerian (ALE) method for fluid model in Eu-lerian description and the St.Venant-Kirchhoff structuralmodel in Lagrangian description, and design its monolithicmixed finite element approximation. In addition, our stud-

ies on fictitious domain method and full Eulerian phasefield method for FSI problems will be also introduced. Inparticular, in terms of ALE method, we developed a non-linear rotational and deformable structural model for FSIfor the first time. The technique of master-slave relations isemployed to realize the interfacial kinematic condition onthe interface of fluid and structure. Velocity is adoptedas the principle unknown to reformulate the structuralmodel. Our algorithm can also handle a large and irregu-lar fluid flow channel in which the rotational structure isimmersed with ALE method. We use Newtons method tolinearize, and Galerkin/least-square (GLS) and streamline-upwind/Petrov-Galerkin (SUPG) schemes to stabilize themixed finite element discretization of fluid equations withALE approach. Numerical experiments are successfullycarried out for a simplified turbine in 2D and a realisticturbine in 3D which is deforming as well as spinning aroundits rotation of axis cases due to the fluid impact.

Pengtao SunUniversity of Nevada Las Vegas, Math. Dept.pengtao.sun@unlv.edu

MS38

Algorithms for Hessenberg-Triangular Reductionin Parallel

A recent improvement of the parallel QZ algorithm hasmade the initial reduction to Hessenberg-Triangular forma new bottleneck in the solution of generalized non-symmetric matrix eigenvalue problems. We propose a newdistributed algorithm for Hessenberg-Triangular reductionbased on a novel static scheduling technique. Experimentsdemonstrate that the new algorithm improves on the cur-rent state-of-the-art and also identifies the factors thatlimit scalability. The developed code is ScaLAPACK com-patible.

Bjorn AdlerbornUmea UniversityComputing Science and HPC2Nadler@cs.umu.se

Lars KarlssonUmea University, Dept. of Computing Sciencelarsk@cs.umu.se

Bo T. KagstromUmea UniversityComputing Science and HPC2Nbokg@cs.umu.se

MS38

Avoiding Communication in Distributed-MemoryTridiagonalization

We discuss theoretical and practical improvements to par-allel symmetric tridiagonalization algorithms, augmentingexisting algorithms with more communication-efficient par-allel QR factorization kernels and multiple steps of bandreduction. Our theoretical analysis suggests that our ap-proach can reduce interprocessor communication and mem-ory bandwidth cost by O(p1/6) on p processors, using someadditional memory. We validate our analysis by imple-menting a three-step approach, which uses our key ideasto reduce interprocessor communication, albeit by a con-stant factor rather than O(p1/6).

Grey Ballard

CS15 Abstracts 49

Sandia National Laboratoriesgmballa@sandia.gov

James W. DemmelUniversity of CaliforniaDivision of Computer Sciencedemmel@berkeley.edu

Nicholas KnightUC Berkeleyknight@cs.berkeley.edu

Edgar SolomonikUniversity of California at Berkeleysolomon@eecs.berkeley.edu

MS38

A Parallel Multishift QZ Algorithm with Aggres-sive Early Deflation for Distributed Memory HPCSystems

Appearing frequently in applications, generalized eigen-value problems represent one of the core NLA problems.We propose a parallelization of the QZ algorithm by Molerand Stewart that incorporates all modern ingredients ofdense eigensolvers, such as multishift and aggressive earlydeflation techniques. To deal with (possibly many) infi-nite eigenvalue, a new parallel deflation strategy is devel-oped. Numerical experiments for random and applicationexamples demonstrate the effectiveness of our algorithm ondistributed memory HPC systems.

Bjorn Adlerborn, Bo T. KagstromUmea UniversityComputing Science and HPC2Nadler@cs.umu.se, bokg@cs.umu.se

Daniel KressnerEPFL LausanneMathicsedaniel.kressner@epfl.ch

MS38

Performance Evaluation of Sparse Matrix-VectorMultiplication Using GPU/MIC Cluster

Sparse matrix-vector multiplication (SpMV) is an impor-tant computational kernel for many applications. Recently,the number of computing systems equipped with NVIDIA’sGPU and Intel’s Xeon Phi coprocessor based on the MICarchitecture has been increasing. In this talk, we present aperformance evaluation of parallel SpMV using GPU/MICcluster. As shown by the results, the implementation forthe GPU/MIC cluster attained higher performance thanthe implementation for the CPU cluster in some matrices.

Hiroshi MaedaGraduate School of Systems and Information EngineeringUniversity of Tsukubamaeda@hpcs.cs.tsukuba.ac.jp

Daisuke TakahashiFaculty of Engineering, Information and SystemsUniversity of Tsukuba

daisuke@cs.tsukuba.ac.jp

MS40

Integrating Mathematical Modeling and ComputerSimulation with Experimental Synthesis and Char-acterization of Materials

To design materials through computational modeling andsimulation requires close collaborations among appliedmathematicians, materials theorists, and experimentalists.The author will discuss his experiences working with ex-perimental groups in synthesis and characterization of ma-terials and with applied math groups in numerical compu-tation. Examples to be discussed include designing domainstructures and properties of oxide thin films. The authorwill share his views on the ideal collaboration mechanismsamong applied mathematicians, materials theorists, andexperimentalists.

Long-qing ChenDepartment of Materials Science and EngineeringPennsylvania State Universitylqc3@psu.edu

MS40

Mathematical Challenges in Nonequilibrium Ap-proaches to Amorphous Solids: Quantifying Disor-der, Predicting Plasticity, Accelerating Simulation

Amorphous solids, materials that exhibit an absence oflong range order, exist in every class of materials. Despitetheir ubiquity few methodologies exist to quantify theirstructure, predict their response or achieve the simulationtime scales necessary to understand their complex behav-ior. I will review some of the underlying gaps in our math-ematical knowledge that make the study of amorphoussolids so demanding. Some of these issues limit progressnot only in amorphous solids, but in atomic simulationgenerally. In particular I will discuss the difficulty of quan-tifying disorder in a mathematically rigorous way throughgeneralizations of the Frank-Kasper criterion. I will alsoconsider the challenges that face modeling the plastic flowof materials that bridge the gap between elastic solids andliquids. Finally I will consider the limitations that atom-istic simulations face when studying materials that haveinherent time scales that may span a broad range fromnanoseconds to seconds.

Michael FalkMaterials Science and EngineeringJohns Hopkins Universitymfalk@jhu.edu

MS40

Structural Optimization and 3D Printing

We have known since the 1980’s that some structural op-timization problems call for designs with a high degreeof spatial complexity. However such results were mainlyviewed as theoretical benchmarks, since the manufactureof spatially complex designs has been difficult. The devel-

opment of 3D printing (also known as additive manufactur-ing) calls for re-examination of this area. With 3D printing,spatially complex structures are relatively easy to manu-facture. It is natural to ask how this capability can be usedto good effect. The optimization of 3D printed structures

50 CS15 Abstracts

raises many challenging questions, most of them open.

Robert V. KohnCourant Institute of Mathematical SciencesNew York Universitykohn@cims.nyu.edu

MS40

DNA-Functionalized Nanoparticle Assembly andCrystallization

The selectivity of DNA recognition inspires an elegantprotocol for designing versatile nanoparticle (NP) assem-blies. We use molecular dynamics simulations to analyzestatic and dynamic aspects of the assembly process andidentify key ingredients for the assembly of NP superlat-tices through DNA hybridization. A scale-accurate coarse-grained model captures the relevant contributions to thekinetics of the DNA hybridization process and is able torecover all experimentally reported to date binary super-lattices of DNA functionalized nanoparticles. Using multi-scale modeling we show that through very slow cooling,DNA functionalized nanoparticles assemble into superlat-tices with a specific crystal habit. We reproduce polyhedragrowth in silico, and confirm the Wulff shape for the BCC.Due to defects including twinning and stacking faults in thelattice, the FCC system does not show any uniform shape.Simulated crystal habits of both the BCC and FCC systemare consistent with experiments.

Monica Olvera De La CruzNorthwestern Universitym-olvera@northwestern.edu

MS41

A New Penalization Method for the Shallow WaterEquations with Applications to Global Ocean Flow

We propose a new mass and energy conserving Brinkmanboundary condition penalization for the rotating shallowwater equations. This penalization does not lead to higherwave speeds in the solid region. The error estimates for thepenalization are derived analytically and verified numeri-cally for linearized one dimensional equations. The penal-ization is implemented in a conservative dynamically adap-tive wavelet method for the rotating shallow water equa-tions on the sphere with bathymetry and coastline datafrom NOAA’s ETOPO1 database. This code could formthe dynamical core for a future global ocean model. Thepotential of the dynamically adaptive ocean model is illus-trated by using it to simulate the 2004 Indonesian tsunamiand wind-driven global ocean circulation.

Nicholas KevlahanDepartment of Mathematics & StatisticsMcMaster Universitykevlahan@mcmaster.ca

MS41

Imposing Dirichlet and Neumann Conditions inFourier Pseudospectral Methods Using Volume Pe-nalization

The volume penalization method for computing confinedfluid and plasma flows in complex geometries while us-ing Fourier pseudo-spectral discretizations is reviewed.The mathematical principle of this technique is describedand simple examples for imposing Dirichlet and Neumannboundary conditions are given. Applications for fluid and

plasma turbulence in two and three space dimensions illus-trate the efficiency of the method.

Kai SchneiderUniversite de Provence, Aix-MarseilleCentre de Mathematiques et Informatiquekschneid@cmi.univ-mrs.fr

MS41

High-Order Fourier-Penalty Methods for PDEs onIrregular Domains

Penalty methods offer an attractive approach for solv-ing partial differential equations (PDEs) on domains withcurved or moving boundaries. The new penalized PDE isthen attractive to solve since one no longer needs to ac-tively enforce the boundary conditions. Despite the sim-plicity, these methods have suffered from poor convergencerates. I will show how to systematically construct a newclass of penalization terms which improve the order of con-vergence. I will then demonstrate that the new approachallows one to devise higher order, stable, Fourier spectralmethods to solve the penalized PDE.

David ShirokoffNew Jersey Institute of Technologydavid.g.shirokoff@njit.edu

MS42

Designing Self-Propelling Microgel Swimmer

Using dissipative particle dynamics, we design a hydro-gel micro-swimmer that is actuated by a periodically ap-plied stimulus. The gel has an X-shaped geometry and twobonded layers, one of which is responsive to the stimulusand the other is passive. When the stimulus is turned on,the responsive layer swells and causes the swimmer to de-form. We demonstrate that when such stimulus-induceddeformations occur periodically, the gel swimmer effec-tively propels forward through the viscous fluid.

Alexander AlexeevGeorge W. Woodruff School of Mechanical EngineeringGeorgia Institute of Technologyalexander.alexeev@me.gatech.edu

Svetoslav Nikolov, Peter YehGeorgia Institute of Technologysnikolov3@gatech.edu, pyeh3@gatech.edu

MS42

The Effect of Curved or Flat Edges Microchan-nels on Vortex Entrapment of Particles as seen inLattice-Boltzmann Simulations

Numerical simulations were conducted to investigate if andhow curved or flat channel wall surfaces, as part of the sur-face topography in micro-flow channel walls, would impactvortex development and vortex entrapments of uniform-size particles in pulsating and non-pulsating flows. Thisresearch also demonstrated the sensitivity of the locationof particle-trapping vortices to particle concentrations.

John CarrolaSouthwest Research Institutejohn.carrola@swri.org

Hakan Basagaoglu

CS15 Abstracts 51

Southwest Research InstituteMechanical Engineering Divisionhakan.basagaoglu@swri.org

MS42

Scaffold-free Three-dimensional Hepatocyte As-sembly for Liver Tissue Engineering

We demonstrate a scaffold-free hepatocyte assemblymethod, which enables generation of repeating and sym-metric cellular structures with high cell-packing densityand viability. Standing waves established at the airliquidinterface are used to pack cells in 3D architecture withoutscaffolding materials. The pattern of 3D architecture is de-termined by the topography of standing waves and can bedynamically controlled by vibrational frequency and am-plitude of standing waves.

Utkan DemirciStanford UniversitySchool of Medicineutkan@stanford.edu

Pu ChenStanford MedicineDepartment of Radiologypuchen@stanford.edu

MS42

Brownian Motion of Arbitrarily Shaped ParticlesConfined in Two-Dimensions

I will present our studies on Brownian motion of micro-fabricated boomerang particles in two-dimensions. Weshow that due to translation-rotation coupling, meansquared displacements of single particles exhibit a non-linear crossover from short time faster to long time slowerdiffusion, and the mean displacements for fixed initial ori-entation are biased. I will also show an analytical modelbased on Langevin theory to explain how the symmetry ofparticle shape affect Brownian motion.

Qi-Huo WeiKent State UniversityLiquid Crystal Instituteqwei@kent.edu

MS43

A Kokkos Implementation of Albany: A Perfor-mance Portable Multiphysics Simulation Code

Albany is a C++ object-oriented, parallel, unstructured-grid, implicit finite element code for solving partial differ-ential equations (PDEs) in various fields of engineering ap-plications and multiphysics simulations in particular. Suchcomplex simulations require to be run on modern Super-computers and performance portability across variety ofHPC architectures has become a critical issue. We havedeveloped a performance portable implementation of theAlbany code, based on Kokkos programming model fromTrilinos. A new Albany-Kokkos implementation is a singlecode base which runs and is performant on diverse HPCarchitectures, and is expected to be performant on futurearchitectures that are supported by the Kokkos library.

Irina Demeshko, H. Carter Edwards, Michael Heroux,Roger P. PawlowskiSandia National Laboratories

ipdemes@sandia.gov, hcedwar@sandia.gov,maherou@sandia.gov, rppawlo@sandia.gov

Eric PhippsSandia National LaboratoriesOptimization and Uncertainty Quantification Departmentetphipp@sandia.gov

Andrew SalingerCSRISandia National Labsagsalin@sandia.gov

MS43

Evaluations of Directive Based ProgrammingModel for GPUs and Extensions for PerformancePortability

Recently, the number of heterogeneous supercomputers us-ing accelerators such as GPUs is increasing. These sys-tems have been showing remarkable performance on real-world applications such as Computational Fluid Dynamics(CFD). However, porting of legacy CPU-based applicationsto systems with accelerators is still big challenge. One ofthe reasons of this problem is low-level programming modelsuch as CUDA, which is the most widely used for port-ing of these applications. To solve this problem, existingapproach includes high-level programming model such asOpenACC but it still has a problem about performanceportability between devices which have different perfor-mance characteristics about data layout. To improve theperformance portability, we suggest an abstraction of datalayout. We also implement and evaluate a directive-basedsource-to-source (extended OpenACC to OpenACC) trans-lator that automatically transforms data layout to suitableform.

Tetsuya HoshinoTokyo Institute of Technologyhoshino@matsulab.is.titech.ac.jp

Naoya MaruyamaRIKEN Advanced Institute for Computational Sciencenmaruyama@riken.jp

Satoshi MatsuokaTokyo Insitute of Technologymatsu@is.titech.ac.jp

MS43

Optimization of Preconditioned Iterative LinearSolvers Using Openmp/openacc on Gpu and Mic

OpenMP is widely used for accelerating programs on CPUand MIC. Also, some people use OpenACC on mainlyGPU. These parallel programming environment can makeparallel programs easy with similar programming fashion.However, in order to obtain good performance, users mayhave to make differ programs in view of target architec-tures. In this talk, we show the implementation and per-formance of ICCG method on OpenMP and OpenACC.We compare the obtained performances with each other.

Satoshi OhshimaThe University of TokyoInformation Technology Centerohshima@cc.u-tokyo.ac.jp

52 CS15 Abstracts

Masaharu MatsumotoInformation Technology CenterThe University of Tokyomatsumoto@cc.u-tokyo.ac.jp

Takahiro KatagiriThe University of Tokyokatagiri@kata-lab.itc.u-tokyo.ac.jp

Toshihiro HanawaInformation Technology CenterThe University of Tokyohanawa@cc.u-tokyo.ac.jp

Kengo NakajimaThe University of TokyoInformation Technology Centernakajima@cc.u-tokyo.ac.jp

MS43

OCCA: An Extensible Portability Layer for Many-Core Programming

There are a number of relatively popular APIs for pro-gramming many-core CPUs, GPUs, and accelerators in-cluding OpenMP, pThreads, CUDA, OpenCL, and Ope-nACC. This manufacturer driven fragmentation echoes thescattershot approach to distributed computing before theMessage Passing Interface standard became the de factostandard. We have developed OCCA as a manufacturerindependent runtime library and abstraction layer. OCCAenables a programmer who is comfortable with the notionsof parallel loops and barriers to write parallel threadedkernel code that is parsable at runtime as either OpenMP,pThreads, CUDA, or OpenCL. The OCCA library is eas-ily extensible and has native interfaces that can be calledfrom C++, C, F90, Python, Java, or Julia. I will showexamples drawn from numerical PDEs that indicate someapplication compute kernels can achieve good performanceacross several platforms while other examples show thatmore than one kernel implementation may be required toachieve best possible performance across platforms.

Tim WarburtonRice UniversityDepartment of Computational and Appliedtimwar@rice.edu

David MedinaRice Universitydsm5@rice.edu

Amik St-CyrComputation and Modeling,Shell International E&P, Inc.amik.st-cyr@shell.com

MS44

An Efficient Spectral Element Helmholtz Solverwith an Accurate Treatment for TransparentBoundary Condition for Periodic Lossy Media

We present a high-order spectral element method for solv-ing layered media scattering problems featuring an opera-tor that transparently enforces the far-field boundary con-dition. The incorporation of this Dirichlet-to-Neumann(DtN) map into the spectral element framework is a novelaspect of this work, and the resulting method can accom-

modate plane-wave radiation of arbitrary angle of inci-dence. In order to achieve this, the governing Helmholtzequations subject to quasi-periodic boundary conditionsare rewritten in terms of periodic unknowns. We constructa spectral element operator to approximate the DtN map,thus ensuring nonreflecting outgoing waves on the artifi-cial boundaries introduced to truncate the computationaldomain. We present an explicit formula that accuratelycomputes the Fourier data involved in the DtN map on thespectral element discretization space. Our solutions arerepresented by the tensor product basis of one-dimensionalLegendre-Lagrange interpolation polynomials based on theGauss-Lobatto-Legendre grids. We will demonstrate thescattered field in singly and doubly layered media withsmooth and nonsmooth interfaces.

Ying HeUC Davisyinghe@math.ucdavis.edu

MS44

Electromagnetic Field Enhancement for MetallicNano-gaps

There has been increasing interests in electromagnetic fieldenhancement and extraordinary optical transmission effectthrough subwavelength apertures in recent years, due to itssignificant potential applications in biological and chemi-cal sensing, spectroscopy, terahertz semiconductor devices,etc. In this talk, I will present a quantitative analysisfor the field enhancement when an electromagnetic wavepasses through small metallic gaps. We focus on a partic-ular configuration when there is extreme scale differencebetween the wavelength of the incident wave, the thicknessof metal films, and the size of gap aperture. Based upona rigorous study of the perfect electrical conductor model,we show that enormous electric field enhancement occursinside the gap. Furthermore, the enhancement strength isproportional to ratio between the wavelength of the inci-dent wave and the thickness of the metal film, which couldexceed 10000 due to the scale difference between the two.On other hand, there is no significant magnetic field en-hancement inside the gap. The ongoing work along thisresearch direction will also be discussed.

Junshan LinAuburn Universityjzl0097@auburn.edu

MS44

Highly tuned hybrid MPI/OpenACC implementa-tion with GPUDirect communication for electro-magnetic solvers based on spectral element dis-cretization

I will present a collaborative work on highly tuned hybridMPI/OpenACC implementation with GPUDirect com-muncation for solving electromagnetic systems based onhigh-order spectral element discretizations. The OpenACCimplementation covers the full solution routines includingelement-by-element operator evaluation as well as tunedMPI communication kernels to effect the near-neighbor fluxexchanges. I will demonstrate performance and analysis onup to 16,384 GPUs on the Cray XK7 supercomputer show-ing more than 3x speedup, compared to the MPI-only CPUperformance on the same number of nodes (262,144 CPUs)for the problem sizes of up to 6.9 billion data points.

MiSun Min

CS15 Abstracts 53

Argonne National LaboratoryMathematics and Computer Science Divisionmmin@mcs.anl.gov

MS44

A High Order Perturbation of Surfaces Method forSimulating Surface Plasmons on Periodic Gratings

In this talk we describe a High Order Perturbation of Sur-faces (HOPS) method for simulating the scattering of elec-tromagnetic waves by periodic grating structures. Themethod amounts to Nystrom’s method applied to a classof Integral Equations for the Helmholtz equation on peri-odic domains inspired by the recent work of Fokas and col-laborators on novel solution formulas for boundary valueproblems. These Integral Equations have a number of ad-vantages over standard alternatives including: (i.) easeof implementation (high-order spectral accuracy is real-ized without sophisticated quadrature rules), (ii.) seamlessenforcement of the quasiperiodic boundary conditions (noperiodization of the fundamental solution, e.g. via Ewaldsummation, is required), and (iii.) reduced regularity re-quirements on the interface proles (derivatives of the defor-mations do not appear explicitly in the formulation). Weshow how these can be efficiently discretized and utilized inthe simulation of surface plasmon excitations on periodicmetal gratings in configurations of engineering interest.

David P. NichollsUniversity of Illinois at Chicagonicholls@math.uic.edu

MS45

Performance of Parallel Algorithms for ParticleTransport on Massively Parallel Architectures

We describe algorithms that execute multi-octant discrete-ordinate transport sweeps in the minimum possible stagecount for a given partitioning across processors and givenwork-unit aggregation. We describe automated selectionof the best partitioning and aggregation for a given prob-lem on a given machine. Spatial grids can be locally un-structured within structured blocks. We present resultsto O(106) parallel processes, including results from nestedparallel algorithms in which each MPI process uses multi-ple threads.

Marvin L. Adams, Michael Adams, W. Daryl Hawkins,Timmie SmithTexas A&M Universitymladams@tamu.edu, i.am.michael.adams@gmail.com,dhawkins@tamu.edu, timmie@tamu.edu

Lawrence RauchwergerComputer Science DepartmentTexas A&M Universityrwerger@cs.tamu.edu

Nancy AmatoTexas A & M Universityamato@tamu.edu

Teresa S. BaileyLLNLbailey42@llnl.gov

Robert FalgoutCenter for Applied Scientific Computing

Lawrence Livermore National Laboratoryrfalgout@llnl.gov

MS45

Particle-Particle, Particle-Mesh Methods for Elec-tromagnetic Problems

In this talk we revisit the topic of subcell methods insideof traditional particle-in-cell methods. The subcell methodproposed in this work is based on using the boundary in-tegral tree code as a subcell model inside of a multidi-mensional PIC code. 1D introduces some some greatlyreduces issues associated with numerical heating and pro-vides greater accuracy in the calculation. This work inves-tigates issues of numerical seating and accuracy in a multi-D setting. Further potential roadmap is presented forproducing heating time domain electromagnetic particle-particle particle-mesh method that is well-suited to thesimulation of non-relativistic plasmas.

Andrew J. ChristliebMichigan State UniverityDepartment of Mathematicsandrewch@math.msu.edu

Eric WolfMichigan State Universitywolferi1@msu.edu

MS45

Stochastic Galerkin Method for Hamilton-JacobiEquations with Uncertainty

Abstract not available at time of publication.

Jingwei HuThe University of Texas at Austinhu342@purdue.edu

Shi JinShanghai Jiao Tong University, China and theUniversity of Wisconsin-Madisonjin@math.wisc.edu

Dongbin XiuUniversity of Utahdongbin.xiu@utah.edu

MS45

Uncertainty Quantification in Kinetic Theory

In this talk we will study generalized polynomial chaos(gPC) approach to transport equation with uncertaincoefficients/inputs and show that they can be madeasymptotic-preserving, in the sense that in the diffusionlimit the gPC scheme for the transport equation ap-proaches to the gPC scheme for the diffusion equation withrandom diffusion coefficient. This allows the implemen-tion of the gPC method without numerically resolving (byspace, time, and gPC modes) the small mean free path fortransport equation in the diffusive regime. We will alsodiscuss more general hyperbolic equations with (random)geometric source terms and the relevant stochastic well-balanced property.

Shi JinShanghai Jiao Tong University, China and theUniversity of Wisconsin-Madison

54 CS15 Abstracts

jin@math.wisc.edu

Dongbin Xiu, Xueyu ZhuUniversity of Utahdongbin.xu@utah.edu, xzhu@sci.utah.edu

MS46

Testing the Multilayer Shallow Shelf Approxima-tion Against Higher-order Models

In this talk, I will introduce a new hybrid ice flow model(called MSSA) which generalises the Shallow Shelf Approx-imation (SSA) by a Multilayer approach. Advantageously,the MSSA keeps intact the elliptic structure of the SSAand is mechanically exhaustive (it contains both: mem-brane and vertical stresses) while being of 2D complexity.Comparative results will be presented to assess the me-chanical and the computational performances of the MSSAwith respect to classical higher-order models.

Guillaume JouvetFreie Universitat BerlinInstitut fur Mathematikjouvet@vaw.baug.ethz.ch

MS46

A Finite Element Three-Dimensional Stokes IceSheet Dynamics Model with Enhanced Local MassConservation

In this paper, we present and discuss a new finite ele-ment Stokes ice sheet dynamics model that enforces localelement-wise mass conservation by enriching the pressurefinite element space by adding the discontinuous piecewiseconstant pressure space to the Taylor-Hood pressure space.Through various numerical tests based on manufacturedsolutions, benchmark test problems, and the Greenlandice-sheet, we demonstrate that, for ice-sheet modeling, theenriched Taylor-Hood finite element model remains highlyaccurate and efficient, and is physically more reliable androbust compared to the classic Taylor-Hood finite elementmodel.

Wei LengChinese Academy of SciencesState Key Laboratory of Scientific and EngineeringComputingwleng@lsec.cc.ac.cn

Lili JuUniversity of South CarolinaDepartment of Mathematicsju@math.sc.edu

Max GunzburgerFlorida State UniversitySchool for Computational Sciencesmgunzburger@fsu.edu

MS46

Improving Grounding Line Discretization using anEmbedded-Boundary Approach in BISICLES

Correctly representing grounding line dynamics is of fun-damental importance in modeling marine ice sheets. Wehave developed a grounding-line discretization based onthe Chombo embedded-boundary cut-cell framework. Thispromises better representation of grounding lines vs. a tra-

ditional stair-step discretization on Cartesian meshes likethose used in the block-structured AMR BISICLES code.Also, the fundamental discontinuous nature of flow acrossthe grounding line is respected.

Daniel MartinLawrence Berkeley National Laboratorydfmartin@lbl.gov

Peter O. SchwartzLawrence Berkeley Laboratoryposchwartz@lbl.gov

Esmond G. NgLawrence Berkeley National Laboratoryegng@lbl.gov

MS46

On the Development and Performance of a FirstOrder Stokes Finite Element Ice Sheet DynamicalCore Built Using Trilinos Software Components

This talk describes the new Albany/FELIX parallel, scal-able and robust First-Order (FO) Stokes finite element icesheet code developed using Trilinos libraries. Focus willbe on the computational aspects of the code: verification;multilevel preconditioning to achieve good parallel scalabil-ity for FO systems; homotopy continuation techniques forrobust nonlinear solves; many-core performance portabil-ity. Coupling of Albany/FELIX to other land ice dycores(CISM, MPAS) for dynamic simulations and global climateruns will also be discussed.

Irina K. TezaurSandia National Laboratoriesikalash@sandia.gov

Andrew SalingerCSRISandia National Labsagsalin@sandia.gov

Mauro PeregoCSRI Sandia National Laboratoriesmperego@fsu.edu

Ray S. TuminaroSandia National LaboratoriesComputational Mathematics and Algorithmsrstumin@sandia.gov

MS47

The most current list of partic-ipating companies is available atwww.siam.org/meetings/cse15/career.php.

For the most recent list of participating companies visithttp://www.siam.org/meetings/cse15/career.php

Bill KolataSIAMkolata@siam.org

MS48

Application of a Speed Up Fast Direct Solver forthe Solution of the Lippmann-Schwinger Equation

In this work, we applied the HODLR fast solver of Sivaram

CS15 Abstracts 55

and Darve on the Lippmann-Schwinger integral equationfor the solution of the Helmholtz problem. We split anddiscretize the domain by using an adaptive level-restrictedtree structure based on its contrast function. To speed upthe solver, we use the series representation of the Hankelfunctions to pre-compute tables that can be used with thetree structure to obtain the far field and local iterationsbetween the discretizartion points.

Carlos C. BorgesWorcester Polytechnic Instituteborges@cims.nyu.edu

Lise-Marie Imbert-GerardCIMS, New York Universityimbertgerard@cims.nyu.edu

Sivaram AmbikasaranDepartment of MathematicsCourant Institute of Mathematical Sciencessivaram@cims.nyu.edu

Leslie GreengardCourant InstituteNew York Universitygreengar@cims.nyu.edu

MS48

Yee Scheme Coupled with Linear Current in Mag-netic Plasmas with Varying Coefficients

We analyze the stability of the Yee scheme for non sta-tionary Maxwell’s equations coupled with a linear currentmodel, with highly varying coefficients. Indeed the usualprocedure is unstable for physical situations that corre-spond to strongly magnetized plasmas in X-mode (TE)polarization. We propose to use first order clustered dis-cretization of the vectorial product that gives back a stablecoupling. Validation is performed with physically basedproblems. The equivalent time harmonic problem (ellipticequation) yields a similar behavior.

Bruno DespresUniversity Paris VILaboratory LJLLdespres@ann.jussieu.fr

Martin Campos PintoCNRS-LJLL UPMCcampos@ann.jussieu.fr

Stephane HeurauxInstitut Jean Lamour, UMR 7198 CNRS-UniversityLorrainestephane.heuraux@univ-lorraine.fr

Filipe da SilvaInstituto de Plasmas e Fusao Nuclear, Instituto Superiortanatos@ipfn.ist.utl.pt

MS48

Approximation of Degenerate Elliptic Equationswith Muckenhoupt Coefficients: a priori and a pos-teriori Analyses and Efficient Solvers

In many problems of interest it is unavoidable to considerelliptic equations with coefficients that either degenerateor become singular. An example of this is the α-harmonic

extension for the localization of fractional powers of uni-formly elliptic operators. In this talk we will develop anapproximation theory for weighted Sobolev spaces whenthe weight belongs to the Muckenhoupt class Ap, which isa class of weights that may degenerate or blow up. Thiswill provide the tools necessary for an optimal a priori er-ror analysis of discretizations of such equations. In addi-tion, we will discuss multilevel methods for the solution ofsuch problems and prove their nearly uniform convergence.Finally, we will show how to exploit the structure of theweight to develop a posteriori error estimators.

Abner J. SalgadoDepartment of MathematicsUniversity of Tennesseeasalgad1@utk.edu

MS48

Discontinuous Enrichment Method for Problemswith Variable Coefficients

Abstract not available at time of publication.

Radek Tezaur, Charbel FarhatStanford Universityrtezaur@stanford.edu, CFarhat@stanford.edu

Irina K. TezaurSandia National Laboratoriesikalash@sandia.gov

MS49

Superconvergence of Discontinuous GalerkinMethods for Hyperbolic Equations in Two SpaceDimensions

We study the superconvergence of discontinuous Galerkinmethods for hyperbolic equations in two space dimensions.We first consider periodic boundary condition, and willprove that with piecewise k-th degree polynomial, the errorbetween the numerical solution and the exact solution atthe downwind-biased Radau points are k+2-th order accu-racy. Moreover, at downwind point, the error is 2k+1-thorder accurate. For Dirichlet boundary condition, we haveto make a special projection of the exact solution at theinflow boundary to obtain similar results. Numerical ex-periments will be given to verify our numerical analysis.

Waixiang CaoBeijing Computational Science Research Centerwxcao@csrc.ac.cn

Yang YangMichigan Technological Universityyyang7@mtu.edu

Zhimin ZhangWayne State UniversityDepartment of Mathematicsag7761@wayne.edu

Chi-Wang ShuBrown UniversityDiv of Applied Mathematicsshu@dam.brown.edu

MS49

Runge-Kutta Discontinuous Galerkin Methods for

56 CS15 Abstracts

the Relativistic Vlasov-Maxwell System

The relativistic Vlasov-Maxwell (RVM) system is a ki-netic model of plasma to describe the phenomena whenthe charged particles move in the relativistiic regime, andthe collisions of the particles are omitted. In this talk,we propose several discontinuous Galerkin (DG) methodswith Runge-Kutta time discretizations to solve the RVMsystem. When the DG methods with the standard poly-nomial spaces are used, the mass conservation of the sys-tem is shown both theoretically and numerically. However,due to the special formulation of the total energy for theRVM system, the energy conservation cannot be obtained.Therefore, we proposed DG methods with non-polynomialspaces to preserve the total energy of the system. We dis-cuss the conservation properties of both semi-discrete andfully discrete schemes, the error estimates, and validatethe theoretical results numerically. Numerical experimentsincluding streaming Weibel instability and wakefield accel-eration are also presented.

He YangRensselaer Polytechnic InstituteDepartment of Mathematical Scienceshyang2@stanford.edu

Fengyan LiRensselaer Polytechnic Institutelif@rpi.edu

MS49

A Simple DG Scheme for Acoustic Wave Equationswith Curved Interfaces and Boundaries

Consider solving acoustic wave equations with presenceof curved boundary or interfaces. The conventional high-order discontinuous Galerkin scheme on straight-sided el-ements suffers from second order errors due to piece-wisesegment approximation to the curve. We propose a simpleflux correction to reduce the errors by projecting quadra-ture points for line integration onto curved interfaces,and evaluating numerical fluxes at projection points. Forcurved interfaces, numerical tests demonstrate that thissimple modification may reduce interface error and non-physical diffractions. For curved boundary conditions, withthe assumption that the exact solution can be smoothlyextended, the local truncation error of the modified DGscheme is high order. Accuracy tests will be shown todemonstrate the effectiveness of this simple correction.

Xiangxiong ZhangMassachusetts Institute of TechnologyDepartment of Mathematicszhan1966@purdue.edu

MS49

Runge-Kutta Discontinuous Galerkin Method witha Simple and Compact Hermit Weno Limiter

In this talk, we propose a new type of weighted essentiallynon-oscillatory (WENO) limiter, which belongs to the classof Hermite WENO (HWENO) limiters, for the Runge-Kutta discontinuous Galerkin (RKDG) methods solvinghyperbolic conservation laws. This new HWENO limiteris a modification of the simple WENO limiter proposedrecently by Zhong and Shu. Both limiters use informa-tion of the DG solutions only from the target cell and itsimmediate neighboring cells, thus maintaining the originalcompactness of the DG scheme. The goal of both lim-

iters is to obtain high order accuracy and non-oscillatoryproperties simultaneously. The main novelty of the newHWENO limiter in this talk is to reconstruct the polyno-mial on the target cell in a least square fashion while thesimple WENO limiter is to use the entire polynomial of theoriginal DG solutions in the neighboring cells with an addi-tion of a constant for conservation. This modification im-proves the robustness in the computation of problems withstrong shocks or contact discontinuities, without changingthe compact stencil of the DG scheme. Numerical resultsfor both one and two dimensional equations including Eu-ler equations of compressible gas dynamics are provided toillustrate the viability of this modified limiter.

Jun ZhuNanjing University of Aeronautics and Astronauticszhujun@nuaa.edu.cn

Xinghui ZhongMichigan State Universityzhongxh@math.msu.edu

Chi-Wang ShuBrown UniversityDiv of Applied Mathematicsshu@dam.brown.edu

Jianxian QiuXiamen Universityjxqiu@xmu.edu.cn

MS50

Compact Scattered RBF-FD Stencils for PDEs onSurfaces

We present a novel high-order meshfree method for the so-lution of PDEs on smooth surfaces embedded in R3, withapplications in biology and chemistry. The approach is acombination of local Hermite RBF interpolation and iter-ated application of the projected gradient, and thus onlyrequires a set of points and the corresponding normal vec-tors. A diagonally dominant sparse matrix is obtained forfourth order discretizations of the Laplace–Beltrami oper-ator, ensuring computational efficiency.

Erik LehtoDepartment of MathematicsRoyal Institute of Technologyelehto@kth.se

Varun ShankarSchool of ComputingUniversity of Utahvshankar@math.utah.edu

Grady B. WrightDepartment of MathematicsBoise State University, Boise IDgradywright@boisestate.edu

MS50

Solving PDEs on the Sphere via Novel GalerkinMethod using Highly Localized Kernel Bases

In this talk we will discuss a novel, kernel-based meshlessGalerkin method for numerically solving partial differentialequations on the sphere. In particular, we will apply thismethod to treat a general PDE describing stationary heat

CS15 Abstracts 57

conduction in an inhomogeneous, anisotropic medium onS2. The Galerkin method used to do this employs spatiallywell-localized, ”small footprint, ” robust bases for the as-sociated kernel space. The stiffness matrices arising in theproblem have entries decaying exponentially fast away fromthe diagonal. Discretization is achieved by replacing thestiffness matrix with one whose entries are computed by avery efficient kernel quadrature formula for the sphere. Thediscretized stiffness matrix retains the exponential decay inits off diagonal entries. We will present error estimates forthis problem and give a numerical example illustrating theresults obtained.

Francis J. NarcowichDepartment of MathematicsTexas A&M Universityfnarc@math.tamu.edu

Joseph WardTexas A&M UniversityDepartment of Mathematicsjward@math.tamu.edu

Stephen RoweDepartment of MathematicsTexas A&M Universitysrowe@math.tamu.edu

MS50

A Least Squares-RBF Approach to TransportProblems on Surfaces

In this this talk, we aim to solve hyperbolic PDEs such asthe wave equation on a given manifold S, using interpola-tion with Radial Basis Functions (RBFs). Our approach isto use the process of approximating the differential opera-tor suggested and outlined originally by Wright. We seekto address challenges involved in solving hyperbolic prob-lems on surfaces. One primary challenge is the need foradded hyper-viscosity in solving hyperbolic problems. Thistalk discusses how hyper-viscosity can be implemented andthe possibility of using an RBF-Least Squares method foravoiding hyper-viscosity altogether.

Daryl J. SpringerDepartment of MathematicsArizona State UniversityDaryl.Springer@asu.edu

MS50

Quadrature on Spheres and Other Manifolds Basedon Kernels

Quadrature formulas for spheres, the rotation group, andother compact, homogeneous manifolds are important ina number of applications. The purpose of this talk is topresent coordinate independent quadrature formulas asso-ciated with certain classes of positive definite and condi-tionally positive definite kernels that are invariant underthe group action of the homogeneous manifold. In par-ticular these formulas are accurate-optimally so in manycases-and stable under anincreasing number of nodes andin the presence of noise, provided the set X of quadraturenodes is quasi-uniform.

Joseph WardTexas A&M UniversityDepartment of Mathematics

jward@math.tamu.edu

MS51

High-Order Finite Element Methods for CardiacElectrophysiology

Finite element and finite difference methods are widelyused for solving problems in computational cardiac elec-trophysiology. However, their computational cost prohibitstheir direct use in online clinical practice during ablationtherapy. In this talk we illustrate how high-order finite ele-ment methods and surface representations of the left atrialchamber can be used to achieve greater accuracy, reducedcomputation times and increased scalability to bring mod-elling closer to achieving clinical utility.

Chris CantwellImperial College Londonc.cantwell@imperial.ac.uk

Sergey B. YakovlevUniversity of UtahSchool of Computingyakovs@sci.utah.edu

Rheeda AliDepartment of BioengineeringImperial College Londonrheeda.ali07@imperial.ac.uk

Nicholas PetersNational Heart and Lung InstituteImperial College Londonn.peters@imperial.ac.uk

Mike KirbyUniversity of UtahSchool of Computingkirby@cs.utah.edu

Spencer SherwinImperial College Londons.sherwin@imperial.ac.uk

MS51

Three-Dimensional Modeling of Ca2+ Signaling inHealthy and Failing Cardiomyocytes

Calcium (Ca2+) is an important ion that drives contrac-tion of muscle cells. In cardiac cells, Ca2+ dependentsteps of the contractile cycle involve influx of the ion intothe cytosol from the extracellular membrane (sarcolemma)and sarcoplasmic reticulum (SR), diffusion to the myofib-ril where it activates force generation, and uptake at thesarcolemma and SR. The presence of intracellular struc-tures including the myofibrils, organelles (SR, mitochon-dria), and myriad protein crowders restrict the volume,through which Ca2+ diffuses and thus reduces the ionsapparent diffusion rate. Theories that account for the ar-rangement and excluded volume of intracellular diffusionobstacles provide accurate estimates of the apparent dif-fusion rate. We extend one of these theories, homogeniza-tion, to explore the impact of diffusional obstacles and non-uniformly distributed Ca2+ fluxes or buffers on Ca2+ sig-naling using realistic cell geometries of from healthy andfailing hearts.

Peter Kekenes-Huskey

58 CS15 Abstracts

University of Kentuckypkekeneshuskey@ucsd.edu

MS51

Assessing the Credibility of Computational Modelsof Cardiac Electrophysiology

There is a much interest in clinical applications of com-putational models of cardiac electrophysiology, which willrequire the reliability of model predictions to be thoroughlyinvestigated. Rigorous methods for assessing credibility ofcomputational models have been developed within engi-neering and physical sciences (’verification, validation anduncertainty quantification’). However, applying such tech-niques to evaluate highly complex physiological modelssuch as cardiac electrophysiology models is extremely chal-lenging. In this talk we will discuss work bridging this gap.

Pras PathmanathanDepartment of Computer ScienceUniversity of Oxfordpras.pathmanathan@fda.hhs.gov

Richard GrayU.S. Food and Drug Administrationrichard.gray@fda.hhs.gov

MS51

Multi-Scale Modeling in Cardiac Electrophysiol-ogy: What Are the Challenges in Front of Us?

Mathematical models of cardiac electrophysiology acrossmany scales, from single ion channels to the whole or-gan, have been developed. However, a multi-scale mod-eling framework, which is key for linking random molec-ular events to organ functions and diseases, has not beendeveloped. This talk will focus on what progress we havemade, what are the hurdles in front of us, and discuss howmathematics may help to overcome these challenges.

Zhilin QuUniversity of CaliforniaDept of Medicinezqu@mednet.ucla.edu

MS52

Conservative and Accurate Geometric TransportMethods for Discontinuous Variables in TurbulentMulti-physics Two-phase Flows

Simulating multiphase flows presents significant challenges:flow variables exhibit discontinuities across the phase in-terface, complex microscale dynamics arise due to surfacetension, and the interface develops highly complex cor-rugations. Fluid turbulence and multi-physics processessuch as electro-hydrodynamics exacerbate these difficulties.We will discuss recently advanced geometric techniquescapable of addressing these challenges conservatively andwith second order accuracy. Applications ranging frominterface-turbulence interaction in homogeneous flows toelectro-hydrodynamic fuel atomization will be presented.

Olivier DesjardinsCornell UniversityDepartment of Mechanical and Aerospace Engineering

olivier.desjardins@cornell.edu

MS52

Modeling and Simulation of Multimaterial Com-pressible Flows

Abstract not available at time of publication.

Marianne M. FrancoisLos Alamos National Laboratorymmfran@lanl.gov

MS52

Methods for Computing Turbulent Phase InterfaceDynamics Across Multiple Scales

Dynamics of turbulent interfaces, e.g. the primary atom-ization of liquid jets, can span several orders of magni-tude in scales ranging from centimeter scales of the injec-tor down to the sub-micron scale of the smallest drops.Strategies and examples to efficiently couple these scalesand enable predictive simulations will be discussed, includ-ing coupling Eulerian interface capturing methods to La-grangian drop models and dual-scale approaches to enableLES-type simulations of the phase interface dynamics inturbulent flows.

Marcus HerrmannSchool of Mechanical, Aerospace, Chemical and MaterialsEngiArizona State Universitymarcus.herrmann@asu.edu

MS52

Direct Numerical Simulations of Multiphase Flow:Now What?

After briefly reviewing the history and current status of di-rect numerical simulations of multiphase flows, two futurechallenges for such simulations are discussed. The first ishow to use the vast quantity of data now available to im-prove modeling of the large scale or average flow and theother is how to efficiently include isolated processes, oftendue to additional physics, taking place on length and timescales much smaller than the dominant flow scale.

Gretar TryggvasonUniversity of Notre DameDepartment of Aerospace and Mechanical Engineeringgretar.tryggvason.1@nd.edu

MS53

Discovering Underlying Nonlinear Dynamics ofComplex Systems from Data

Abstract not available at time of publication.

Steven BruntonUniversity of Washingtonsbrunton@uw.edu

MS53

Common Manifold Learning Using Alternating Dif-fusion for Multimodal Signal Processing

One of the true challenges in signal processing is to dis-tinguish between different sources of variability. In this

CS15 Abstracts 59

work, we consider the case of multiple multimodal sensorsmeasuring the same physical phenomenon, such that theproperties of the physical phenomenon are manifested as ahidden common source of variability (which we would liketo extract), while each sensor has its own sensor-specific ef-fects. We will address the problem from a manifold learn-ing standpoint and show a method based on alternatingproducts of diffusion operators and local kernels, which ex-tracts the common source of variability from multimodalrecordings. The generality of the addressed problem setsthe stage for the application of the developed method tomany real signal processing problems, where different typesof devices are typically used to measure the same activity.In particular, we will show application to sleep stage assess-ment. We demonstrate that through alternating-diffusion,the sleep information hidden inside multimodal respiratorysignals can be better captured compared to single-modalmethods.

Ronald CoifmanYale UniversityDepartment of Computer Sciencecoifman@math.yale.edu

Roy LedermanYale Universityroy.lederman@yale.edu

Ronen TalmonTechnionronenta2@gmail.com

MS53

Title Not Available at Time of Publication

Abstract not available at time of publication.

Surya GanguliStanford Universitysganguli@stanford.edu

MS53

Data-Driven Model Reduction to Support DecisionMaking in Complex Systems

The next generation of complex engineered systems willbe endowed with sensors and computing capabilities thatenable new modes of decision-making. For example, newsensing capabilities on aircraft will be exploited to assim-ilate data on system state, make inferences about systemhealth, and issue predictions on future vehicle behavior—with quantified uncertainties—to support critical opera-tional decisions. Model reduction is one way to achievethis challenging task, in particular through data-driven re-duced models that exploit the synergies of physics-basedcomputational modeling and physical data.

Karen E. WillcoxMassachusetts Institute of Technologykwillcox@MIT.EDU

MS54

PhySense: Social and Organizational Network Ac-tivity Simulation for Signature Generation and Ex-traction

We present PhySense an agent-based temporal event sim-ulator that addresses signal propagation in online social

and organizational networks. Probabilistic linear and non-linear models for node activity and edge interactions char-acterize network activity. PhySense includes algorithms topost-process the resulting temporal data to generate met-rics such as node-to-node influence, activity-based central-ity and transfer entropy. The framework serves as a virtuallaboratory for generation and extraction of signatures tounderstand phenomena in a class of social networks.

Vikram JandhyalaUniversity of Washingtonvj@u.washington.edu

Arun SathanurDept. of Electrical EngineeringUniversity of Washingtonarunsv@uw.edu

MS54

Computational Analysis of Ensemble Neural DataRecorded From An Insect Brain

Methods to simultaneously monitor neural activity acrossan ensemble of neurons with fine temporal precisions andacross multiple trials/conditions have become standardpractices in systems neuroscience. However, analysis ofsuch datasets to reveal the underlying neural representa-tion on a trial-by-trial basis has been a challenge. Since,these neural datasets are high dimensional: neurons vs.time vs. trials; we present methods that take advantage ofthis data-structure to extract meaningful response featuresin these neural datasets.

Debajit Saha, Chao LiWashington University in St. Louissahad@seas.wustl.edu, li.chao@wustl.edu

Barani RamanBiomedical EngineeringWashington University in St. Louisbarani@wustl.wdu

MS54

Computational Tools and Methods for SignatureDiscovery (Session Overview)

Scientists engaged in signature discovery have developednumerous analytic algorithms for data processing, featureextraction, machine learning, and classification. These al-gorithms are written in a wide variety of programming lan-guages and utilize data stored in many types of databases.We will discuss analytic tools we developed for signa-ture discovery and a supporting framework that allows re-searchers to easily use (and reuse) analytic codes, regard-less of the language in which they were originally written.

Landon H. SegoPacific Northwest National Laboratorylandon.sego@pnnl.gov

MS54

Statistics, Learning, and Optimization for DataAnalysis and Visualization

A variety of technologies in diverse areas such as medi-cal imaging, industrial inspection, and oil and gas sharecommon underlying challenges. Many of these problemslend themselves to statistical methods that entail estima-

60 CS15 Abstracts

tion, learning, or regression. We motivate these ideas fromsome traditional problems in image processing and developthe concepts of nonparametric modeling with applicationsto data analysis and visualization more generally. Applica-tions from simulations, demographics, and industrial pro-cesses will be discussed.

Ross WhitakerSchool Of Computing, Scientific Computing and ImagingInst.University of Utahwhitaker@cs.utah.edu

MS55

Real-Time Data-to-Decision Using Adaptive Sur-rogate Modeling Strategies

This talk presents an approach to achieve a dynamic data-to-decision process in real-time. We use a non-intrusiveadaptive strategy that combines reduced-order modelingand localization techniques. The methodology is demon-strated for a self-aware autonomous vehicle that relies onthe ability to dynamically process sensor data, assess sys-tem state and capabilities, and make decisions accordingly.We consider the specific case of real-time structural assess-ment in the presence of damage.

Laura MaininiPolitecnico di Torinolmainini@mit.edu

Karen E. WillcoxMassachusetts Institute of Technologykwillcox@MIT.EDU

MS55

An Occam’s Razor Strategy for Field Estimationfrom Wall-Mounted Sensors

We present a field estimation technique suitable for exper-imental closed-loop control. The method relies on an of-fline/online strategy where an approximation basis is learntusing information provided by very few, wall-mounted, sen-sors. Offline derivation of the basis uses sparsity promo-tion techniques and an informative sequence while onlineestimation is achieved by sparse recovery from the sensorsinformation only. The method is illustrated with the flowaround a cylinder and its performance is compared withPOD.

Kevin KasperSATIE - ENS Cachan, Francekevin.kasper@ens-cachan.fr

Lionel MathelinLIMSI - CNRSmathelin@limsi.fr

Mohamed Abbas-Turki, Hisham Abou-KandilSATIE - ENS Cachan, Francemohamed.abbas-turki@satie.ens-cachan.fr, hisham.abou-kandil@satie.ens-cachan.fr

MS55

Thermal Reduced Order Model Adaptation toAero-Thermo-Structural Interactions

Predicting the behavior of hypersonic vehicles components

requires fully coupled structural/aerodynamic/thermalanalyses. This effort being computationally very demand-ing on full order models, reduced order modeling tech-niques have been developed for this multidisciplinary prob-lem. Central to these approaches is the selection of appro-priate bases to represent the solutions. This talk focuseson the determination both a-priori and during computa-tions of bases to represent the temperature field which arerepresentative of the multidisciplinary interactions.

Andrew MatneyArizona State Universityandrew.matney@asu.edu

Marc P. MignoletArizona Statemarc.mignolet@asu.edu

MS55

Numerical Study of Local Reduced Basis withAdaptive Training for Incompressible Navier-Stokes Flows

In this work, we combine a set of reduced-order repre-sentation techniques for simulating incompressible Navier-Stokes flows over a range of physical parameters and il-lustrate that an adaptive time-integration scheme can effi-ciently accelerate the generation of snapshots as well as thesimulations with the reduced-order representations. Thenumber of training configurations selected in snapshots isadaptively increased until the norms of residuals are re-duced below a user-specified tolerance. The reduced-orderrepresentation is further accelerated by combining the ideasof local bases and hyper-reduction of nonlinear terms. Theaccuracy and efficiency of the proposed method is illus-trated on numerical examples with parameter sweeps.

Yuqi WuDepartment of Applied Mathematics, University ofWashingtonyuqiwu@uw.edu

Ulrich HetmaniukUniversity of WashingtonDepartment of Applied Mathematicshetmaniu@uw.edu

MS56

Hierarchical Tensor Approximation of Parameter-Dependent PDEs

Parametric PDEs appear in a large number of applications,as e.g. in uncertainty quantification or optimisation. Typ-ically, the amount of data to approximate and representthe solution scales exponentially in the parameter dimen-sion. Therefore, a crucial task is to develop special numer-ical techniques that rely on data-sparsity in order to copeeven with high parameter dimensions. In this talk, we willdiscuss low-rank tensor techniques that allow to reduce thecomplexity to a linear dependence on the parameter dimen-sion. In particular, our aim is to adaptively construct anapproximation of the solution in the hierarchical tensor for-mat from a relatively small set of data samples. Once thisapproximation from an offline computation is available, theevaluation of quantities of interest becomes a cheap onlinetask. Moreover, the explicit tensor representation can beused to compute stochastic properties of the solution ina straightforward way. The potential of this approach is

CS15 Abstracts 61

illustrated by numerical examples.

Jonas BallaniEPF Lausannejonas.ballani@epfl.ch

Lars GrasedyckMax-Planck-InstituteMath in Scienceslgr@igpm.rwth-aachen.de

Daniel KressnerEPFL LausanneMathicsedaniel.kressner@epfl.ch

MS56

Tensor Format Representations and OptimalModel Reduction for Uncertainty Quantification

In this talk I will give an introduction to the basic principlesof tensor format representations with a special focus onapplications from uncertainty quantification.

Mike EspigMax Planck Institute for Mathematics in the Sciencesmike.espig@alopax.de

MS56

High-Dimensional Tensor Sampling

The hierarchical tensor format allows for the low-parametric representation of tensors even in high dimen-sions d. On the one hand, this format provides a robustframework for approximate arithmetic operations with ten-sors based on rank truncations, which can be exploited initerative algorithms. On the other hand, it can be used forthe direct approximation of high-dimensional data stem-ming, e.g., from the discretisation of multivariate functions.In this talk, we discuss several strategies for an adaptive ap-proximation of tensors in the hierarchical format by blackbox sampling techniques.

Lars GrasedyckMax-Planck-InstituteMath in Scienceslgr@igpm.rwth-aachen.de

Jonas BallaniEPF Lausannejonas.ballani@epfl.ch

Melanie KlugeRWTH Aachenkluge@igpm.rwth-aachen.de

MS56

Novel Tensor-Product Representations for Uncer-taintiy Quantification

Hierarchical Tucker tensor format (HT - Hackbusch ten-sors ) and Tensor Trains (TT- Tyrtyshnikov tensors,I.Oseledets) have been introduced recently for low ranktensor product approximation. Hierarchical tensor decom-positions are based on sub space approximation by extend-ing the Tucker decomposition into a multi-level framework.Therefore they inherit favorable properties of Tucker ten-sors, e.g they offer a stable and robust approximation, but

still enabling low order scaling with respect to the dimen-sions. For many high dimensional problems, hard to behandled so far, this approach may offer a novel strategyto circumvent the curse of dimensionality. For uncertaintyquantification we cast the original boundary value prob-lem, with uncertain coefficients problem into a high dimen-sional parametric boundary value problem, discretized byGalerkin method. The high dimensional problem is castinto an optimization problems, constraint by the restric-tion to tensors of prescribed ranks r. This problem couldbe solved by optimization on manifolds, or more simply byalternating least squares. Since the norm of the underlyingenergy-space is a cross norm, preconditioning is requiredonly for the spatial part and e.g. performed by standardmulti grid approaches, e.g BPX. This leads to a modifica-tion of the orthogonality of the used component tensors. Aimportant task is a posteriori error control, with respect tothe spatial discretization and also w.r.t. the tensor productapproximation.

Reinhold SchneiderTechnische Universitat Berlinschneidr@math.tu-berlin.de

MS57

Fluid-composit Structure Interaction

We focus of the interaction between a multi-layered, com-posite structure, and the flow of an incompressible, vis-cous fluid, giving rise to a fully coupled, nonlinear movingboundary, fluid-multi-structure interaction problem. Ex-amples include arterial walls interacting with blood flow,and oil platforms interacting with water. We present anovel stable, modular, loosely coupled scheme for the nu-merical simulation of the coupled problem, and prove thatthe scheme converges to a weak solution of the nonlinear,fully coupled problem. Our numerical and analytical re-sults reveal new physical regularizing mechanism: the pres-ence of a thin fluid-structure interface with mass regularizesthe evolution of the entire FSI solution.

Suncica CanicDepartment of MathematicsUniversity of Houstoncanic@math.uh.edu

Martina BukacUniversity of Notre Damemartina@nd.edu

Boris MuhaUniversity of Zagreb, Croatiaboris@math.hr

MS57

Second Order Embedded Boundary Methods forFluid-Structure Interaction

This talk presents a second order accurate embeddedboundary method for fluid-structure interaction. First,a spatially second order accurate embedded boundarymethod for first order hyperbolic systems is presented. Sec-ond, existing time discretizations for fluid-structure inter-action are reviewed, with an emphasis on partitioned in-tegrators, and then an extension for embedded boundarymethods is described. Finally, the framework is verified ona set of fluid structure interaction test problems.

Alex Main, Charbel Farhat

62 CS15 Abstracts

Stanford Universityalexmain@stanford.edu, CFarhat@stanford.edu

MS57

A Tetrahedral Method for Transient Nonlinear Dy-namics Computations in Solids, Fluids and Cou-pled Fluid Structure Problems

A new mixed tetrahedral finite element formulation is pre-sented, aimed at transient dynamic computations of flu-ids, solids, and fluid/structure interaction. It utilizes verysimple approximation spaces: Piece-wise linear continu-ous functions for displacements and pressures, and dis-continuous constants for the deviatoric part of the stresstensor (if present, as in solids.) A variational multi-scale stabilization eliminates possible pressure checker-board instabilities. Extensive simulations of compressiblefluids, nonlinear elastic/visco-elastic/elastic-plastic solids,and fluid/structure interaction will conclude the presenta-tion.

Guglielmo Scovazzi, Xianyi ZengDuke Universityguglielmo.scovazzi@duke.edu, xy.zeng@duke.edu

Brian Carnes, David HensingerSandia National Laboratoriesbcarnes@sandia.gov, dmhensi@sandia.gov

MS57

Fractional Modeling of Brain Aneurysms

The arterial wall is typically described using integer-orderPDEs. Recently, 1D simulations indicate that fractional-order models is a powerful alternative because they areless sensitive to the parameter estimation. We develop nu-merical methods for fractional-order models, and for thefirst time employ them in 3D fluid-structure interactionaneurysm simulations. Comparison studies indicate thatalthough the 3D models are more sensitive to the frac-tional order compared to 1D cases, they are insensitive tothe relaxation parameters.

Yue YuBrown Universityyuy214@lehigh.edu

George E. KarniadakisBrown UniversityDivision of Applied Mathematicsgeorge karniadakis@brown.edu

MS58

Exploiting Active Subspaces to Quantify Uncer-tainty in the Numerical Simulation of the HyShotII Scramjet

We present the computational analysis of the reactive flowin a hypersonic scramjet engine with emphasis on effectsof uncertainties in the operating conditions. The activesubspaces methodology is used to characterize the effectsof the input uncertainty on the scramjet performance. Inaddition to discussing the computational cost benefits as-sociated with this dimension reduction technique, we focuson interpretation of the active variable and how it comparesto expertise/intuition and sensitivity analysis

Michael A. Emory

Stanford Universitymemory@stanford.edu

Gianluca IaccarinoStanford UniversityMechanical Engineeringjops@stanford.edu

Johan LarssonUniversity of Marylandjola@umd.edu

MS58

Influence of Surface and Subsurface Parameter Un-certainty and Sensitivity on the Latent Heat FluxUsing An Integrated Hydrologic Model

Integrated hydrologic models simulate surface, subsurfaceand land-surface water and energy fluxes and require pa-rameters to characterize land cover, describe hydraulicproperties and specify initial and boundary conditions. Un-certainty will be propagated through ParFlow, a nonlinearintegrated hydrologic model, using a Monte Carlo simula-tion approach. Results will then be used to understand pa-rameter sensitivity through an active subspace technique;identification of the active subspace will help explain whichparameters result in the greatest model variability.

Jennifer JeffersonColorado School of Minesjejeffer@mymail.mines.edu

Reed M. MaxwellDepartment of Geology and Geologic EngineeringColorado School of Minesrmaxwell@mines.edu

MS58

Dimension Reduction in MCMC using Active Sub-spaces

Markov Chain Monte Carlo is a useful tool for samplingfrom the posterior distribution in Bayesian inverse prob-lems, though it often struggles to converge in high dimen-sions. We discover and exploit active subspaces—an emerg-ing set of tools for dimension reduction—in the misfit termof the likelihood to focus sampling along important direc-tions in the parameter space, which improves mixing andconvergence. We develop the framework and demonstrateits capabilities on a 100-dimensional model inverse prob-lem.

Carson KentColorado School of Minesckent@mines.edu

Paul ConstantineColorado School of MinesApplied Mathematics and Statisticspconstan@mines.edu

MS58

Discovering An Active Subspace in a Single-DiodeSolar Cell Model

Single-diode models for solar cells contain several parame-ters, so sensitivity analyses and UQ can be computationallyexpensive. We employ active subspaces for the solar cell’s

CS15 Abstracts 63

the maximum power functiona function of the single-diodemodel parametersto discover a one-dimensional subspacethat enables us to reduce the dimension for UQ parameterstudies.

Mark CampanelliNational Renewable Energy Laboratorymark.campanelli@nrel.gov

Brian ZaharatosColorado School of Minesbzaharat@mymail.mines.edu

MS59

Operator Weighted MCMC on Function Spaces

Many inference problems require exploring the posteriordistribution of high-dimensional parameters, which in prin-ciple can be described as functions. We introduce a familyof operator-weighted MCMC samplers that can adapt tothe intrinsically low rank and locally complex structure ofthe posterior distribution while remaining well defined onfunction space. Posterior sampling in a nonlinear inverseproblem and a conditioned diffusion process are used todemonstrate the efficiency of these dimension-independentoperator-weighted samplers.

Tiangang CuiMassachusetts Institute of Technologytcui@mit.edu

Kody LawSRI UQ Center, CEMSE, KAUSTkodylaw@gmail.com

Youssef M. MarzoukMassachusetts Institute of Technologyymarz@mit.edu

MS59

Estimation of Parameters of Chaotic Dynamic Sys-tems

To estimate parameters of chaotic dynamical systems ameasure to quantify the likelihood function of chaotic vari-ability (the ’distance’ between different trajectories) isneeded. We review problems encountered by previouslyused methods and propose a method related to fractal di-mension concepts. The methodology is illustrated usingclassical chaotic examples, the Lorenz 63 and Lorenz 95systems, as well as higher dimensional fluid systems.

Heikki HaarioLappeenranta University of TechnologyDepartment of Mathematics and Physicsheikki.haario@lut.fi

MS59

Mapped Stochastic Newton Sampling

Different sampling algorithms for inverse UQ problemswith high-dimensional parameters are reviewed and com-pared. A method that combines ideas from stochastic New-ton MCMC sampling and implicit sampling is proposedand its efficiency is studied numerically.

Georg StadlerCourant Institute for Mathematical Sciences

New York Universitystadler@cims.nyu.edu

Omar GhattasThe University of Texas at Austinomar@ices.utexas.edu

Noemi PetraUniversity of California, Mercednpetra@ucmerced.edu

MS60

RBF Response Surfaces with Inequality Con-straints

In this talk, we describe how to construct RBF interpolantsthat have given function values at some sample points andsatisfy upper and lower bound constraints at other points.Our approach is based on a constrained quadratic mini-mization problem that leads to a unique, parsimonious in-terpolant in which RBF centers appear only as they areneeded to enforce an equality or inequality constraint. Wealso show that this method always improves the nativespace error over an interpolant subject to the equality con-straints alone.

David BindelCornell Universitybindel@cs.cornell.edu

MS60

Miso: Mixed-Integer Surrogate Optimization forComputationally Expensive Black-Box Problems

We present an algorithm framework that uses surrogatemodels for solving mixed-integer global optimization prob-lems whose objective function evaluation requires a com-putationally expensive computer simulation, and thus theanalytical description and the derivatives are not available(black-box). Using a range of benchmark problems andtwo applications arising from groundwater remediation, weshow that a combination of stochastic and deterministicsampling techniques leads to significantly improved solu-tions as opposed to using only a single sampling strategy.

Juliane MuellerLawrence Berkeley National Labjuliane.mueller2901@gmail.com

MS60

Parallel Surrogate Global Optimization withPareto Centers for Single Objective ExpensiveFunctions

In single objective optimization with surrogates there aretypically two criteria when searching on the surrogate sur-face for the next x for expensive function evaluation, a)that s(x), the surrogate surface, is small and b) evaluatingf(x) will improve the overall quality of the accuracy of thesurrogate approximation. In this new algorithm, a multi-objective optimization method is used to select the nextpoints for multiple parallel processors. Solution accuracyis shown to improve.

Christine A. ShoemakerCornell Universitycas12@cornell.edu

64 CS15 Abstracts

Tipaluck KrityakierneCenter for Applied Mathematics, Cornell Universitytk338@cornell.edu

Taimoor AkhtarCornell Universitytaimoor.akhtar@gmail.com

MS60

Efficient Multi-Start for Global Optimization inAccelerator Design

We present a scalable, asynchronous algorithm for locatingseveral/many high-quality local minimizers of expensivecomputer simulations for which derivatives are unavailable.Our method adjusts the amount of exploration/refinementperformed depending on the observed function values anduser desires. We highlight how our method scales as morecomputational resources become available. We lastly em-ploy our algorithm on particle accelerator design prob-lems, performing our computational studies on some of thelargest supercomputers in the US.

Jeffrey M. Larson, Stefan WildArgonne National Laboratoryjmlarson@anl.gov, wild@mcs.anl.gov

MS61

Symmetry-adapted No-core Shell Model for FirstPrinciple Lage Scale Computations of Atomic Nu-clei

We introduce Symmetry-adapted No-core Shell Model (SA-NCSM) approach—an emerging tool for first principlestudies of light and medium mass nuclei. We review thepillars of the SA-NCSM framework and discuss techniquesand algorithms that facilitate its implementation in formof a highly scalable computer code for modern petascalesystems. We also outline future research directions anddevelopments.

Tomas DytrychLouisiana State Universitytdytry1@lsu.edu

MS61

Add, Multiply, Divide and Conquer: On-the-fly Al-gorithms for Many-body Calculations

Quantum many-body systems can be cast as a large-dimension matrix eigenvalue problem. The dimensional-ity is not the only challenge; even with very sparse matri-ces, simply storing the non-zero matrix elements can re-quire terabytes or even petabytes. I discuss how on-the-flymethods can dramatically reduce storage by factorizing thematrix exactly using additive and multiplicative quantumnumbers. Any machine, whether a laptop or a supercom-puter, can thus run much larger problems.

Calvin W. JohnsonSan Diego State Universitycjohnson@mail.sdsu.edu

MS61

Multi-Level LOBPCG Method in MFDn

Many Fermion Dynamics for nuclei (MFDn) is a state-of-the-art software package for nuclei configuration inter-

action calculation. The locally optimal block precondi-tioned conjugate gradient (LOBPCG) method is used inMFDn to compute a few lowest eigenpairs of the verylarge, sparse many-body nuclear Hamiltonian matrix. Wepresent a multi-level strategy that exploits the structureof the Hamiltonian matrix and accelerate the convergenceof the LOBPCG method. Some preliminary results of pre-conditioning are also presented.

Meiyue ShaoLawrence Berkeley National Laboratorymyshao@lbl.gov

MS61

Derivative-free Optimization Techniques in ab ini-tio Nuclear Structure Calculations

Many tasks in ab initio nuclear structure calculationsmay rely on search techniques, such as tuning of nucleon-nucleon and three-nucleon interactions to fit light nuclei,optimizing of basis functions, and reducing 3-body forceeffects by optimizing freedoms in chiral effective-field the-ory NN interactions. This field is still under-served, how-ever, by the existing optimization software, mainly due tothe complexity of the underlying function evaluations. Inthis talk, we will first show a flexible framework for in-terfacing the MFDn package for performing ab initio nu-clear structure calculations with derivative-free optimiza-tion packages. We demonstrate a few examples of tun-ing the interaction parameters and compare results usingPOUNDeRs and QNSTOP optimization algorithms, andnote on efficient function evaluations when several nucleiare fitted simultaneously.

Masha SosonkinaOld Dominion Universitymasha@scl.ameslab.gov

MS62

Hdg Method for Linear Elasticity

This paper presents a new hybridizable discontinuousGalerkin (HDG) method for linear elasticity on generalpolyhedral meshes, based on a strong symmetric stressformulation. The key feature of this new HDG methodis the use of a special form of the numerical trace of thestresses, which makes the error analysis different from theprojection-based error analyzes used for most other HDGmethods. For arbitrary polyhedral elements, we approxi-mate the stress by using polynomials of degree k¿=1 andthe displacement by using polynomials of degree k+1. Incontrast, to approximate the numerical trace of the dis-placement on the faces, we use polynomials of degree konly. This allows for a very efficient implementation ofthe method, since the numerical trace of the displacementis the only globally-coupled unknown, but does not de-grade the convergence properties of the method. Indeed,we prove optimal orders of convergence for both the stressesand displacements on the elements. These optimal resultsare possible thanks to a special superconvergence propertyof the numerical traces of the displacement, and thanks tothe use of a crucial elementwise Korn’s inequality.

Weifeng QiuCity University of Hong Kong

CS15 Abstracts 65

qiuw78@gmail.com

MS62

HDG Methods for the p-Laplacian

We propose a hybridizable discontinuous Galerkin (HDG)method for the p-Laplacian equation. The numericalscheme inherits two distinctive features when the solutionis sufficiently regular. First, when using polynomial of de-gree k ≥ 0 for h, h and uh, our scheme exhibits optimalk + 1 order of convergence for all of them in L2, Lp andL∞ norm. Second, when k ≥ 1, by applying an element-by-element postprocessing technique, we can obtain a newapproximation u∗

h that converges at order k + 2 to u. Inaddition, we formulate two efficient nonlinear conjugategradient algorithms to solve our HDG methods from theminimization standpoint. We carefully compare these twoalgorithms in terms of convergence speed, memory require-ment and robustness. To improve the efficiency further,we construct a class of remarkable preconditioners basedon the unifying hybridization framework. In addition, forthe first time, we postprocess the numerical trace uh forconstructing a quality initial guess as an implementationtechnique.

Bernardo Cockburn, Jiguang ShenSchool of MathematicsUniversity of Minnesotacockburn@math.umn.edu, shenx179@math.umn.edu

MS62

Parallel hp-multigrid for HDG

We present a parallel algorithm for hp-adaptive multigridfor the HDG method. We first coarsen in p, smoothingonly on the skeletal system, until we obtain an HDG sys-tem with p = 1. We switch to a linear CG grid at this stageand continue to coarsen in h. This allows us to create adeep grid hierarchy and obtain optimal multigrid conver-gence. We compare the performance of different smoothersand with our recent work on high-order multigrid using aCG discretization. We also present early scalability resultsfrom a parallel implementation.

Tan BuiUniversity of Texas at Austintanbui@ices.utexas.edu

Hari SundarInstitute for Computational and Engineering SciencesUniversity of Texas at Austinhari@cs.utah.edu

MS63

Solving a Parameterized Eigenvalue Problem fromRegularized Total Least Squares

The solution of an ill-conditioned total least squares (TLS)problem by a regularization approach of Golub et al.[SIAM J. Matrix Anal. Appl. 21(1):185-194,1999] is con-sidered. That regularized TLS formulation can be viewedas a parameterized eigenvalue problem. The approachgiven here is a Newton method that iterates for the param-eter and the associated parameterized eigenvalue. The twononlinear equations are formulated from a standard reg-ularization bound constraint and a spectral function fromthe parameterized eigenvalue problem. The Jacobian of thesystem can be computed inexpensively and can be proven

to be nonsingular under certain reasonable assumptions. Abasic Newton method is presented as well two approximateNewton methods based upon Krylov space and generalizedKrylov space projections. The resulting algorithms are ap-plied to a problem from high-resolution image reconstruc-tion that is appropriately modeled by total least squares.

Jesse L. BarlowPenn State UniversityDept of Computer Science & Engbarlow@cse.psu.edu

Geunseop LeeThe Pennsylvania State Universitygxl174@cse.psu.edu

Haoying FuPenn State UniversityComputer Science & Engineering Departmenthaoyingfu@gmail.com

MS63

Performance Evaluation of EigenExa Dense Eigen-solver on the Oakleaf-Fx Supercomputer System

We have developed a dense eigensolver named EigenExa,which employs the divide-and-conquer method for abanded matrix (currently penta-diagonal). To capture itscurrent performance in detail, we conducted an evalua-tion by using the whole supercomputer system Oakleaf-FX, which consists of 4800 nodes and has the almost samearchitecture as the K computer. In this talk, we presentthe results of the evaluation, which shows advantages ofour eigensolver and issues we face.

Takeshi FukayaRIKEN, JapanJapantakeshi.fukaya@riken.jp

Toshiyuki ImamuraRIKEN Advance Institute for Computational Scienceimamura.toshiyuki@riken.jp

MS63

Scaling Comparison of Dense Eigensolvers and Pu-rification Techniques to Large Node Counts

This talk focuses on the case when large parallel resourcesare available for computing the spectral projector of a rela-tively small matrix. This is the case, for example, in quan-tum chemistry where large parallel resources are neededfor computing the Fock matrix, and then all the resourcesare available to diagonalize the Fock matrix. We examinethe scaling of communication and computation for vari-ous dense eigensolvers, and also for a Newton-Schulz ap-proach for computing the spectral projector which is basedon matrix-matrix multiplications.

Xing Liu, Edmond ChowSchool of Computational Science and EngineeringGeorgia Institute of Technologyxing.liu@gatech.edu, echow@cc.gatech.edu

MS63

Revisiting SVD(A) through EIG(T) for

66 CS15 Abstracts

Sca/LAPACK

It is well known that the SVD of a matrix A, A =USV T , can be obtained from the eigenpairs of the ma-trix CV = ATA or CU = AAT . Alternatively, the SVDcan be obtained from the eigenpairs of the augmented ma-trix CUV = [0 A,AT 0]. This presentation focuses on CUV

in the context of bidiagonal matrices and Sca/LAPACK’stridiagonal eigensolvers, and discusses accuracy and imple-mentation issues.

Osni A. MarquesLawrence Berkeley National LaboratoryBerkeley, CAoamarques@lbl.gov

MS64

Higher-Order Filtered Methods for Nonlinear Par-tial Differential Equations

The theory of viscosity solutions has been effective for rep-resenting and approximating weak solutions of nonlinearpartial differential equations such as Hamilton-Jacobi andsecond-order elliptic equations. The approximation theoryof Barles and Souganidis requires that numerical schemesbe monotone. However, monotone schemes have limitedaccuracy. We introduce a framework for using monotoneschemes as the foundation for filtered schemes, which arealmost-monotone. This allows us to construct higher-orderdiscretisations that provably converge to the viscosity so-lution of the underlying PDE.

Brittany FroeseUniversity of Texas at Austinbfroese@math.utexas.edu

Adam M. ObermanMcGill U.adam.oberman@mcgill.ca

MS64

High Order Methods for Traveltime and Amplitudein Geometrical Optics

In geometrical optics approximation for the Helmholtzequation, accurate and efficient computation of traveltimeand amplitude is important. We present an approach to re-solving the source singularities and high order methods tocompute the traveltime and amplitude efficiently. Numer-ical examples are presented to demonstrate the methods.

Songting LuoDepartment of Mathematics,Iowa State Universityluos@iastate.edu

Jianliang QianDepartment of MathematicsMichigan State Universityqian@math.msu.edu

Robert BurridgeDepartment of Mathematics and StatisticsUniversity of New Mexico

burridge137@gmail.com

MS64

High-Order Gas Evolution Model for Computa-tional Fluid Dynamics

The foundation of compressible flow solver is based on thefirst order gas dynamic model, i.e., the Riemann solutionof the Euler equations, where the spatial and temporal dis-cretizations are decoupled. Here, we will present a high-order gas evolution model based on the Boltzmann equa-tion, and develop the corresponding high-order schemes. Inthe high-order gas-kinetic schemes, the spatial and tempo-ral discretization are fully coupled starting from a piecewisediscontinuous high-order initial condition. The necessity tocouple spatial and temporal evolution nonlinearly is impor-tant to construct high order compact schemes.

Kun XuUniversity of Science & TechnologyHong Kongmakxu@ust.hk

MS64

An Efficient Spectral Method for the Euler-Lagrange Equations of Minimum Action Methods

Minimum Action Method is one of the popular approachesto study phase transitions of dynamical systems. Accord-ing to the Freidlin-Wentzell theory, at zero temperaturelimit, transitions happen along the path which takes min-imum action. Minimum Action Method converts a phasetransition problem to an optimal control problem. Tradi-tional method to solve the optimal control problem usuallyfirst discretize the problem, then use a general purpose op-timization package to solve the discretized problem. Inthis talk, we will propose another approach, which firstderive the Euler-Lagrange equation of the minimum ac-tion, then solve this high-order partial differential equa-tion directly. By taking advantage of good properties ofthe Euler-Lagrange equation, we establish an efficient spec-tral solver. Numerical results for phase transitions of bothODEs and PDEs, gradient and non-gradient systems willbe presented.

Haijun YuLSECAcademy of Mathematics and Systems Science, Chinahyu@lsec.cc.ac.cn

Xiaoliang WanLouisiana State UniversityDepartment of Mathematicsxlwan@math.lsu.edu

MS65

Title Not Available at Time of Publication

Abstract not available at time of publication.

Mary Galvin-DonoghueNational Science FoundationDiv. of Materials Research

CS15 Abstracts 67

mgalvind@nsf.gov

MS65

Materials from Mathematics

We present examples of new materials whose synthesiswas guided by some essentially mathematical ideas. Thesematerials undergo phase transformations from one crystalstructure to another, without diffusion. The underlyingmathematical theory was designed to identify alloys thatshow exceptional reversibility of the transformation. Someof these alloys convert heat to electricity (without a sepa-rate electrical generator), and provide an interesting pos-sible route to recover the vast amounts of energy stored onearth at small temperature difference. The broader lessonsfrom this research are: 1) mathematics can be used for un-expected discovery, but nonstandard approaches are help-ful (what if?, rather than what? and why?), 2) an algorith-mic approach (theorems =⇒ algorithms) seems to be use-ful, 3) a functioning feedback loop with experiment is desir-able, 4) a useful development would be to integrate modernapplied mathematics with the synthesis/characterizationtools that play such an essential role in materials science.

Richard JamesDepartment of Aerospace Engineering and MechanicsUniversity of Minnesotajames@umn.edu

MS65

Computational Materials Design: Challenges inPractical Applications

Abstract not available at time of publication.

Sadasivan ShankarHarvard Universitysshankar@seas.harvard.edu

MS65

Title Not Available at Time of Publication

Abstract not available at time of publication.

Michael S. VogeliusRutgers University, New Brunswickvogelius@math.rutgers.edu

MS66

Penalty Methods for the Hyperbolic System Mod-eling the Wall-Plasma Interaction in a Tokamak

One main challenge for producing energy using magneticconfinement fusion in a tokamak is the control of wall-plasma interactions. Thus, numerical tools with efficientimplementations of the boundary conditions are needed.This talk presents several penalty methods. A penalizationmethod for a non linear hyperbolic problem is provided andanalyzed theoretically and numerically: this method doesnot generate any boundary layer and the convergence rate,when the penalty parameter goes to 0, is optimal.

Philippe Angot, Thomas Auphan, Olivier GuesAix-Marseille Universitephilippe.angot@univ-amu.fr, tauphan@cmi.univ-mrs.fr,

olivier.gues@univ-amu.fr

MS66

A Dispersionless Fourier Method for the MaxwellEquations Using Volume Penalization

We develop numerical Fourier methods for solving the timedependent boundary value problem for Maxwell’s equa-tions in the vicinity of perfect electric conductors. Thehigh order methods are obtained by analytically modifyingthe standard Maxwell equations with a volume penaliza-tion term. The absence of strong dispersive effects and theefficiency of the fast Fourier transform make this approachpotentially well suited for high frequency applications. Wedemonstrate the approach with several simulations of scat-tering and wave guide problems (with the inclusion of per-fectly matched layers where appropriate).

Ryan GalaguszMcGill UniversityDepartment of Electrical Engineeringryan.galagusz@mail.mcgill.ca

MS66

Fourier based PDE Solution on Complex Domains

Fourier continuation/extension (FC) methods allow forhighly-accurate Fourier representations of non-periodicfunctions. FFT speed algorithms, including the FC(Gram)algorithm, have been developed for these Fourier approx-imations and subsequently applied to the solution of par-tial differential equations. In particular, a new analysisapproach has been utilized to ensure unconditional stabil-ity for some FC alternating direction solvers. A uniquecharacter of solutions generated from the Fourier approx-imations is the lack pollution error for wave propagationproblems while avoiding many of the limitations of tradi-tional spectral methods. Various methods for the solutionof partial differential equations and other applications ofFC algorithms will be discussed.

Mark LyonUniversity of New Hampshiremark.lyon@unh.edu

MS66

New Active Penalty Methods with Applications toFluid Flow

In this talk I will present a new active penalty method.This method relies on a construction that systematicallyimproves the amplitude of the boundary layer that resultsfrom the penalty term. As a result, convergence rate isimproved. I will present a Fourier Spectral 4th order glob-ally convergent version of this approach for the heat equa-tion with internal non-mesh-conforming Dirichlet bound-ary conditions. I will then extend this to the solution ofincompressible Navier-Stokes equations in the presence ofsolid non-mesh-conforming boundaries. I will finish by dis-cussing convergence rate and stability of the method ingeneral.

Jean-Christophe NaveMcGill Universityjcnave@math.mcgill.ca

MS67

The Use of Residual-Based Compact Schemes for

68 CS15 Abstracts

Industrial Les

The use of suitable high accurate numerical techniques isof the utmost importance for the simulation of turbulentflows since they enable capturing flow structures from largeto small scales at an acceptable computational cost. Inthis sense, compact schemes appears to be particularly at-tractive because of their spectral-like accuracy. Moreover,for industrial aerodynamics computations, robustness andshock capturing capabilities are also crucial issues. In thiswork, we discuss the capabilities of a family of high orderresidual-based compact (RBC) schemes, characterized byodd orders of accuracy and a genuinely multidimensionalnumerical dissipation, for the implicit large eddy simula-tion (ILES) of compressible turbulent flows in complex con-figurations.

Paola CinnellaENSAM, ParisTechpaola.cinnella@ensam.eu

Cedric ContentLaboratoire DynFluidArts et Metiers ParisTechcedric.content@ensam.eu

Luca SciacovelliLaboratoire DynFluid, Arts et Metiers Paristechand Politecnico di Bariluca.sciacovelli@ensam.eu

MS67

The Application of High Order Dgm for Resolvedand Wall-Modeled Les of Full Scale Turbomachin-ery Passages

Large Eddy Simulations of turbulent flows require highlyaccurate discretisations in order to minimise the impactof discretisation errors for inevitably underresolved com-putations. Although extremely accurate methods are usedin academia, industry relies low order finite volume meth-ods, mainly due to their geometric flexibility. The dis-continuous Galerkin Method promises to be an enabler ofhigh-resolution LES in an industrial context, as it provideshigh-accuracy on unstructured meshes and therefore com-plex geometry, but also provides excellent parallel scaling.It furthermore offers the perspective of adaptive computa-tions. The current contribution describes the developmentof an industrial CFD code for LES, including validation,optimisation and extreme scalability, and concludes withpractical examples.

Koen HillewaertCenaeroCenaerokoen.hillewaert@cenaero.be

Corentin Carton de WiartCenaerocorentin.carton@cenaero.be

Guillaume VerheylewegenUniversite catholique de Louvainguillaume.verheylewegen@uclouvain.be

Ariane FrereCenaero

ariane.frere@cenaero.be

MS67

Validation of a High-Order Implicit Les Solverfor the Simulation of a Low-Reynolds-NumberVertical-Axis Wind Turbine

We use a high-order DG scheme for the ILES simulationof a straight-bladed Vertical Axis Wind Turbine (VAWT).We validate the solver by simulating the flow field abouta single static NACA0012 airfoil over a range of anglesof attack. Using an ALE-scheme in both 2D and 3D, wesimulate a real-world VAWT configuration at low chordReynolds number (about 50,000) for which experimentaldata is available, and determine the accuracy for variousflow conditions.

Samuel KannerUniversity of California, Berkeleykanners@berkeley.edu

Per-Olof PerssonUniversity of California BerkeleyDept. of Mathematicspersson@berkeley.edu

MS67

Applications of the Spectral/hp Element Methodto Complex Flow Geometries

As industrial requirements evolve to require both transientand scale-resolving capabilities, the use of under-resolvedDNS and implicit LES methods is needed to capture theessential flow features. In this talk, we give some examplesof industrially-relevant simulations, and highlight some ofthe challenges that arise when performing simulations incomplex three-dimensional geometries. Furthermore wedemonstrate how the spectral/hp element method com-bined with appropriate stabilisation and discretisations canresolve flow features in these complex domains.

David MoxeyImperial College Londond.moxey@imperial.ac.uk

Joaquim PeiroDept of AeronauticsImperial College London, UKj.peiro@imperial.ac.uk

Spencer SherwinImperial College Londons.sherwin@imperial.ac.uk

MS68

Unit and Conquer Algorithms for Large EigenvalueProblems

The emerging new multi-level and heterogeneous computerarchitectures, gearing up the road to exascale computing,are requiring numerical algorithmic revisions and their cor-responding implementations to achieve performance scala-bility. We present unite and conquer approach as a solutionto achieve this goal. That consists to accelerate the rateof convergence of a restarted method by coupling eithersynchronously or asynchronously, several restarted meth-ods called also co-methods. Some experiments validating

CS15 Abstracts 69

the approach will be presented.

Nahid EmadPRiSM laboratory and Maison de la Simulation,University ofNahid.Emad@prism.uvsq.fr

MS68

Performance of Algebraic Multigrid Precondition-ers for Large-Scale Finite Element Simulations

Finite element method (FEM) approaches are used forthe large-scale, high fidelity simulation of many impor-tant physical phenomena, e.g. fluid flow or magnetohy-drodynamics (MHD). Our solution approach for the re-sistive magnetohydrodynamics (MHD) equations employsan FEM discretization with an algebraic multigrid precon-ditioned Newton-Krylov method on unstructured meshes.We present scaling results for resistive MHD test cases, in-cluding results on 500,000 cores on an IBM Blue Gene/Qplatform.

Paul LinSandia National Laboratoriesptlin@sandia.gov

John ShadidSandia National LaboratoriesAlbuquerque, NMjnshadi@sandia.gov

MS68

Intelligent Iterative Methods : the Future of Par-allel and Distributed Runtime Tuned Linear Alge-bra?

We discuss some recent comparisons on clusters of accelera-tors between orthogonal, incompletely orthogonal and non-orthogonal Krylov Basis computing, focusing on communi-cations and orthogonality accuracy. Then, we discuss someresults for the ERAM method with respect to the restart-ing strategies. We survey some smart-tunning strategies weproposed and evaluated for some of the Krylov method pa-rameters. As a conclusion, we propose auto-tuning strate-gies for future hybrid methods on future exascale hyper-computers, on the road to intelligent linear algebra meth-ods mixing both distributed and parallel programmingmodels.

Serge G. PetitonUniversity Lille 1, Science and Technologies - CNRSserge.petiton@lifl.fr

MS68

Divide and Conquer Algorithms for Large Hermi-tian Eigenvalue Problems

A number of eigenvalue problems are considered from thepoint of view of highly parallel distributed environments.We first discuss a polynomial filtering technique for ex-tracting extreme or interior eigenvalues of large sparse ma-trices. This general approach can be effective in the situa-tion when a large number of eigenvalues is sought, as is thecase in electronic structure calculations for example. Themethod presented relies on a combination of the Lanczosalgorithm with partial reorthogonalization and polynomialfiltering based on least-squares polynomials. We also dis-cuss the problem of updating eigenvalues and eigenvectors

of large dense matrices when a small rank perturbation isapplied. Here several different practical scenarios are con-sidered: partial or full spectrum to be computed, interioror extreme eigenvalues, etc.

Yousef SaadDepartment of Computer ScienceUniversity of Minnesotasaad@cs.umn.edu

Vasilis KalantzisCEID, School of EngineeringUniversity of Patras, Greecekalantzis@ceid.upatras.gr

MS69

Augmenting the One-Shot Framework by Addi-tional Constraints

The multi-step Oneshot method for design optimizationproblems has been successfully implemented for various ap-plications. To this end, a slowly convergent primal fixedpoint iteration of the state equation is augmented by an ad-joint iteration and a corresponding preconditioned designupdate. Within this talk we present a modification of themethod that allows for additional equality constraints be-sides the usual state equation. A retardation analysis andthe local convergence of the method in terms of necessaryand sufficient conditions are given, which depend on keycharacteristics of the underlying problem and the qualityof the utilized preconditioners.

Torsten F. BosseHumboldt-Universitat zu Berlin,Institut fur Mathematikmail@torsten-bosse.de

Andreas GriewankHU Berlin, Germanygriewank@math.hu-berlin.de

MS69

Fixed-Point Iterations for Simultaneous One-ShotOptimization of Unsteady Flows

The One-shot method has proven to be very efficient inoptimization with steady PDEs which are solved by fixed-point iterations. We provide a framework that extendsthe method to unsteady problems that are solved by clas-sical time-marching schemes. The One-shot method isapplied to an optimal control problem with unsteady in-compressible Navier-Stokes equations. The unsteady fixed-point iteration is further improved applying adaptive timescales. Opportunities and first results on integrating One-shot optimization into parallel-in-time simulation will bepresented.

Stefanie Gunther, Nicolas R. GaugerRWTH Aachen Universitystefanie.guenther@scicomp.uni-kl.de,nicolas.gauger@rhrk.uni-kl.de

Qiqi WangMassachusetts Institute of Technologyqiqi@mit.edu

MS69

Towards Second Order One-Shot Methods in the

70 CS15 Abstracts

Context of Shape Calculus

One-shot methods aim at efficient implementation of gra-dient based optimization methods. Highest efficiency isreached, if second order methods can be employed. Thisposes a certain challenge for shape optimization methods,which employ shape calculus for efficiency reasons. Thechallenge lies in the fact that the space of shapes is nota linear space. This talk proposes the usage of Rieman-nian shape manifolds in order to carry over second orderproperties to shape optimization problems. Numerical re-sults for PDE constrained shape optimization problems areprovided.

Volker H. SchulzUniversity of TrierDepartment of MathematicsVolker.Schulz@uni-trier.de

MS69

On An Extension of the Augmented LagrangianApproach for One-Shot Optimization

One-shot approaches for design optimization augment thesolution of the state equation with an adjoint solver yield-ing approximate derivatives to change the design. The co-ordination of these iterative processes is well establishedwhen only the state equation serves as equality constraint.We propose a modified augmented Lagrangian function forthe handling of additional equality constraints. We showthat this augmented Lagrangian can be used in gradient-based optimization to solve the original design task.

Andrea WaltherUniversitat Paderbornandrea.walther@uni-paderborn.de

Nicolas R. GaugerRWTH Aachen Universitynicolas.gauger@rhrk.uni-kl.de

MS70

Energy-Conserving Schemes for Vlasov-Type Sys-tems

In this talk, we present the discontinuous Galerkin (DG)methods to solve the Vlasov-Maxwell system. The schemeemploys DG discretizations for both the Vlasov and theMaxwells equations, resulting in a consistent description ofthe probability density function and electromagnetic fields.We prove that using this description the total particle num-bers are conserved, and the total energy could be preservedupon a suitable choice of numerical flux for the Maxwellsequations and the underlying polynomial spaces on thesemi-discrete level, if boundary effects can be neglected.We further established error estimates based on several fluxchoices. We test the scheme on the Weibel instability andverify the order and conservation of the method.

Yingda ChengDepartment of MathematicsMichigan State Universityycheng@math.msu.edu

MS70

High Order Asymptotic Preserving Projective In-tegration Methods

In order to introduce new asymptotic preserving schemes

for kinetic equations in regimes leading to hyperbolic ordiffusive systems of conservation laws appearing e. g. insome models of radiative transfer or fluid-particle interac-tions, we apply the projective integration method devel-oped by Gear and Kevrekidis in the context of large mul-tiscale differential systems appearing in Chemistry. Thecrucial point of this work is our obtaining high order intime asymptotic preserving schemes.

Pauline LafitteProject team SIMPAF, INRIA Lillepauline.lafitte@ecp.fr

Annelies Lejon, Ward MelisKU Leuvenannelies.lejon@cs.kuleuven.be, ward.melis@cs.kuleuven.be

Giovanni SamaeyDepartment of Computer Science, K. U. Leuvengiovanni.samaey@cs.kuleuven.be

MS70

Effective High-Order Diffusive Moment Closureswith the StaRMAP Software

StaRMAP is a software to efficiently compute linear mo-ment models of radiative transfer (e.g., PN, SPN, FPN)using staggered grid finite difference approximations. Wepresent the extension of the method and software to diffu-sive closures that possess a “viscosity” in the highest re-solved moment. We show how the new term can be incor-porated into the numerical approach without incurring areduction in convergence order or a requirement for unde-sirably small time steps. Then, using the StaRMAP code,the benefits and drawbacks of various diffusive closures arediscussed. The StaRMAP code is available for download,and the results are easily reproducible.

Benjamin SeiboldTemple Universityseibold@temple.edu

Martin FrankRWTH Aachen UniversityCenter for Computational Engineering Sciencefrank@mathcces.rwth-aachen.de

MS70

An Asymptotic-preserving Scheme for Linear Ki-netic Equation with Fractional Diffusion Limit

We present an asymptotic-preserving scheme for the linearBoltzmann equation with fractional diffusion limit. Theequilibrium is a fat tail function, which disables any trun-cation in the velocity space numerically. The stiffnessadds more numerical difficulty. Our idea is based on amacro/micro/tail decomposition, where the macro/microcomponents support on a compact velocity space and de-compose the equation following a reshuffled Hilbert expan-sion. The tail that collects all the rest information solvesa limit equation.

Li WangUCLA Mathematicsliwang@math.ucla.edu

MS71

Multilevel Methods for Forward and Inverse Ice

CS15 Abstracts 71

Sheet Modeling

We present our work on recovering ice sheet modelingparameter fields (such as basal slipperiness) from obser-vations, using both deterministic and Bayesian inversion.The scalability of our adjoint- and Hessian-based meth-ods is determined by the scalability of two sub-problems:the solution of the state PDEs (Stokes equations of icesheet dynamics), and the approximation and precondition-ing of the parameter-to-observation Hessian. For the for-mer problem, we compare the effectiveness of geometricand algebraic multigrid within the solution of the statePDEs; for the latter, we discuss the use of multilevel ap-proximations to improve on Hessian approximation by low-rank updates. The scalability of our work is tested on full-scale models of the Antarctic ice sheet.

Toby IsaacICESThe University of Texas at Austintisaac@ices.utexas.edu

Georg StadlerCourant Institute for Mathematical SciencesNew York Universitystadler@cims.nyu.edu

Omar GhattasThe University of Texas at Austinomar@ices.utexas.edu

MS71

Assessment of Finite Element Schemes for Accu-rate Modeling of the Grounding Line

Modeling grounding line dynamics is critical in order to im-prove the projections of the contribution of the ice sheetsto sea level rise. The most advanced way of modeling thegrounding line consists of formulating a contact criterion,where the normal stress at the base of the ice is comparedto the ocean pressure in the vicinity of the grounding line.The grounding line is also the location of a sharp changein boundary condition, which generates a singularity in thepressure field. The contact condition is therefore applied ata location where the basal stress is most challenging to cap-ture accurately. Here, we present a new approach for thevalidation of Stokes Free-Surface flow with friction bound-ary conditions based on analytical-numerical solutions. Wethen compare the performance of several full-Stokes finiteelement solvers and show that the solvers currently used inthe glaciological community are not capable of capturingthe pressure field when there is a non-penetration condi-tion. These results show that the grounding line cannot beaccurately modeled with the current solvers. Finally, wepropose an algorithm that reaches a precision at the per-cent level in the pressure field for a typical ice flow regime.This work has vast implications for the modeling of ground-ing lines and the ice sheets in a warming climate.

Mathieu MorlighemUniversity of California - Irvinemathieu.morlighem@uci.edu

Jerome MonnierMathematics Institute of Toulousejerome.monnier@insa-toulouse.fr

Helene SeroussiJet Propulsion Laboratory

helene.seroussi@jpl.nasa.gov

Nathan MartinIMT CNRS/INSA/UPS, Toulouse, France.nathan.mar7in@gmail.com

MS71

Advances on Ice-Sheet Model Initialization usingthe First Order Model

Ice sheet initialization is critical for performing reliable for-ward simulations. We propose an adjoint-based optimiza-tion algorithm for the ice-sheet initialization, where we in-vert for basal topography and basal friction fields simul-taneously, minimizing the mismatch between: 1. observedand computed surface velocity data, and 2. surface massbalance forcing and modeled flux divergence. We showthe effectiveness of the initialization on the Greenland icesheet. We mention ongoing work on quantifying uncertain-ties in the optimized parameters.

Mauro PeregoCSRI Sandia National Laboratoriesmperego@fsu.edu

Stephen PriceLos Alamos National Laboratorysprice@lanl.gov

Georg StadlerCourant Institute for Mathematical SciencesNew York Universitystadler@cims.nyu.edu

Michael S. EldredSandia National LaboratoriesOptimization and Uncertainty Quantification Dept.mseldre@sandia.gov

Charles JacksonUTIGUniversity of Texas at Austincharles@ig.utexas.edu

John D. JakemanSandia National Labsjdjakem@sandia.gov

Irina K. TezaurSandia National Laboratoriesikalash@sandia.gov

Andrew SalingerCSRISandia National Labsagsalin@sandia.gov

MS71

Uncertainty Quantification for Large-ScaleBayesian Inverse Problems with Applicationto Ice Sheet Models

We consider the estimation of the uncertainty in the so-lution of large-scale ice sheet inverse problems within theframework of Bayesian inference. The ice flow is modeledas a three-dimensional, creeping, viscous, incompressible,non-Newtonian fluid via the nonlinear Stokes equations.

72 CS15 Abstracts

The observational data come from InSAR satellite mea-surements of surface ice flow velocity, and the uncertainparameter field to be inferred is the basal friction param-eter. We show that the work required for applying ourframework–measured in number of forward (and adjoint)ice sheet model solves–is independent of the state and pa-rameter dimensions.

Noemi PetraUniversity of California, Mercednpetra@ucmerced.edu

Toby IsaacICESThe University of Texas at Austintisaac@ices.utexas.edu

Georg StadlerCourant Institute for Mathematical SciencesNew York Universitystadler@cims.nyu.edu

Omar GhattasThe University of Texas at Austinomar@ices.utexas.edu

MS72

The most current list of partic-ipating companies is available atwww.siam.org/meetings/cse15/career.php.

For the most recent list of participating companies visithttp://www.siam.org/meetings/cse15/career.php

Bill KolataSIAMkolata@siam.org

MS73

Fast Direct Solver based on the Cyclic ReductionAlgorithm and Hierarchical Matrix Arithmetic forthe Solution of Variable-coefficient Elliptic PDEs

We present a fast direct solver for variable-coefficient el-liptic partial differential equations on a Cartesian productmesh. We combine the Cyclic Reduction algorithm withHierarchical Matrix arithmetic to reduce the fill-in blocks,resulting in an O(Nk2 log2N) flop quasi-linear complexitysolver. We compare against three techniques exploiting hi-erarchical low-rankness in the context of matrix bisection,nested dissection, and multifrontal ordering. Comparisonshighlight algorithmic differences and implementation de-tails with particular consideration to memory locality.

Gustavo ChavezKAUSTgustavo.chavezchavez@kaust.edu.sa

George M. TurkiyyahAmerican University of Beirutgt02@aub.edu.lb

Rio YokotaKing Abdullah University of Science and Technologyrio.yokota@kaust.edu.sa

David E. KeyesKAUST

david.keyes@kaust.edu.sa

MS73

A Polarized-Trace Preconditioner for 2DHelmholtz and Frequency Domain Full-WaveformInversion

Full-waveform inversion, a method for recovering Earth’sphysical parameters by matching seismic observations withsimulations, can be treated in the frequency domain. Ascalable solver for Helmholtz’s equation is necessary tomake feasible imaging in high resolution and in 3D; how-ever, this remains an open problem. We present recentdevelopments on a domain-decomposition solver for theacoustic Helmholtz equation, based on the notion of polar-ization, that demonstrates substantial scalability and per-formance improvements over the state-of-the-art.

Russell HewettTotalrussell.hewett@total.com

Leonardo Zepeda-NunezMITlzepeda@math.mit.edu

Laurent DemanetProfessor of Mathematics, MITlaurent@math.mit.edu

MS73

Fast Multipole Method as a Preconditioner forFinite Discretizations of Elliptic Boundary ValueProblems

We employ the Fast Multipole Method to preconditionsparse iterative solvers. FMM solves certain elliptic PDEswith O(N) complexity via kernels of high thread unifor-mity, high arithmetic intensity, and relaxed synchroniza-tion compared with factorization-based or multilevel ap-proaches. Combined, these features make FMM an in-teresting preconditioner on future architectures, even onproblems where FMM is not an ”exact” solver. We com-pare FMM-preconditioned Krylov solvers with multileveland sparse direct solvers on a variety of elliptic problems.

Huda Ibeid, Rio YokotaKing Abdullah University of Science and Technologyhuda.ibeid@kaust.edu.sa, rio.yokota@kaust.edu.sa

David E. KeyesKAUSTdavid.keyes@kaust.edu.sa

MS73

Generalized Plane Waves Adapted to Varying Co-efficients

This talk will focus on new shape functions adapted to thescalar wave equation with smooth coefficients. It followsthe idea of approximating the solution by basis functionsthat have the appropriate oscillatory behavior. The lo-cal design procedure of these generalized plane waves isdevelopped to fit the varying coefficients. High order ap-proximation is achieved, provided that a sufficient numberof basis functions is used. Both theoretical and numerical

CS15 Abstracts 73

aspects will be investigated.

Lise-Marie Imbert-GerardCourant Institute of Mathematical sciences, NYUimbertgerard@cims.nyu.edu

MS74

Accelerating MCMC with Parallel Local Approxi-mations

In many inference problems, the cost of MCMC analy-sis is dominated by repeated evaluations of expensive for-ward models. We have previously shown that when themodel is well behaved, locally-constructed surrogates cansignificantly reduce the number of evaluations required byMCMC while preserving the asymptotic exactness of theresulting inference. We extend those results with parallelcomputing resources and adjoint techniques, demonstrat-ing strong improvements in run-time on challenging exam-ple inference problems.

Patrick R. Conrad, Youssef M. MarzoukMassachusetts Institute of Technologyp.conrad@warwick.ac.uk, ymarz@mit.edu

Natesh PillaiStatisticsHarvardpillai@fas.harvard.edu

Aaron SmithUniversity of Ottawaasmith3@math.stanford.edu

MS74

Convex Relaxations of Polynomial Imaging Prob-lems

Recent work on phase retrieval suggests that quadratic op-timization problems can sometimes be solved by lifting intothe space of PSD matrices. This approach can be seen asa special case of sum-of-squares moment relaxation, whichis known in theory to convexify much more general poly-nomial optimization problems. We show that this set ofideas offers a fresh point of view toward resolving the hardnonlinearities of inverse wave scattering. Joint work withAugustin Cosse.

Laurent DemanetProfessor of Mathematics, MITlaurent@math.mit.edu

Augustin CosseMITacosse@math.mit.edu

MS74

Fast Algorithms for Linear Inverse Problems withGaussian Priors

A common theme in Gaussian process methods for inverseproblems is the need to work with dense covariance matri-ces. Standard approaches based on the Cholesky decom-position have cubic complexity. In this talk, we describea method to construct a generalized Cholesky decompo-sition of many commonly used covariance matrices (e.g.,squared exponential, Matern, rational quadratic) in lin-ear time. The algorithm is based on hierarchical matrix

approximation and borrows heavily from fast multipole-type ideas for compressing structured linear operators. Thefactorization allows us to efficiently apply the matrix andits inverse (inference), apply the matrix square root (sam-pling), and compute the log-determinant (likelihood calcu-lations), among other related capabilities. We anticipatethat such fast techniques will have a significant impact onlarge-scale inversion. This is joint work with Lexing Ying.

Kenneth L. HoDepartment of MathematicsStanford Universityklho@stanford.edu

Lexing YingStanfordlexing@math.stanford.edu

MS74

Stochastic inadequacy operators with applicationsto chemical kinetics

We investigate model form uncertainty for a reaction mech-anism model in hydrocarbon combustion. In a typi-cal reaction, the complete mechanism is either not well-understood, or too complex to effectively use as part of alarger combustion problem, necessitating a reduced model.To account for the discrepancy between the full model andits reduced version, we propose an additive, linear, prob-abilistic formulation. This representation is encoded in arandom matrix, whose entries are calibrated using a hier-archical Bayesian scheme. In particular, this formulationis designed to respect certain physical constraints, but alsobe flexible enough to apply to multiple reactions.

Rebecca MorrisonUT Austinrebeccam@ices.utexas.edu

Robert D. MoserUniversity of Texas at Austinrmoser@ices.utexas.edu

MS75

Multilevel Collocation with Radial Basis Functions

In this talk, we discuss multilevel radial basis functioncollocation methods for solving elliptic partial differentialequations on bounded domains. The approximate solutionis constructed in a multilevel fashion, each level using com-pactly supported radial basis functions with smaller sup-port radius on an increasingly fine mesh. A convergencetheory is given, which builds on recent theoretical advancesfor multilevel interpolation using compactly supported ra-dial basis functions. If time permits, we also discuss thecondition numbers of the arising systems as well as theeffect of a simple, diagonal preconditioner.

Patricio FarrellWeierstrass Institute for Applied Analysis and Stochasticsfarrell@maths.ox.ac.uk

MS75

A Reduced Radial Basis Function Method for Par-tial Differential Equations on Irregular Domains

We propose and test the first Reduced Radial Basis Func-tion Method (R2BFM) for solving parametric partial dif-

74 CS15 Abstracts

ferential equations on irregular domains. The two ma-jor ingredients are RBF-FD solver and a collocation-basedmodel reduction approach that systematically generates areduced-order approximation whose dimension is orders ofmagnitude smaller than the total number of RBF centers.The resulting algorithm is demonstrated through two- andthree-dimensional test problems.

Alfa HeryudonoUniversity of Massachusetts DartmouthDepartment of Mathematicsaheryudono@umassd.edu

Yanlai ChenDepartment of MathematicsUniversity of Massachusetts Dartmouthyanlai.chen@umassd.edu

Sigal GottliebDepartment of MathematicsUniversity of Massachusetts Dartmouthsgottlieb@umassd.edu

Akil NarayanUMass Dartmouthanarayan@umassd.edu

MS75

Kernel-based Image Reconstruction from Scat-tered Radon Data

A novel kernel-based algebraic reconstruction method forimage reconstruction from scattered Radon data is pro-posed. The reconstruction relies on generalized Hermite-Birkhoff interpolation by positive definite kernel functionsin combination with a well-adapted regularization of theRadon transform. This leads to a very flexible image re-construction method, which works for arbitrary distribu-tions of Radon lines, unlike in classical Fourier-based meth-ods relying on the filtered back projection formula. Thegood performance of the proposed kernel-based image re-construction method is supported by numerical examplesand comparisons.

Armin IskeUniversity of HamburgDepartment of Mathematicsarmin.iske@uni-hamburg.de

MS75

RBF-Based Partition of Unity Collocation Meth-ods for the Numerical Solution of PDEs

Numerical methods based on radial basis function (RBF)approximation are attractive because they can achievehigh-order accuracy and can handle non-trivial geometries.Global RBF methods can be computationally expensive.Therefore, we propose a localized approach where RBFs areused in a partition of unity framework. We have shown the-oretically that the resulting method converges spectrally inthe node distance and algebraically in the patch size. Wepresent numerical experiments for elliptic and parabolicPDEs.

Elisabeth LarssonUppsala University, SwedenDepartment of Information TechnologyElisabeth.Larsson@it.uu.se

Alfa HeryudonoUniversity of Massachusetts DartmouthDepartment of Mathematicsaheryudono@umassd.edu

MS76

Human Fetal Growth Model of Hypoplastic LeftHeart Syndrome

Abstract not available at time of publication.

Adarsh KrishnamurthyUC San Diegoadarsh@ucsd.edu

MS76

A Computational Model of Reverse CardiacGrowth in Response to Mechanical Stimulus

Abstract not available at time of publication.

Lik Chuan LeeCollege of EngineeringMichigan State Universitylclee@egr.msu.edu

MS76

Modeling Growth and Remodeling in Heart MuscleTissue

Abstract not available at time of publication.

Joakim SundnesSimula Research Laboratorysundnes@simula.no

MS76

Finite Element Models of Growth and Remodellingin the Infarct Injured Left Ventricle

Abstract not available at time of publication.

Samuel WallSimula Research LaboratoryCenter for Biomedical Computingsamwall@simula.no

MS77

Tribits: Tribal Build, Integrate, and Test System

The Tribal Build, Integrate, and Test System (TriBITS)is a framework built on top of the open-source CMaketools which is designed to handle large software develop-ment projects involving multiple independent developmentteams and multiple source repositories. TriBITS also de-fines a complete software development, testing, and deploy-ment system consistent with modern agile software devel-opment best practices. TriBITS is used by Trilinos, the Ad-vanced Simulation of Light Water Reactors (CASL) VERAcodes, and other projects.

Roscoe BartlettOak Ridge National Laboratory

CS15 Abstracts 75

bartlettra@ornl.gov

MS77

Computational Model Builder and ParaView Cat-alyst: Empowering HPC Workflows

A key metric for computational scientists is how quicklythey gain insight into their problem from simulations. Bar-riers include developing complex input models and analyz-ing results. We discuss how Computational Model Builder(CMB) can create simulation input models starting fromthe problem geometry. We show multiple CMB configura-tions targeting various simulators. Additionally, we discusshow to perform in situ analysis and visualization with Par-aView Catalyst to reduce the time spent post-processingsimulation results.

Andrew BauerKitware Inc.andy.bauer@kitware.com

Patrick O’LearyKitware, Inc., USApatrick.oleary@kitware.com

Robert O’Bara, Berk GeveciKitwarebob.obara@kitware.com, berk.geveci@kitware.com

MS77

Developing Hydra-TH: A Vertical, VERA-integrated Application based on the Hydra Toolkit

Hydra is an extensible C++ toolkit that provides a richsuite of software components for rapid scientific applica-tion development. Hydra supports multiple discretizationtechniques and many different physics. This talk describesthe development of Hydra-TH, a vertical application forthermal-hydraulics specifically targeted for direct integra-tion into VERA, the Virtual Environment for Reactor Ap-plications. Here, attention is given to the unique aspectsof Hydra that enable Hydra-TH (single/multiphase flowphysics) to be automatically integrated into VERA.

Mark ChristonLos Alamos National Laboratorieschriston@lanl.gov

Jozsef BakosiComputational Physics GroupLos Alamos National Laboratoryjbakosi@lanl.gov

Markus BerndtLos Alamos National Laboratoryberndt@lanl.gov

Andrew BauerKitware Inc.andy.bauer@kitware.com

Alan StaggOak Ridge National Laboratorystaggak@ornl.gov

Balasubramanya NadigaLos Alamosbalu@lanl.gov

Patrick O’LearyKitware, Inc., USApatrick.oleary@kitware.com

MS77

Software Quality with the Open Source ToolsCMake, CDash, CTest

CMake has been used on several large projects such asKDE, ITK, Hydra, VTK, ParaView, VXL, Trilinos andCMake itself. In addition to building software, CMakeprovides a testing client (CTest) that integrates with theweb-based CDash testing server. This talk will cover howthese tools can be leveraged in the context of an integrateddevelopment environment to properly manage the softwareprocess. This speeds up development while maintaining ahigh quality code-base.

Bill HoffmanKitwarebill.hoffman@kitware.com

MS78

Teaching Computing to Engineers

The term ”computational thinking” became quite popularsome years ago with a viewpoint piece at the CACM byWang (2006), but the term goes back to Papert 10 yearsbefore. Wang explained it as the ability to think algorith-mically and apply problem-solving computation in otherfields. We’ve been talking about teaching computationalthinking ever since. With an interest in reforming how weteach computing to engineering students, I stumbled ontoan extension of this idea that defines the pedagogical valueof computation. With modern tools for interactive com-puting (e.g. IPython Notebooks), it becomes possible tolearn by computing, to actually create knowledgesimilarto what we do in scientific computing to make discoveries,but in education. I will describe how this thinking has beeninspiring several educational initiatives aiming at makingcomputing a core pedagogical instrument.

Lorena A. BarbaDepartment of Mechanical and Aerospace EngineeringGeorge Washington Universitylabarba@gwu.edu

MS78

Teaching Data Science from a Computer SciencePerspective: Experience from a First Mooc

In Spring 2013 and Summer 2014, we ran a first massivelyopen online course in Data Science, attracting over 160,000students. In this talk, Ill describe our motivation for de-signing this course, some unique aspects of the curriculum,our results from the first two offerings, and finally some rec-ommendations around how training students to participatein data-intensive science has become essentialy to preparethem for both research and industry roles.

Bill HoweUniversity of Washingtonbillhowe@cs.washington.edu

MS78

Opportunities and Experiences with TeachingComputational Science from the Very Start of Uni-

76 CS15 Abstracts

versity Studies

Over the last 10 years, newcomers to science programs atthe Univ. of Oslo have been exposed to a tandem of an-alytical and numerical methods together with computerprogramming. The talk will provide examples on how suchan approach enhances the understanding of mathematicalconcepts and how it enables a new pedagogical approach,more relevant working styles, and a tighter coupling to re-search in traditional science subjects, with physics as pri-mary example.

Hans Petter LangtangenCenter for Biomedical ComputingSimula Research Laboratory and University of Oslohpl@simula.no

MS78

Teaching Statistical Computing to Undergraduates

We frame the minisymposium in the context of our experi-ence teaching computing with data to undergraduates. Wediscuss our recent efforts to automate grading student com-putational work in Python and R. Automating grading canimprove pedagogy by making it easier to assign studentsmore work, reducing latency in providing feedback, andenabling TAs to spend more time working directly withstudents by freeing them from the ”busy work” of grading.

Kenneth J. MillmanUniversity of California, Berkeleymillman@berkeley.edu

Philip B. StarkStatisticsUniversity of California, Berkeleystark@stat.berkeley.edu

MS79

Parallel Scalable FETI Methods for NonlinearProblems

The solution of nonlinear problems requires fast and highlyscalable parallel solvers. FETI-DP domain decomposition(DD) methods are parallel solution methods for implicitproblems. A common iterative DD approach for nonlin-ear problems is a Newton-Krylov-DD strategy where thenonlinear problem is linearized using a Newton method.Then, the linear system associated with the tangent stiff-ness matrix is solved with a preconditioned Krylov spacemethod. The preconditioner is an efficient and parallelscalable domain decomposition method where local sub-domain problems and a sufficiently small global problemhave to be solved. The local problems are inherently par-allel, the global problem is needed to obtain numerical andparallel scalability. FETI-DP domain decomposition meth-ods have been shown to be scalable for linearized elasticityproblems on up to 65 536 cores of a BlueGene/P super-computer (JUGENE, JSC, Germany) in 2009. Recently,nonlinear versions of the well-known FETI-DP methodsfor linear problems have been introduced. Here, the non-linear problem is decomposed directly before linearization.The new approaches have the potential to reduce commu-nication and to show a significantly improved performance,especially for problems with localized nonlinearities, com-pared to a standard Newton-Krylov-FETI-DP approach.Another new approach can be viewed as a strategy to fur-ther localize computational work and to extend the scala-bility of FETI-DP methods towards extreme-scale super-

computers. Here, a recent nonlinear FETI-DP method iscombined with an approach that allows an inexact solutionof the FETI-DP coarse problem. We combine the nonlinearFETI-DP domain decomposition method with an algebraicMultigrid method and obtain a hybrid nonlinear domaindecomposition/multigrid method. Parallel scalability re-sults for up to 262 144 cores on the MIRA BlueGene/Qsupercomputer (Argonne National Laboratory, USA) areshown for our new implementation.

Axel KlawonnUniversitat Duisburg-Essen, Germanyaxel.klawonn@uni-koeln.de

Martin LanserMathematical InstituteUniversitmlanser@math.uni-koeln.de

Oliver RheinbachTechnische Universitat Bergakademie Freibergoliver.rheinbach@math.tu-freiberg.de

MS79

Fluid-Structure-Interaction in ComputationalHemodynamcis using Nonlinear HyperelasticArterial Wall Models

We consider the fluid-structure-interaction problem in ablood vessel. We follow a monolithic coupling approach(P. Crosetto, S. Deparis, G. Fourestey, A. Quarteroni,Parallel algorithms for fluid structure-interaction prob-lems in haemodynamics. SISC, 33(4), 1598-1622, 2011),applying a Convective Explicit approach for the fluid.To obtain an accurate prediction of transmural stresseswe make use of sophisticated nonlinear material mod-els for the vessel wall. Fortunately, such models havebeen developed in the past and their parameters havebeen adapted to experimental data. Here, we use ananisotropic, polyconvex hyperelastic material model for thestructure (D. Balzani, P. Neff, J. Schroder, G.A. Holzapfel,A polyconvex framework for soft biological tissies. Ad-justment to experimental data. IJSS, 43(20), p. 6052–6070, 2006). The coupled simulations build on the LifeVsoftware library (LifeV Software Library, www.lifev.org)and FEAP (R.L. Taylor, Finite Element Analysis Pro-gram,http://www.ce.berkeley.edu/projects/feap/). Ab-sorbing boundary conditions on the outflow are imposedto reduce reflections.

Daniel BalzaniInstitute of MechanicsUniversitdaniel.balzani@uni-due.de

Simone DeparisEcole Politechnique Federale de Lausannesimone.deparis@epfl.ch

Simon FaustenInstitute of MechanicsUniversitsimon.fausten@uni-due.de

Davide FortiChair of Modeling and Scientific Computing,Ecole Politechnique Federale de Lausannedavide.forti@epfl.ch

CS15 Abstracts 77

Alexander HeinleinMathematical InstituteUniversitalexander.heinlein@uni-koeln.de

Axel KlawonnUniversitat Duisburg-Essen, Germanyaxel.klawonn@uni-koeln.de

Alfio QuarteroniEcole Pol. Fed. de LausanneAlfio.Quarteroni@epfl.ch

Oliver RheinbachTechnische Universitat Bergakademie Freibergoliver.rheinbach@math.tu-freiberg.de

Jorg SchroderInstitute of MechanicsUniversitj.schroeder@uni-due.de

MS79

A Scalable Monolithic Solver for the Coupling ofa Finite Element and a Finite Volume Method forFluid-Structure-Interaction

We use two different discretization methods for the fluidand the structure sub-problems in a monolithic approach,i.e both sub-problems as well as the coupling conditionsare assembled into one large algebraic system. Our solverbases on the application of Newtons method using iterativesolvers with different multi-level methods. In this talk wediscuss both, the coupling approach of the two differentdiscretizations as well as the efficient solution of the arisinglarge nonlinear system.

Johannes SteinerUniversity of Luganojohannes.steiner@usi.ch

Rolf KrauseInstitute of Computational ScienceUniversity of Luganorolf.krause@usi.ch

MS79

Adaptive Spectral Deferred Correction Methodsfor Cardiac Simulation

The electrical excitation of the heart as described by themonodomain equations exhibits a wide range of temporaland spatial scales. In this talk we will explore the possibili-ties of combining spectral deferred correction (SDC) meth-ods for time stepping with spatial and temporal adaptivity,in particular using optimized DIRK sweeps, interleavingmesh refinement with SDC iteration, inexact linear solves,and local time stepping. The efficiency of correspondingadaptive algorithms are illustrated at some numerical ex-amples.

Martin WeiserZuse Institute (ZIB)Berlin, Germany

weiser@zib.de

MS80

A High-order Finite Element Method for MovingBoundary Problems Using Universal Meshes

Abstract not available at time of publication.

Evan GawlikStanford Universitytba@siam.org

MS80

Towards a Hybrid Parallelization of Chebyshev Fil-tered Subspace Iteration

Abstract not available at time of publication.

Maria KranjcevicUniversity of Zagrebtba@siam.org

MS80

Computational Reduction Strategies for Bifurca-tion and Stability Problems

Abstract not available at time of publication.

Giuseppe PittonSISSA, Trieste, Italytba@siam.org

MS80

Nonlinear Frequency Response Analysis of Me-chanical Vibrations based on Isogeometric Dis-cretization and Model Order Reduction

Abstract not available at time of publication.

Oliver WeegerTU Kaiserslauterntba@siam.org

MS81

Low-Rank Adaptive Tensor Approximation

A strategy to mitigate the curse of dimensionality”, whichroughly means that the computational work, needed to ap-proximate a given function within a desired target accu-racy increases exponentially in the spatial dimension, is toseek problem dependent dictionaries with respect to whichthe function pos- sesses sparse approximations. In thistalk we highlight some recent developments centering onthe adaptive solution of high dimensional elliptic operatorequations in terms of linear combinations of particularlyadapted rank-one tensors. An adaptive iterative coarse-to-fine algorithm is presented that produces near-minimalrank approximation in stable hierarchical tensor formatswhere the adaptive identification of corresponding sub-spaces and sparse approximations of the low-dimensionaltensor factors are intertwined. We highlight the main con-ceptual ingredients as well as some essential obstructiondue to the fact that the underlying energy spaces are notendowed with cross norms. The theoretical results are il-lustrated by some numerical tests.

Wolfgang Dahmen

78 CS15 Abstracts

RWTH AachenIGPMdahmen@igpm.rwth-aachen.de

MS81

A Theory for Model Verification

Model verification tries to capture the solution u to a para-metric PDE when the parameters that determine u are notknown but other information about u is present. The formof this other information is typically (i) a posteriori mea-surements in the form of linear functionals applied to u and(ii) knowledge that u is well approximated by elements ofa known finite dimensional space V . We describe theoret-ically, the best we can approximate u from this knowledgeand then discuss numerical algorithms which perform nearthese best bounds.

Ronald DeVoreDepartment of MathematicsTexas A&M Universityrdevore@math.tamu.edu

MS81

High-Order Digital Nets for Parametric andStochastic Operator Equations

We present sparsity theory for direct and inverse problemsfor PDEs with infinite-dimensional uncertain input param-eters, stemming from parametrization of distributed uncer-tainty.It reduces the direct and inverse problem to integra-tion problem over infinite-dimensional parameter spaces.Based on a holomorphy condition on the parameteric de-pendence in [1], we present regularity estimates for theparametric integrand functions and for uniform prior mea-sure on the parameter uncertainty in classes of weightedRKHS introduced in [2]. Related recent results (joint withJ. Dick, F. Kuo, T. LeGhia and D. Nuyens) [3] on dimen-sion independent convergence rates of the deterministic,higher order QMC quadrature for integrand functions inweighted function spaces will be presented. The densityof the posterior measure in Bayesian inverse problems asconsidered in [5, 4] is shown to belong to the class of ad-missible integrand functions with a hybrid of product andsPOD weights. Research supported in part under ERCAdG 247277.

Christoph SchwabETH ZuerichSAMchristoph.schwab@sam.math.ethz.ch

MS81

Multivariate Decomposition Methods ∞-VariateProblems

We present the Multivariate Decomposition Method for ap-proximation of functions of infinitely many variables Itworks for functions that admit a decomposition f =

∑u fu,

where the sum is with respect to finite subsets u of posi-tive integers, and for each u = (i1, . . . , ik) the function fudepends only on xi1 , . . . , xik . For a number of weightedspaces of such functions, the complexity of the correspond-ing problem is small.

Grzegorz W. WasilkowskiUniversity of KentuckyDepartment of Computer Science

greg@cs.uky.edu

MS82

Title Not Available at Time of Publication

Abstract not available at time of publication.

George BosilcaUniversity of Tennessee - Knoxvillebosilca@icl.utk.edu

MS82

Portable Programming and Runtime Support forApplication-Controlled Resilience in Large-ScaleScientific Applications

The Global View Resilience (GVR) system supportsflexible, scalable, application-controlled resilience with aportable abstraction versioned, distributed arrays. Wehave evaluated GVRs utility on both a number of mini-apps (miniMD, miniFE), and larger applications (a PCGsolver, OpenMC, ddcMD, and Chombo). Our results showprogramming effort (code change) is small (< 1% code)and localized. Studying the same applications, we findthat GVR version-based resilience can be achieved withlow overhead for all of them.

Andrew A. ChienThe University of ChicagoArgonne National Laboratorachien@cs.uchicago.edu

Hajime FujitaDepartment of Computer ScienceUniversity of Chicagohfujita@cs.uchicago.edu

Zachary RubensteinDepartment of Computer Science, The University ofChicagozar1@uchicago.edu

Nan Dun, Aiman FangDepartment of Computer ScienceUniversity of Chicagodun@cs.uchicago.edu, aimanf@cs.uchicago.edu

Ziming ZhengDepartment of Computer Science, The University ofChicagozimingzheng@uchicago.edu

MS82

Resilient Programming Models

Today’s leadership computing systems and scalable clus-ters already exhibit significant failure rates that impactoverall results rates and scientific productivity. Current is-sues are expected to persist, and new issues to emerge. Inthis presentation we discuss several abstract programmingmodels that permit application and algorithm developersto reason about and develop resilience capabilities. Wepresent the basic models and then discuss specific strate-gies for how to design and implement applications to beresilient to system failures such as local process loss, silentdata corruption, and the performance variability that is

CS15 Abstracts 79

inherent in aggressive failure detection and correction.

Michael HerouxSandia National Laboratoriesmaherou@sandia.gov

MS82

MPI Fault Tolerance: The Good, The Bad, TheUgly

The MPI forum is currently investigating the inclusion offault tolerance as a feature in the MPI specification. Thisissue has raised and continuous to raise some controversyabout what MPI implementations can reasonably be ex-pected to provide and what is useful for application devel-opers. In this talk I will present the main proposals thatare currently on the table, their advantages and the mainconcerns against them. The goal of this talk is to expandthe discussion and to gather feedback that will help theMPI forum to come to a solution that is helpful for thelarger HPC community.

Martin SchulzLawrence Livermore National Laboratoryschulzm@llnl.gov

MS83

Preconditioning for Various Cahn-Hilliard Systems

The Cahn-Hilliard equation models the motion of inter-faces between several phases and has many applicationsincluding materials science and image inpainting. Besidestheir smooth formulations we study the nonsmooth oneswhich result in variational inequalities. The focus is onthe efficient solution of the arising large and sparse linearsystems. Further, we study fractional-in-space versions ofCahn-Hilliard systems. Numerical results illustrate the ef-ficiency of the approaches.

Jessica BoschMPI Magdeburgbosch@mpi-magdeburg.mpg.de

Martin StollMax Planck Institute, Magdeburgstollm@mpi-magdeburg.mpg.de

MS83

Null-Space Based Preconditioners for Saddle-PointSystems

We derive a formula for the inverse of a nonsingularsaddle-point matrix whose leading block is maximally rank-deficient, which is based on the null-space of that block. Wethen use the formula to develop a class of indefinite blockpreconditioners. When a sparse form of the null space isapproximately available, a preconditioned Krylov iterativesolver converges rapidly. We give a couple of examples,discuss spectral properties, and present some numerical re-sults that validate the analysis.

Ron EstrinThe University of British Columbiaronestrin756@gmail.com

Chen GreifDepartment of Computer ScienceThe University of British Columbia

greif@cs.ubc.ca

MS83

Unreduced Symmetric KKT Systems Arising fromInterior Point Methods

We consider symmetrized KKT systems arising in the solu-tion of quadratic programming problems by Interior Pointmethods. Two strictly related and well established formu-lations for such systems are studied, with particular em-phasis on their spectral properties and how these are af-fected by preconditioning. Constraint and augmented pre-conditioners are considered here. Both a theoretical andexperimental analysis is conducted in order to assess whichof the two formulations should be preferred when solvinglarge scale problems.

Mattia Tani, Valeria SimonciniUniversita’ di Bolognamattia.tani2@unibo.it, valeria.simoncini@unibo.it

Benedetta MoriniDipartimento di Ingegneria IndustrialeUniversita’ di Firenzebenedetta.morini@unifi.it

MS83

Convergence of Stationary Iteration with IndefinitePreconditioner

The relationship of diagonal dominance ideas to the con-vergence of stationary iterations is well known. There are amultitude of situations where such considerations are usedto guarantee convergence when the splitting matrix (thepreconditioner) is positive definite. In this talk we will de-scribe and prove sufficient conditions for convergence of astationary iteration based on a splitting with an indefinitepreconditioner. Simple examples covered by this theoryfrom Optimization and Economics will be described.

Andy WathenOxford University, UKwathen@maths.ox.ac.uk

MS84

Quantifying Errors in a Probabilistic Solutionto Stochastic Inverse Problems for Physics-BasedModels

We define a measure-theoretic framework to formulate andsolve a stochastic inverse problem for deterministic physics-based models. Computational algorithms are presentedand analyzed to solve problems within this framework in-volving high dimensional input parameter and output dataspaces. Sources of statistical and deterministic errors areidentified and full a priori and a posteriori error analyseson computed probabilities of events are presented includingnumerical examples.

Troy ButlerUniversity of Colorado Denvertroy.butler@ucdenver.edu

MS84

Region of Influence Sensitivty Analysis for TimeDependant Problems

We review existing strategies for implementing adjoint-

80 CS15 Abstracts

based sensitivity analysis on HPC architectures. We focuson strategies based on space-time local adjoint problems,posed in the ”Region of Influence”(RoI), motivated by theapplication to uncertainty quantification of DNS-scale tur-bulent combustion. In addition, we discuss ramificationsand potential benefits from implementing this approach onpotential exascale systems.

Varis Carey, Robert D. MoserUniversity of Texas at Austinvariscarry@googlemail.com, rmoser@ices.utexas.edu

MS84

Adaptive Measure-Theoretic Inverse Techniquesfor High Dimensional Parameter Domains andComplex Multi-Scale Models

The application of uncertainty quantification methodolo-gies to computationally complex models often involves theexploration of a high-dimensional parameter space. It iswell known that this endeavor is plagued by the “curse ofdimensionality.” We explore the scalability of adaptive al-gorithms for solving the stochastic inverse problem withinthe context of a measure-theoretic solution framework towith the goal of reducing error in approximating the prob-ability of implicitly defined “rare” events.

Lindley C. GrahamUniversity of Austin at TexasInstitute for Computational Engineering and Sciences(ICES)lgraham@ices.utexas.edu

Troy ButlerUniversity of Colorado Denvertroy.butler@ucdenver.edu

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu

MS84

Optimizing Quantities of Interest in High Dimen-sions to Improve Solutions to Inverse Problems

The predictive capabilities of physics-based models are im-proved by reliably decreasing the size of the sets defin-ing the uncertain input parameters. These sets are ofteninferred by solution to an inverse problem. We exploretechniques for identifying the optimal quantities of inter-est within a high dimensional output data set for use in theinverse problem to improve the predictive capabilities of amodel. Numerical results on physically relevant models areprovided.

Scott WalshUniversity of Colorado Denverscott.walsh@ucdenver.edu

MS85

Modeling Magneto-Mechanical Interactions in De-formable Solids

A new class of ”smart” materials, magneto-sensitive ma-terials (MSMs), is at the frontier of research in mate-rial design. The mechanical properties of these materialschange dramatically in the presence of an applied mag-

netic field. Such materials undergo finite deformations andthe magneto-mechanical coupling requires nonlinear mod-els. Incompressible MSMs are then modeled by heuristicequations that minimize the elastic and electromagnetic en-ergy in the form of a coupled free energy. In this talk, wefocus on modeling and developing finite-element methodsfor incompressible magneto-elasticity, and we present the-oretical results and numerical experiments for such prob-lems. The exterior of the material body is also taken intoconsideration due to the magnetic field, resulting in a muchbigger discrete system. Even within uncoupled incompress-ible elasticity, many open questions remain about optimalfinite-element approximation and these, of course, impactour choices for the more complicated coupled problems con-sidered here.

James H. Adler, Luis DorfmannTufts Universityjames.adler@tufts.edu, luis.dorfmann@tufts.edu

Dong HanTufts UniversityDepartment of Mathematicsdong.han@tufts.edu

Scott MaclachlanDepartment of MathematicsTufts Universityscott.maclachlan@tufts.edu

Chris PaetschTufts Universitychris.paetsch@tufts.edu

MS85

First-Order System Least Squares for Isotropic andAnisotropic Materials in Hyperelasticity

We present least squares finite element methods based onthe conservation of linear momentum and nonlinear consti-tutive equations for hyperelastic materials. Our approachis motivated by a well-studied least squares formulationfor linear elasticity. This idea was already generalized tononlinear elasticity using a special Neo-Hooke model. Werecall essential theorems and illustrate the performance us-ing adaptive refinement strategies. Additionally we extendthis approach to transversely isotropic materials adaptingthe isotropic model and give examples.

Benjamin MullerUniversity of Duisburg-Essenbenjamin.mueller@uni-due.de

Gerhard StarkeUniversity of Duisburg-EssenFakultat fur Mathematikgerhard.starke@uni-due.de

Jorg SchroderUniversitat Duisburg-EssenInstitut fur Mechanik, Abteilung Bauwissenschaftenj.schroeder@uni-due.de

MS85

Advanced Finite Element Methods for Chemo-Electromechanical Skeletal Muscle Mechanics

Simulating the mechanical behavior of (soft) biological ma-

CS15 Abstracts 81

terials is challenging as one does not only need to considera highly nonlinear material behavior within a complex do-main, but also often needs to consider different scales, e.g.the cellular scales, to accurately model functional aspects,e.g. for simulating the chemo-electromechanical behaviorof skeletal muscles. Furthermore, due to high uncertaintieswithin material parameters, one needs fast, efficient, andaccurate solution strategies.

Oliver Rohrle, Thomas Heidlauf, Mylena Mordhorst,Daniel WirtzInstitute of Applied MechanicsUniversity of Stuttgart, Germanyroehrle@simtech.uni-stuttgart.de, heidlauf@mechbau.uni-stuttgart-de, mylena.mordhorst@mechbau.uni-stuttgart.de, daniel.wirtz@simtech.uni-stuttgart.de

MS85

Momentum Balance Accuracy in Finite ElementMethods for Elastoplasticity

First-order system least squares formulations involvingstresses and displacement as process variables are inves-tigated for elastoplasticity models. Optimal order conver-gence is shown for the stress approximation with respectto the H(div) norm using Raviart-Thomas finite elementsin the context of von Mises flow with isotropic hardening.In particular, the implications on the accuracy of momen-tum balance and surface forces is studied. Computationalresults for a realistic benchmark problem illustrate the ef-fectiveness of this approach.

Gerhard StarkeUniversity of Duisburg-EssenFakultat fur Mathematikgerhard.starke@uni-due.de

MS86

A Coupled CFD CAA Adjoint Method for Aeroa-coustic Optimization and Error Estimation

Adjoint techniques have played a major role in gradientbased steady state aerodynamic optimization, especially in3D, since the full sensitivity vector of a single objectivefunction with respect to any number of design variablescan be computed with a single adjoint solution, at a costroughly equivalent to a single flow solution. On the con-trary adjoint methods for unsteady problems have receivedless attention, their development having been hindered bythe inherent computational cost and the complexity of theassociated flow physics. Recently unsteady adjoint tech-niques have been proposed for both two-dimensional andthree-dimensional problems. In this work we apply the un-steady adjoint method to a two dimensional blade vortexinteraction noise problem. An Euler near field flow solveris coupled to an FW-H aeroacoustic code to propagate thenoise to a far field observer. The discrete adjoint solversfor both the flow and the acoustic codes are derived byexact linearization and transposition of each subroutine inthe analysis code and finally coupled together. We applythe newly developed adjoint solver to blade vortex interac-tion noise in the context of gradient based optimization, toinvestigate optimal passive noise minimization technique,and a posteriori error estimation to improve the accuracyof the coupled aeroacoustic analysis.

Enrico FabianoUniversity of Wyomingefabiano@uwyo.edu

Dimitri MavriplisDepartment of Mechanical EngineeringUniversity of Wyomingmavripl@uwyo.edu

Jay SitaramanUniversity of Wyomingjsitaraman@uwyo.edu

MS86

Efficient Approaches for Optimal Active Flow Con-trol

For efficient optimal active control of unsteady flows, theuse of consistent and robust adjoint approaches is a firstessential ingredient. For the generation of discrete adjointsolvers, we discuss the use of Automatic Differentiation(AD) and its combination with checkpointing techniques.Furthermore, we discuss so-called one-shot methods. Here,one achieves simultaneously convergence of the primal stateequation, the adjoint state equation as well as the designequation.

Nicolas R. GaugerRWTH Aachen Universitynicolas.gauger@rhrk.uni-kl.de

Anil Nemili, Emre zkayaTU Kaiserslauternanil.nemili@rhrk.uni-kl.de, emre.oezkaya@rhrk.uni-kl.de

Stefanie GuntherRWTH Aachen Universitystefanie.guenther@scicomp.uni-kl.de

MS86

Aerodynamic Design for Unsteady Flows Using AnAdjoint Approach

A discrete adjoint-based design methodology for unsteadyturbulent flows on three-dimensional dynamic overset un-structured grids is described. The methodology sup-ports both compressible and incompressible flows and isamenable to massively parallel computing environments.The approach provides a general framework for performinghighly efficient and discretely consistent sensitivity anal-ysis. Meshes consisting of mixed-element topologies andoverset component grids are supported, where grids may bestatic, dynamic, or deforming, including any combinationthereof. An overview of a broad range of aerospace applica-tions for which the implementation has been demonstratedwill be shown.

Eric NielsenNASA Langleyeric.j.nielsen@nasa.gov

Boris DiskinNational Institute of Aerospace, Hampton, VAbdiskin@nianet.org

MS86

Optimal Wall-Forcing for Compressible Wall-Bounded Flows Using Adjoint Techniques

Adjoint operators are vastly used in many applications,ranging from linear stability analysis and optimization toflow control. Although highly valuable, the derivation of

82 CS15 Abstracts

these operators in the case of compressible and higher-ordersolvers is often a tedious task. This is particularly dueto the complexity of the governing equations and of thehigher-order numerical schemes. In this study, we haveadopted a novel technique for the evaluation of the directand adjoint operators directly from the flow solvers (Fosaset al., 2012) which requires minimal additional program-ming efforts, and automatically takes into account subse-quent modifications in the governing equations and bound-ary conditions. This approach is applied to a compressible,staggered and curvilinear framework, allowing higher-orderinterpolation and derivation schemes. The original nonlin-ear solver has been used to perform large-scale turbulentflow simulations, and shown to scale well on up to 62K pro-cessors. The adjoint solver features similar performances.The developed methodology is first validated in the con-text of a three-dimensional compressible boundary layer,by extracting the optimal initial condition, and comparingthe results to that of the linear stability analysis. Finally,this method is used to extract the optimal wall-forcing ina compressible wall-bounded flow.

Taraneh Sayadi, Peter SchmidImperial College Londonsayadi@illinois.edu, peter.schmid@imperial.ac.uk

MS87

Stable and Robust Hybridized DiscontinuousGalerkin Methods for High Reynolds Number FlowProblems

We present an output-based anisotropic hp-adaptivemethod for high-order hybrid discontinuous Galerkin(HDG) discretizations of the Navier-Stokes equations. Theadaptive framework uses a discrete adjoint on refinedspaces to compute error estimates. The effectiveness ofrefinement options is determined by solving local adjointproblems. We discuss the effects of different stabilizationmethods on solver robustness and compare the effective-ness of HDG and traditional discontinuous Galerkin (DG)methods.

Krzysztof Fidkowski, Johann DahmUniversity of Michigankfid@umich.edu, jdahm@umich.edu

MS87

Multiscale Hybridizable Discontinuous GalerkinMethods

We present the recent development of multiscale hybridiz-able discontinuous Galerkin (MHDG) methods for com-putational electromagnetics and fluid dynamics. The es-sential ingredients are (i) a HDG discretization of the un-derlying PDEs at the subdomain level to parametrize thenumerical solution in terms of a Lagrange multiplier; (ii)a judicious choice of the numerical flux to provide stabil-ity and consistency; and (iii) a global jump condition thatenforces the continuity of the numerical flux across sub-domain boundaries to arrive at a global weak formulationin terms of the Lagrange multiplier. The MHDG methodsinherit all the properties of the HDG method and possessadditional advantages. First, they reduce the globally cou-pled unknowns to the approximate trace of the solution onsubdomain boundaries, thereby leading to a significant re-duction in the degrees of freedom. Second, they make useof the similarity of the subdomain structures to efficientlyaccommodate very large-scale simulations. And third, theMHDG methods lend themselves efficient for paralleliza-

tion. We will present several examples in nanophotonicsand turbomachinery to demonstrate the performance ofthe MHDG method.

Cuong NguyenMassachusetts Institute of Technologycuongng@mit.edu

Joel Saa-SeoaneM.I.T.jsaa@mit.edu

David Moro, Francisco J. Roca, Jaime PeraireMassachusetts Institute of Technologydmoro@mit.edu, xeviroca@mit.edu, peraire@MIT.EDU

MS87

A Computational Framework for Target-BasedHP-Adaptation in Compressible Flow SimulationUsing HDG Methods

We present a conceptual overview of our computationalframework which includes both standard and hybridizedDG methods and offers both isotropic and anisotropic hp-adaptation based on adjoints. The framework is designedin such a way that both discretizations and physical modelscan be exchanged rapidly by making heavy use of object-orientation and C++ templates. We will show examplesin a variety of flow regimes.

Georg May, Michael WoopenAICESRWTH Aachenmay@aices.rwth-aachen.de, woopen@aices.rwth-aachen.de

MS87

To CG or HDG: Updates on Our ComparativeStudy

Since the inception of discontinuous Galerkin (DG) meth-ods for elliptic problems, there has existed a question ofwhether DG methods can be made more computationallyefficient than continuous Galerkin (CG) methods. Fewerdegrees of freedom, approximation properties for ellipticproblems together with the number of optimization tech-niques, such as static condensation, available within theCG framework made it challenging for DG methods to becompetitive until recently. However, with the introduc-tion of a static-condensation-amenable DG method, thehybridizable discontinuous Galerkin (HDG) method, it hasbecome possible to perform a realistic comparison of CGand HDG methods when applied to elliptic problems. Inthis talk, we extend upon an earlier 2D comparative study,providing numerical results and discussion of the CG andHDG method performance in three dimensions. The com-parison categories covered include steady-state elliptic andtime-dependent parabolic problems, various element typesand serial and parallel performance.

Mike Kirby, Sergey B. YakovlevUniversity of UtahSchool of Computingkirby@cs.utah.edu, yakovs@sci.utah.edu

MS88

Partitioned Low Rank fast and Efficient Compres-sion of Absorbing Boundary Conditions for the

CS15 Abstracts 83

Helmholtz Equation

Absorbing layers are sometimes required to be impracti-cally thick to offer an accurate Absorbing Boundary Con-dition (ABC) for the Helmholtz equation in heterogeneousmedia. In previous work [BR and Demanet, submitted,2014], we used matrix probing to compress an ABC from afew exterior Helmholtz solves with random Dirichlet data.We now present an algorithm (nearly linear in the dimen-sion of the matrix) for applying this compressed ABC usingPartitioned Low Rank matrices.

Rosalie Belanger-RiouxMassachusetts Institute of TechnologyDepartment of Mathematicsrobr@math.mit.edu

Laurent DemanetProfessor of Mathematics, MITlaurent@math.mit.edu

MS88

Comparison Between DG and Finite DifferenceMethods for Acoustics with Smooth Coefficients

This work analyzes the computational efficiency of twotypes of numerical methods, finite difference (FD) and dis-continuous Galerkin (DG) methods, in the context of 2Dacoustic equations in pressure-velocity form with smoothcoefficients. The acoustic equations, which model propa-gation of sound waves in elastic fluids, are used throughoutseismic imaging with applications in oil prospecting. Theubiquity of smooth trends in real data, and thus in theacoustic coefficients, validates the importance of this novelstudy. Previous work, from the discontinuous coefficientcase of a two-layered media, demonstrates the efficiency ofDG over FD methods but does not provide insight for thesmooth coefficient case. Running-times and floating pointoperations are compared, relative to a prescribed accuracy,for standard 2-2 and 2-4 staggered grid FD methods, anda standard DG methods

Mario BencomoDepartment of Computational and Applied MathRice Universitymario.j.bencomo@rice.edu

MS88

Analysis and Numerical Approximation for Ad-sorption Models

We focus on the structure of an adsorption model as sys-tems of conservation laws (multicomponent case for ad-sorption), with equilibrium and non-equilibrium type non-linearities, where the latter are associated with microscalediffusion. We also work with an unusual type isothermcalled Ideal Adsorbate Solution, which is defined implicitly.For the IAS adsorption system, we show sufficient condi-tions that render the system hyperbolic. We also constructnumerical approximations for equilibrium and nonequilib-rium models.

Francis P. MedinaOregon State Universitymedinaf@math.oregonstate.edu

Malgorzata PeszynskaDepartment of MathematicsOregon State University

mpesz@math.oregonstate.edu

MS88

Microseismic Event Location Via Full WaveformInversion

The process of hydraulic fracturing involves injecting largevolumes of water into impermeable rocks such as shale inan effort to create flow paths for fluids such as oil andgas. This process often generates tiny earthquakes (or mi-croseismic events) which in turn can be used as passiveseismic sources for imaging the subsurface. In this workwe describe estimating the location of these microseismicevents and the uncertainty inherent in this process.

Susan E. MinkoffUniversity of Texas at DallasDept of Mathematical Sciencessminkoff@utdallas.edu

MS89

Recovering Exponential Accuracy in SpectralMethods Involving Piecewise Smooth Functionswith Unbounded Derivative Singularities

Techniques will be presented to overcome the Gibbs phe-nomenon for functions with unbounded derivative singu-larities, resulting in recovering exponential accuracy in themaximum norm from the knowledge of the first N Fouriercoefficients or standard collocation point values of suchfunctions. With these post-processing methods, we areable to obtain exponential accuracy of spectral methodsapplied to linear transport equations involving such func-tion.

Zheng ChenIowa State Universityzchen@iastate.edu

MS89

Efficient High-Order Algorithms for Solving Drift-Diffusion Systems

I will discuss about recent developments of spectral ele-ment method (SEM) for solving drift-diffusion equations,with applications in semi- conductor device simulation, bi-ological ion channels problems, etc. The drift-diffusion sys-tem is a non-linear system, involving the coupling of twotransport equations for the carrier concentrations with thePoisson equa- tion for the electric potential. I will presentour SEM algorithms, focusing on stable, efficient, and ac-curate time-splitting schemes, properly designed for thehigh-order spectral element discretizations. I will demon-strate the computational results for the study of potassiumchannel in a biological membrane, provided with the vali-dation.

Ying HeUC Davisyinghe@math.ucdavis.edu

MS89

Estimating Residual Stresses in Arteries by an In-verse Spectral Technique

A mathematical model is studied to estimate residualstresses in the arterial wall using intravascular ultrasound(IVUS) techniques. A BVP is formulated for the nonlinear,

84 CS15 Abstracts

slightly compressible elastic wall, the boundary of which issubjected to a quasi-static blood pressure, and then anidealized model for IVUS is constructed by superimpos-ing small amplitude time harmonic vibrations on large de-formations. Using the classical theory of inverse Sturm-Liouville problems and op- timization techniques, an in-verse spectral algorithm is developed to approximate theresidual stresses, given the first few eigenfrequencies of sev-eral induced pressures.

Sunnie JoshiTemple Universitysjoshi@temple.edu

MS89

Force-based Blended Atomistic-to-continuum Cou-pling Method for Crystals: Theory and Computa-tions

We formulate a multiscale method based on blending atom-istic and continuum forces. We present a comprehensiveerror analysis whichis valid in two and three dimensions,for finite many-body interactions, and in the presence ofdefects. Based on a precise choice of blending mechanism,the error estimates are considered in terms of degrees offreedom. The numerical experiments confirm and extendthe theoretical predictions, and demonstrate a superior ac-curacy of our method over other schemes.

Xingjie LiBrown Universityxingjie li@brown.edu

MS90

On-Lattice and off-Lattice Hybrid Simulation Us-ing the Smoldyn Software

The Smoldyn simulator is a tool for modeling biochemicalspatial organization on nanometer to micron size scales.It represents proteins and other molecules of interest asindividual point-like particles that diffuse, react, and in-teract with membranes, all in continuous space. Althougheffective, this is computationally expensive, so colleaguesand I recently added on-lattice capabilities to Smoldyn aswell. Simulated molecules are able to freely diffuse backand forth between the two regions of space.

Steven AndrewsFred Hutchinson Cancer Research Centersteven.s.andrews@gmail.com

MS90

MCell/CellBlender: An Environment for SpatiallyRealistic Simulation of Cellular Microphysiology

MCell is a simulation kernel for biophysically realistic3D simulations of reaction-diffusion processes occurring incells. A major stumbling block for new and experiencedusers of MCell is the effort required to create 3D mod-els. To remedy this situation we have created CellBlender,a complete integrated development environment for creat-ing and visualizing MCell and SBML/Spatial models. Anoverview of the design of CellBlender will be presented, in-cluding the model creation/simulation/visualization pipe-line.

Thomas M. BartolThe Salk Institute

bartol@salk.edu

MS90

From Macroscopic to Microscopic Simulations Us-ing Mesord

MesoRD simulates both the spatial and stochastic aspectsof intracellular chemical reactions using a spatially dis-crete and temporally continuous framework. Spatially dis-crete stochastic simulators may give incorrect results forbi-molecular reactions. We have incorporated a solutionto this problem into MesoRD. Using these new features ofMesoRD we could simulate a number of simple exampleswhere it is shown how strikingly important it is to choosea correct modelling-framework for the problem at hand.

David FangeUppsala UniversityDepartment of Molecular Biologydavid.fange@icm.uu.se

MS90

E-Cell System Version 4.0: an Integrated Platformfor Single-particle-level Simulations

Here, we present a novel software for cellular simulations,E-Cell System version 4, which provides an integrated plat-form with a rule-based modeling environment, bioimagingvisualizations and a variety of single-particle level simula-tion algorithms including an exact event-driven particle al-gorithm, the enhanced Greens Function Reaction Dynam-ics method, and a microscopic lattice-based method, Spa-tiocyte. Moreover, we also introduce the parallelizationtechniques for these particle methods toward the whole-cell-scale simulation on high-performance computers.

Kazunari Kaizu, Kozo Nishida, Masaki Watabe, ArjunanSatya, Kazunari Iwamoto, Koichi TakahashiRIKEN Quantitative Biology Center, Osakakaizu@riken.jp, knishida@riken.jp, masaki@riken.jp,satya@riken.jp, kiwamoto@riken.jp, ktakahashi@riken.jp

MS91

Multiscale Model Reduction for PDE-ConstrainedOptimization

In parameter estimation and data fitting problems, reducedorder models are usually built from the forward map thatdepends on the unknown parameters. This implies thatthe reduced model is parameter dependent. Typically, thisdependence is ignored and the reduced model is either notupdated in the process of the data fitting process or, itsdependency is not considered when computing gradientsand Hessians. The consequences of this approach can leadto inefficient algorithms as well as unacceptable solution.In this talk we discuss a framework that allow us to thedifferentiation of the reduced model with respect to theparameter. We show that this framework can yield robustestimates for some model inverse problems.

Eldad HaberDepartment of MathematicsThe University of British Columbiahaber@math.ubc.ca

Lars RuthottoDepartment of Mathematics and Computer ScienceEmory University

CS15 Abstracts 85

lruthotto@emory.edu

MS91

Model Mis-Specification and Model Reduction -Connecting the Dots

In addressing large-scale inverse problems, great care needsto be devoted to attainment of appropriate balance of in-exactness throughout the various stages of modeling andinversion. Disregard to such objective, either entails re-dundant computation or impairment of the overall fidelityof the inversion process. Model reduction is instrumentalin trading-off fidelity for computation, yet, in some situa-tions, it is essential to perform the opposite action, and en-hance model fidelity and thereby inversion output. In thistalk, we shall describe the interplay between model reduc-tion and model mis-specification mitigation and provide ageneric infrastructure for model re-specification based upona hybrid first principles and data-driven approach.

Lior HoreshMathematical Sciences & AnalyticsIBM TJ Watson Research Centerlhoresh@us.ibm.com

MS91

Inference for Prediction in Nonlinear Systems

When only sparse data are available for the calibration ofa many-parameter model that will be used to make onlya few decisions or predictions, not all parts of the poste-rior parameter space are either informed by the data orinformative to the output. This talk presents an adap-tive sampling method to preserve the posterior predictivedistribution without fully exploring the large posterior pa-rameter distribution.

Harriet LiMITkameeko@mit.edu

MS91

Model Reduction for Some Inverse Problems in Fi-nance

Implied volatility is a key value in financial mathematics.We discuss some of the pros and cons of the standard waysto compute this quantity, i.e. numerical inversion of thewell-known Black-Scholes formula or asymptotic expansionapproximations, and propose a new way to directly calcu-late the implied variance in a local volatility frameworkbased on the solution of a quasilinear degenerate parabolicpartial differential equation using POD and DEIM. Numer-ical results prove the quality of our approach compared toother methods.

Ekkehard W. Sachs, Marina SchneiderUniversity of Triersachs@uni-trier.de, marina.schneider@uni-trier.de

MS92

Mathematical Modeling at Two Opposite Ends ofthe Scale Spectrum with the Same Objective inMind: Improve Human Health

Osteoporosis is a common age related chronic disorder ofthe skeleton. It constitutes a considerable global publichealth problem currently affecting more than 200 million

people worldwide. We will present an overview of osteo-porosis, describe the bone remodeling process, and high-light the fundamental elements involve in determining bonestrength in vivo. The talk will show why mathematicalmodeling is playing an increasingly relevant role in the re-search, diagnosis, and monitoring of osteoporosis. We willillustrate how modeling has been used at Merck in the de-velopment of novel osteoporosis treatments.

Antonio CabalMerck Research LaboratoriesQuantitative Pharmacology and Pharmacometricsantonio.cabal@merck.com

MS92

A Simultaneous Approach to Parameter Estima-tion with Ode Models: a Case Study with ViralDynamics Models

The successful application of mathematical models and ver-ifying their underlying hypotheses rely critically on ourability to estimate their parameters. Parameter estima-tion is usually performed using a sequential approach: anoptimization algorithm calls the model independently toevaluate the agreement with data. Here, using an ODE-based viral dynamics model as an example, we explore andevaluate a simultaneous approach where the model is dis-cretized and explicitly introduced as equality constraintsto the optimization algorithm.

Khamir MehtaApplied Mathematics and ModelingMerck & Co, Inc.khamir mehta@merck.com

Junghoon LeeMerck & Co, Incjung hoon lee@merck.com

MS92

Numerical Solutions of a Partial Differential Equa-tions in a Pharmacometric Context

Pharmacometricians develop quantitative models of the ef-ficacy, potency and safety of drug compounds under devel-opment. These models are often constrained to systems ofordinary differential equations (ODEs) because simulationand analysis tools are designed to work with ODEs. Emerg-ing models are starting to clash with these constraints. Forexample, so-called age structured partial differential equa-tions (PDEs) have potential utility in oncology and safety.We discuss these models and how they may be incorporatedinto current tools.

Jeffrey SaltzmanAstraZenecaResearch and Development Information ServicesJeffrey.Saltzman@astrazeneca.com

MS92

Applications of Modeling and Simulation in DrugDiscovery and Development

Model based drug discovery has the potential to increaseefficiency at various stages of drug discovery and devel-opment by reducing the cost and time required to makego/no-go decisions. Often times, a mathematical modelis developed based on what is known about a particular

86 CS15 Abstracts

compound, such as its pharmacokinetic and pharmacody-namic properties. Such models can be used to simulate thebehavior of a compound under multiple scenarios and un-derstand various properties of the compound such as theparameters that drive efficacy, the efficacy/toxicity trade-off or the most effective dosing regimen for the compound.The insight obtained using such models can be used toguide decisions such as the selection of the most promis-ing pre-clinical compound or the selection of a dosing reg-imen in the pre-clinical or clinical space. The modelingtechniques used in developing these models are usually tai-lored to the questions that arise at the different stages ofdrug discovery and development. For example, a systemof ordinary differential equations can be used to representthe mechanistic model for a particular compound. Sucha mechanistic model could then be analyzed to identifythe parameters that affect the efficacy of a compound. Inother cases, a simpler empirical model could be used tocapture and assess the efficacy/toxicity tradeoff. In thistalk I will present a few examples of how various model-ing techniques can be used to answer important questionsin the pre-clinical and clinical space of drug discovery anddevelopment.

Chandni ValiathanMerckchandni.valiathan@merck.com;

MS93

Extreme Scale Solution of Engineering Applica-tions Using Uintah

Solving extreme scale problems using the Uintah compu-tational framework was achieved with the development ofa general runtime system capable of solving a broad classof problems using a graph-based approach. Important as-pects of the solution process, adaptive approach involvingdynamic out-of-order execution of tasks, the strengths andweaknesses of this approach are addressed, in particularwith future architectures in mind. Examples of scaling toabout 700K cores are shown on Blue Waters and Mira.

Martin BerzinsScientific Computing and Imaging InstituteUniversity of Utahmb@sci.utah.edu

MS93

GPU for Adaptive Optics on Ground Based As-tronomical Telescopes: Simulations and Real-TimeControl

The European Extremely Large Telescope project (E-ELT)is one of Europe’s highest priorities in ground-based astron-omy. ELTs are built on top of several highly sensitive andcritical astronomical instruments. Particularly, AdaptiveOptics (AO), used to stabilize image quality, is essential fortelescope routine operations. Designing and driving AOsystems requires fast and high fidelity numerical simula-tions. We describe the simulation framework and highlightthe extreme need for petascale computation to maintainreal-time processing.

Damien Gratadour, Eric GendronObservatoire de Parisdamien.gratadour@obspm.fr, eric.gendron@obspm.fr

Hatem LtaiefExtreme Computing Research Center

KAUSThatem.Ltaief@kaust.edu.sa

MS93

Exascale: the Why and the How

Applications demand scale for resolution, dimension,multi-physics fidelity, isolation from artificial boundaries,parameter inversion, optimal control, uncertainty quan-tification, and the statistics of ensembles. Are extreme-scale systems able to effectively host state-of-art algorithmsfor these pursuits, however, or are advances in hardwareand algorithms becoming than multiplicative? We exam-ine this question of with respect to algorithmic premiumson uniform-thread concurrency, arithmetic intensity, asyn-chronicity, and fault-tolerance and from the perspective ofrecent Gordon Bell prize finalist computations.

David E. KeyesKAUSTdavid.keyes@kaust.edu.sa

MS93

From Optimal Algorithms to Fast Petascale Solvers

Scalability beyond petascale requires algorithms with opti-mal complexity, but optimal algorithms are not automati-cally fast. The power of current and future supercomputercan only be unleashed, when grid structure, discretization,solver, parallel implementations are carefully co-designedby using predictive performance models exploiting concur-rency on all levels. We will describe the design of FEsolvers for creeping flow solving a trillion degrees of free-dom in around one minute and using up to a million parallelthreads.

Bjorn GmeinerComputer Science 10 - System SimulationFriedrich-Alexander-University Erlangen-Nuremberg,Germanybjoern.gmeiner@informatik.uni-erlangen.de

Holger StengelErlangen regional Computing Center, Germanyholger.stengel@fau.de

Christian WalugaM2 Center of MathematicsTechnical University of Munichwaluga@ma.tum.de

Barbara WohlmuthM2, Centre for Mathematical Sciences,Technische Universitat Munchen, Germanywohlmuth@ma.tum.de

Ulrich J. RuedeUniversity of Erlangen-NurembergDepartment of Computer Science (Simulation)ulrich.ruede@fau.de

MS94

Affirmative Actions in Education Creating Divisionand Inefficiency Among Beneficiary Groups in In-dia

The paper discusses the social and economic disparitywithin the group benefitting from affirmative actions in

CS15 Abstracts 87

educational sector of India and also tests this hypothesis-revealing that a major chuck of population is becominginefficient because of these actions. With the help of math-ematical tools it identifies negative cycle present in the so-ciety and calculates the economic cost due to this disparity.It concludes with a solution to this complex socio-politicalissue regarding affirmative actions.

Aprant AjayDelhi Techinical University, INDIAaprant@gmail.com

MS94

System Architecture for a Cooperative Fleet of Au-tonomous Underwater Vehicles (AUVs)

The Eco-Dolphin system of AUVs has been engineered todeploy for the acquisition of coastal ecological data. Eachmember of the fleet has its own payload and objective inarriving at a predefined destination. The talk will detailthe components of each vehicle, their characteristics, andwhat requirements are needed for the successful launch,maneuver, and recovery within the systems control center.

Stacey Joseph-Ellison, Qi ZhouEmbry-Riddle Aeronautical Universityellisos1@my.erau.edu, zhouq@my.erau.edu

Zhaoyang FuEmbryRiddle Aeronautical Universityfuz@my.erau.edu

Zakaria DaudEmbry-Riddle Aeronautical Universitydaudz@my.erau.edu

Hong LiuDepartment of MathematicsEmbry-Riddle Aeronautical Universityliuho@erau.edu

MS94

Interfacial Motion by Mean Curvature in LiquidCrystals

Liquid crystals are mesogenic phases of matter betweenconventional solid and liquid phases. Nematic liquid crys-tals are anisotropic liquids with directional order. Weuse the gradient-flow model associated with the Landau-deGennes free energy to study interfaces in nematic samplesat the nematic-isotropic transition temperature, demon-strating that they propagate according to mean curvatureflow in some asymptotic limits. We numerically computedynamically metastable nematic configurations in cylindersand study their delicate dependence on initial conditions.

Amy SpicerUniversity of Bath, UKA.Spicer@bath.ac.uk

Apala MajumdarUniversity of Batha.majumdar@bath.ac.uk

MS94

On Strategic Defense in Stochastic Networks

In this paper, we discuss a particular class of stochastic

processes used for modeling the accumulation of damage tonetworks or systems experiencing a sequence of attacks orfailures incapacitating random numbers of nodes (e.g. com-ponents), each with a random weight (e.g. a cost). Eachcomponent has threshold(s) whose crossing indicate thesystem entering a critical state. An operational calculusstrategy is used to derive probabilistic information aboutthe process within random vicinities of passage times.

Ryan White, J. H. DshalalowFlorida Institute of Technologyryan@chasnet.com, eugene@fit.edu

MS94

Theory and Computation for Bilinear Quadratures

We present a general framework for constructing numeri-cal integration rules over an arbitrary domain in R

d thatare exact when the integrand is the product of two func-tions belonging to prescribed subspaces. Such integralsare useful in Galerkin methods, for example. We provethat this framework reduces to Gaussian quadrature forunivariate polynomials and trapezoid rule for trigonomet-ric polynomials. We then describe a numerical procedurefor constructing these integration rules and present somenumerical results.

Christopher WongUniversity of California, Berkeleycawong@math.berkeley.edu

MS94

Survival Probability of Beneficial Mutations inBacteria

Most novel mutations, even if they confer a benefit to theorganism, are ultimately lost during the stochastic popula-tion growth process. Their survival probability is sensitiveto the organism’s life history details and the traits affectedby the mutation. We develop a continuous time multitypebranching process to predict the survival of initially rarebeneficial mutations in bacteria. Predicting bacterial adap-tation rates is critical to public health issues such as theevolution of drug resistance.

Anna Zhu, Lindi M. WahlWestern University Canadaazhu4@uwo.ca, lwahl@uwo.ca

MS95

Asymptotic-Preserving Scheme for the Fokker-Planck-Maxwell System in the Quasi-NeutralRegime

Abstract not available at time of publication.

Stephane BrullInstitut de Mathematiques de Bordeaux UMR 5251Universite Bordeauxstephane.brull@math.u-bordeaux1.fr

MS95

Solving Kinetic Equations to Model the Core-Collapse Supernova Explosion Mechanism

Core-collapse supernovae (CCSNe) are the explosive deathsof massive stars. CCSN explosions are driven by energytransfer from neutrinos to the stellar fluid. This neutrino

88 CS15 Abstracts

heating occurs under non-equilibrium conditions, and a ki-netic description based on the Boltzmann equation is war-ranted. We describe our recent efforts to develop numericalmethods to model neutrino transport in CCSNe with dis-continuous Galerkin methods, including ongoing efforts tomodel neutrino-matter interactions.

Eirik Endeve, Cory HauckOak Ridge National Laboratoryendevee@ornl.gov, hauckc@ornl.gov

Yulong XingDepartment of MathematicsUniveristy of Tennessee / Oak Ridge National Labxingy@math.utk.edu

Tony MezzacappaORNLmezzacappa@phy.ornl.gov

MS95

Versions of Discontinuous Galerkin Algorithms forDiffusion and for Energy-Conserving HamiltonianDynamics

We present mixed continuous/discontinuous Galerkinschemes for solution of a class of kinetic Vlasov-Boltzmannproblems in Hamiltonian Poisson-bracket form (plus colli-sions). These schemes conserve energy, and optionally theL2 norm, exactly. Application to electromagnetic gyroki-netic problems requires novel extension to avoid the Am-pere cancellation problem and significant time step limita-tions. There are subtle properties of commonly used DGschemes for second order derivatives, such as from diffu-sion, which we compare with a recovery-based approach.

Ammar HakimPrinceton Plasma Physics Laboratoryahakim@pppl.gov

Greg HammettPrinceton Plasma Physics LaboratoryPrinceton Universityhammett@princeton.edu

Eric Shi, Ian Abel, Tim Stoltzfus-DueckPrinceton Universityeshi@pppl.gov, iabel@princeton.edu,tstoltzf@princeton.edu

MS95

Numerical Simulation of the Crookes Radiometer

The Crookes radiometer is a small mill enclosed in a glassbulb containing a partial vacuum. Its vanes rotate whenexposed to light. This is due to the thermal transpiration,as explained by the kinetic theory of gases. In this talk,a numerical method to make full 3D simulations of thisradiometer will be presented. It is based on a discretiza-tion of the Boltzmann equation by a cut-cell approach thatallows to easily handle moving boundaries.

Guillaume DechristeInstitut de Mathematiques de Bordeauxguillaume.dechriste@math.u-bordeaux1.fr

Luc Mieussens

Institut de Mathematiques de Bordeauxluc.mieussens@math.u-bordeaux1.fr

MS96

Swimming Dynamics of Microorganisms in Vis-coelastic Fluids Near a Wall

Microorganisms swimming in viscoelastic fluids are ubiq-uitous in nature; this includes biofilms grown on surfaces,Helicobacter pylori colonizing in the mucus covering thestomach and spermatozoa swimming through cervical mu-cus. Previous studies have focused on the locomotion ofmicroorganisms in unbounded viscoelastic fluids. How-ever in many situations, microorganisms interact with solidboundaries. In this work, we numerically study the effectof solid boundaries on the swimming of an archetypal low-Reynolds number swimmer in viscoelastic fluids.

Gaojin LiUniversity of Notre Damegli5@nd.edu

Arezoo ArdekaniNotre Dame UniversityDepartment of Aerospace and Mechanical Engineeringardekani@purdue.edu

MS96

Stabilizing the Collective Motion of Micro-swimmers using Confinement

Concentrated suspensions of swimming microbes and otherforms of active matter are known to display intricate, self-organized spatiotemporal patterns on scales larger thanthose of the individual motile units. The collective dy-namics of swimming microorganisms exhibits a complexinterplay with the surrounding fluid: the motile cells stirthe fluid, which in turn can reorient and advect them. Thisfeedback loop can result in long-range interactions betweenthe cells. We present a computational model that takes intoaccount these cell-fluid interactions and cell-cell forces andthat predicts counterintuitive cellular order driven by long-range flows. The predictions are confirmed by experimentswith Bacillus Subtilis bacteria which measure the flagellabundle orientation and tracks the cells in the self-organizedstate. Simulations and experiments show that if the micro-swimmers are confined inside thin cylindrical chambers thesuspension self-organizes into a stable swirling vortex. Ifthe micro-swimmers are confined in thin racetracks, a per-sistent unidirectional stream can be observed. Both thesephenomena emerge as a result of the complex interplaybetween the swimmers, the confining boundaries and thefluid flow. The study highlights the importance of modelsand simulations of micro-swimmers needing to correctlyinclude both steric and hydrodynamic interactions in oderto capture the dynamics observed in experiments. Collab-orators: Hugo Wioland and Raymond Goldstein, DAMTP,University of Cambridge, UK.

Enkeleida LushiBrown Universityenkeleida lushi@brown.edu

MS96

Dynamics of Micro-Swimmers Inside a PeristalticPump

Peristaltic pumping is a form of fluid transport along the

CS15 Abstracts 89

length of a tube containing liquid when the tube undergoesa contractile wave. While much is known about the peri-stalsis of Newtonian liquids, complex ones have receivedlimited attention. There are many examples in naturewhere motile micro-particles or micro-swimmers (such asbacteria or spermatozoa) are suspended in the fluid insidea peristaltic micro-pump. We present a simulation methodthat accounts for the coupling of the dynamics of manymicro-swimmers with each other, the pump, and the fluidflow. The pump and the fluid flow it drives can affectthe swimmer dynamics in interesting ways. Moreover, thepresence of the swimmers and their collective motion canaffect the net transport and mixing in the pump. The effi-ciency of mixing the suspension for a variety of parameterswill be discussed.

Adam StinchcombeUniversity of Michiganstinch@umich.edu

Enkeleida LushiBrown Universityenkeleida lushi@brown.edu

MS96

Flagellar Activity Influences Self-Organization inConfined Microswimmer Suspensions

Motile microorganisms are often subject to different typesof boundary confinement in their natural environment, butthe effects of confinement on their dynamics are poorlyunderstood. We consider a model of microswimmers re-stricted to move in a 2D Hele-Shaw cell. In an unboundedperiodic domain, we show that decreasing flagellar activ-ity induces a hydrodynamically triggered transition in con-fined microswimmers from turbulentlike swimming to ag-gregation and clustering. We then impose two differenttypes of boundary confinement: circular and sidewalls con-finement and study how additional boundaries influencethe emergence of global modes. In the case of circular con-finement, the microswimmers can spontaneously organizeinto a single vortex, reminiscent to what have been ob-served in recent experiments of bacterial suspensions. Inthe case of sidewalls confinement, the microswimmers formdensity shock, via interaction with the sidewalls and back-ground flow.

Alan Cheng Hou Tsang, Eva KansoUniversity of Southern Californian/a, kanso@usc.edu

MS97

Threading Mesh Optimization Codes Using Trans-actional Memory

As threading becomes a necessity on multi- and many-coremodern computers, Transactional Memory (TM) has re-ceived much attention as a thread synchronization mech-anism that promises both coding elegance and efficiency.We study the effects of TM on mesh optimization algo-rithms using the IBM BG/Q and Intel Haswell platforms.Our preliminary results indicate that these iterative meth-ods are good candidates for TM when the new metric of”time-to-convergence” is used instead of simple wall clocktime.

Barna BihariLawrence Livermore National Labbihari1@llnl.gov

Lori A. DiachinLawrence Livermore National Laboratorydiachin2@llnl.gov

Patrick M. KnuppSandia National Laboratoriespknupp@sandia.gov

MS97

An Array-Based Mesh Topological RepresentationThat Effectively Supports General Mesh Modifica-tion

A parallel mesh data structure is presented which storeseach part using a few arrays. It is flexible enough to allowconstant-time insertion and removal of elements,enablingfully general mesh adaptation. Multiple element types de-fined at compile time can co-exist in one mesh. The mem-ory usage is four times less than object-based structureswith the same features. It can also be configured to repre-sent reduced meshes, and various other adjacency-storageschemes.

Dan A. IbanezRensselaer Polytechnic InstituteSCORECdibanez@scorec.rpi.edu

Mark S. ShephardRensselaer Polytechnic InstituteScientific Computation Research Centershephard@rpi.edu

MS97

Efficient Unstructured Mesh Traversal MethodsBased on Array-Based Half Facets

Mesh-based discretization methods for solving PDE’s de-pend on local mesh traversals for various purposes suchas linear system formation, boundary conditions, etc.We present efficient traversal methods for unstructuredmeshes based on an array-based half-facet data structure.The half-facet representation is generalized from the half-edge/face representations in 2D/3D with support for non-manifold mixed meshes. We present the main constructsof the data structure and analyze several efficient entitytraversal schemes for the discrete operator assembly.

Navamita RayArgonne National Labratorynray@mcs.anl.gov

Xinglin ZhaoStony Brook Universityxinglin.zhao@stonybrook.edu

Vijay MahadevanArgonne National Laboratorymahadevan@anl.gov

Xiangmin JiaoStony Brook Universityxiangmin.jiao@stonybrook.edu

MS97

M3D-C1 Adaptive Loop Going from 2D Axisym-

90 CS15 Abstracts

metric to Full 3D

Tokamak fusion reactors are the experimental approach tostudy magnetically confined sustainable fusion reactions.The tokamak is a symmetric torus along the toroidal di-rection and the fusion material exists as the state of plasmain the torus. M3D-C1 simulates non-linear instabilities ofplasmas in the tokamak. The on-going effort and results ofM3D-C1 adaptive loop in coordination of SCOREC toolsto change the simulation mode from axisymmetric to full3D torus are presented.

E. Seegyoung Seol, Mark S. ShephardRensselaer Polytechnic InstituteScientific Computation Research Centerseols@rpi.edu, shephard@rpi.edu

Fan ZhangRPIfzhang@scorec.rpi.edu

MS98

Comparison of Continuous, Discontinuous and Hy-brid Finite Element Methods for Accuracy and Ef-ficiency

We compare and contrast continuous, discontinuous andhybrid (HDG/EDG) finite element methods for the scalaradvection-diffusion problem. For each method we examineeffectiveness of preconditioners for linear solves, an impor-tant consideration in the efficiency of each method as itwill affect both convergence rates and overall run time. Wealso examine accuracy of both discretization and error es-timates, the latter an important factor in the effectivenessof solution adaptation methods.

Steven R. Allmaras, Marshall GalbraithMassachusetts Institute of Technologyallmaras@mit.edu, galbramc@mit.edu

David l. DarmofalDepartment of Aeronautics & AstronauticsMassachusetts Institute of Technologydarmofal@mit.edu

MS98

Goal-Oriented Curved Mesh Optimization forHigh-Order Finite-Element Methods

High-order finite element methods generally require curvedgeometry representations, and hence curved elements, tomaintain accuracy. While mesh validity is paramount, wetake a further step and present a method for optimizingthe shape of the curved elements to improve their approx-imation capabilities. The method optimizes the reference-to-global high-order mapping and yields curved elementsideally suited for representing a target solution, or for pre-dicting outputs in a goal-oriented setting.

Krzysztof Fidkowski, Devina SanjayaUniversity of Michigankfid@umich.edu, dsanjaya@umich.edu

MS98

Equivalence between the Energy Stable Flux Re-construction and Filtered Discontinuous Galerkin

Schemes

We demonstrate the equivalence between DiscontinuousGalerkin (DG) schemes, in strong and weak form, andthe Energy Stable Flux Reconstruction (ESFR) schemesthrough the application of a generalized filter to the penal-ized flux terms in the DG formulation. While the essenceof the idea, the filtering of the highest mode of the correc-tion functions, was given previously, an elegant extensionto higher dimensional non-constant Jacobian formulationsin arbitrary bases is presented here.

Philip Zwanenburg, Siva NadarajahMcGill Universityphilip.zwanenburg@mail.mcgill.ca,siva.nadarajah@mcgill.ca

MS98

Theoretical Aspects of High-Order Flux Recon-struction Schemes

In this talk I will discuss recent theoretical advances inthe area of high-order Flux Reconstruction (FR) schemes.In particular I will discuss the influence of solution pointplacement on the stability and accuracy of FR schemes,and I will present a new extended family of energy-stableFR schemes for one-dimensional linear advection problems.

Peter E. VincentDepartment of AeronauticsImperial College Londonp.vincent@imperial.ac.uk

MS99

The Method of Regularized Stokeslets: Motivationand Applications

Since its introduction in 2001, the method of regular-ized Stokeslets has been very useful in the simulation ofmany small scale fluid flows. Biological applications in-clude swimming motions of microorganisms, cell growth,biofilm/fluid interactions, microfiltration for removing par-ticulate matter, flagellar bundling, sperm motility, peri-staltic pumping, ciliary motion, and other microscopic phe-nomena. We will describe the method, its motivation andthe flexibility in choosing its components. We will alsoshow applications to flagellar motion.

Ricardo CortezTulane UniversityMathematics Departmentrcortez@tulane.edu

MS99

Bacteria Association with Ciliated Surfaces

Abstract not available at time of publication.

Eva KansoUniversity of Southern Californiakanso@usc.edu

MS99

Modeling Sperm Motility Using a Kirchhoff RodModel

Sperm flagella have been observed to propagate different

CS15 Abstracts 91

waves of bending, depending on the fluid environment.In this talk, we will discuss modeling aspects of the rel-evant fluid environment and chemical concentrations, re-lating emergent waveforms and interactions to current ex-periments. The sperm flagellum is represented as a Kirch-hoff rod and a regularized Stokes formulation will be usedto solve for the local fluid flow. Results will be shown todescribe emergent waveforms and swimming speeds.

Sarah D. OlsonWorcester Polytechnic Institutesdolson@wpi.edu

MS99

The Effects of Rotation and Translation on Flagel-lar Synchronization

Many flagellated microswimmers exhibit some form of flag-ellar synchronization. For instance, the bundling and un-bundling of flagella in E. coli is responsible for their run-and-tumble behavior. In this talk, we look in detail at themechanisms responsible for phase synchrony in a pair ofrigid side-by-side helices. Using an “end-pinned’ model, weare able to isolate the effects of translation from those of ro-tation, finding synchrony in some cases and anti-synchronyin others.

Jonathan H. TuUC Berkeleyjhtu@berkeley.edu

Murat ArcakUniversity of California-Berkeleyarcak@eecs.berkeley.edu

Michel M. MaharbizUC Berkeleymaharbiz@eecs.berkeley.edu

MS100

Analysis and Control of Cascading Failures ofPower Transmission Systems: a Macro View

Cascading failures of power systems are complex phenom-ena that are governed by a combination of existing low-levelcontrol mechanisms, physics, human input and exogenousfactors (such as weather-related factors). In the event ofa cascading failure, a goal is to arrest the failure with aminimum of demand lost. We describe ongoing researchwith a provably good control methodology that relies ona combinatorial algorithm, augmented with tools derivedfrom the SAA (sample average approximation) approachfor stochastic optimization. We describe our results in thecontext of simulations involving several large-scale grids,in particular the Eastern Interconnect.

Daniel BienstockColumbia University IEOR and APAM DepartmentsIEOR Departmentdano@columbia.edu

Guy GreblaColumbia Universityguy@ee.columbia.edu

MS100

Visual Analytics for Detection and Tracking of

Emergent Subgraphs in Social Networks

Social media networks, and more specifically Twitter re-tweet networks, are both very large and incredibly noisy.At the same time, analysis of Twitter networks has the po-tential to have both a predictive capability and detection ofemergent trends. In this talk, we combine and co-optimizevisual analytics with statistical graph analysis algorithmsfor detection and tracking of emergent subgraphs in dy-namic graphs. A case study focused on movie name hash-tag networks will be discussed.

Nadya Bliss, Ross MaciejewskiArizona State Universitynadya.bliss@asu.edu, rmacieje@asu.edu

MS100

Epidemic in Time and Space: Modeling SpatialOutbreak Dynamics

Most epidemic models represent the progression of the con-tagion process by estimating the number of infectious indi-viduals per time unit. While this is a valid representation,it neglects to include the spatial progression of the epi-demic. This presentation will focus on representing thespatio-temporal progression of an epidemic and highlightsome of the factors that will effect the spatial path a diseaseoutbreak will follow in the derived contact network.

Armin MiklerDepartment of Computer Science & EngineeringUniversity of North Texasmikler@cs.unt.edu

MS100

Spectral Subgraph Detection in Noisy, UncertainNetworks

Network analysis in practice may involve considering rela-tionships that must be observed through some noisy mech-anism. This additional stochasticity compounds the un-certainty due to random connectivity fluctuations of theunderlying graph. This presentation discusses various sim-ple mechanisms for noise and uncertainty in network anal-ysis and demonstrates their impact on the ability to detectsmall anomalous subgraphs using spectral techniques. Wealso demonstrate fusion of multiple noisy datasets to re-cover performance achievable on the uncorrupted data.

Benjamin A. MillerMIT Lincoln Laboratorybamiller@ll.mit.edu

MS101

Fast Computation of Orthonormal Bases for RBFNative Spaces

We proposed in a recent work the so called WSVD basis,which is strictly connected to the eigendecomposition ofthe integral operator (of Mercer’s theorem) and allows oneto overcome some problems related to the stability of thecomputation of the approximant for a wide class of radialkernels. Although effective, this basis is computationallyexpensive to compute. We discuss here a method to im-prove and compute in a fast way the basis using methodsrelated to Krylov subspaces. After reviewing the connec-tions between the two bases, we concentrate on the prop-erties of the new one, describing its behavior by various

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numerical tests.

Stefano De MarchiUniversity of Padova (Italy)demarchi@math.unipd.it

Gabriele SantinUniversity of Padovasantin.gabriele@gmail.com

MS101

Meshless Vector Field Approximation with RadialBasis Functions

In this talk we will discuss customized radial basis func-tion kernels for vector-field problems. Using shifts of asingle scalar-valued kernel and its derivatives, one can eas-ily construct approximation bases that are analyticallydivergence-free (or curl-free). Such bases lead to mesh-less methods that are suitable for problems involving elec-tromagnetic fields, fluid flow, or other applications wherea divergence-free or curl-free property must be preserved.Our focus will be on approximations designed to natu-rally ”split” into divergence-free and curl-free components.We will present approximation rates of the resulting field-splittings, briefly consider a few applications, and sharesome numerical observations.

Edward FuselierHigh Point UniversityDepartment of Mathematics and Computer Scienceefuselie@highpoint.edu

Grady B. WrightDepartment of MathematicsBoise State University, Boise IDgradywright@boisestate.edu

MS101

Beyond Quasi-unifomity: Kernel Approximationwith a Local Mesh Ratio

Many theoretical results in RBF interpolation assume thatdata is sampled in a quasi-uniform way. This is somewhatsupported by empirical evidence – as centers are badly ar-ranged, the underlying interpolation matrices become ill-conditioned. In this talk we present a relaxed notion ofquasi-uniformity by locally controlling the mesh-ratio. Un-der this type of assumption, and with the aid of recentlydeveloped localized bases for RBF approximation, centersmay cluster or form gaps without giving rise to instabil-ity. At the same time, approximation error is controlledby a local density parameter, meaning that pointwise errorresponds to the local distribution of data.

Thomas C. HangelbroekDepartment of MathematicsUniversity of Hawaii at Manoahangelbr@math.hawaii.edu

MS101

Oversampling Near the Boundary and ImprovedExponential Convergence Rates

We consider the reconstruction of smooth functions fromscattered data. If the data are exact, then one theo-retically expects exponential convergence rates for manykernel-based reconstruction processes. However, the as-

sociated schemes are notoriously ill-conditioned and oftenshow strong boundary effects. We discuss a convergenceanalysis for a wide class of regularized reconstruction pro-cesses by means of sampling inequalities. In particular, wepresent improved convergence rates if the scattered datapoints are distributed more densely near the boundary.This is based on joint work with Christian Rieger (Univer-sity of Bonn).

Barbara ZwicknaglUniversity of Bonnzwicknagl@iam.uni-bonn.de

MS102

Parallel, Adaptive, Multi Block Methods for Carte-sian Grids using ForestClaw

We will discuss recent multiblock and parallel capabilitiesin ForestClaw, an adaptive mesh refinement code basedon the patched-based multi-rate Berger-Oliger algorithmicstrategy coupled with quad/octree mesh refinement. Thesupport for multiblock capabilities now allows for domainscomposed of quadrilaterals, (with up to four quads meetingat a vertex), each of which is refined as a quadtree. Oneimportant example of such a domain is the cubed sphere.We will also show results from parallel computations on theBlue Gene/Q supercomputer JUQUEEN, based in Julich,Germany. ForestClaw uses the dynamic grid managementlibrary p4est (C. Burstedde, Univ. of Bonn).

Donna CalhounBoise State Universitydonnacalhoun@boisestate.edu

Carsten BursteddeUniversitat Bonnburstedde@ins.uni-bonn.de

MS102

Using Explicit Filtering and Reconstruction to Im-prove Large-Eddy Simulation of the Atmosphereon Adaptive Grids

Large-eddy simulation (LES) and adaptive mesh refine-ment reduce the computational cost of turbulence model-ing by restricting resolved length scales. Combining thesetechniques generates errors at grid refinement interfaces.This talk explores using the LES formulation to mitigatethese errors. Explicitly filtering the advection term andthe mixed model are compared to implicit filtering andthe eddy viscosity model. Explicitly filtering the advectionterm reduces interpolation errors, and the mixed modeldecreases wave reflection.

Lauren Goodfriend, Fotini Katopodes ChowUC Berkeleylgoodfriend@berkeley.edu, tinakc@berkeley.edu

Marcos Vanella, Elias BalarasGeorge Washington Universitymvanella@gwu.edu, balaras@gwu.edu

MS102

Local Time Stepping for Parallel Adaptive MeshRefinement Simulation

In this talk we present a linear, multistep approach to localtime stepping for parallel, adaptively refined discontinuous

CS15 Abstracts 93

Galerkin and multiblock finite difference methods. Thescheme is efficiently initialized and, following mesh adapta-tion, restarted using a fixed number of Runge-Kutta steps;the number of Runge-Kutta steps is independent of thenumber of time levels. The coupled multiphysics problemof earthquake rupture dynamics is used to demonstrate theefficiency and accuracy of the method.

Jeremy E. KozdonStanford UniversityGeophysicsjekozdon@nps.edu

Lucas WilcoxDepartment of Applied MathematicsNaval Postgraduate Schoollwilcox@nps.edu

MS102

Progress in Parallel Adaptive Methods for StormSurge Forecasting

Today the threat of coastal hazards such as storm surge andtsunamis has become increasingly critical to the sustain-ability of coastal infrastructure and communities. Leverag-ing adaptive mesh refinement approaches to these problemshas proven to be an effective way to tackle these multi-scaleproblems, lowering the computational barrier substantiallyin some cases. In this talk progress in parallelizing thesemethods will be discussed including recent work on usingmany-core technologies.

Kyle T. MandliUniversity of Texas at AustinICESktm2132@columbia.edu

MS103

Applying Object-oriented Programming to PDESolutions

Object-oriented program design is very appealing for de-sign of PDE solvers since many of the ideas fit well withtop-down design, abstraction from the underlying discreti-sation, and high-level code re-use. However, too much datahiding and encapsulation, commonly espoused for object-oriented methods, leads to memory-use redundancy andinefficient codes. We will examine some lessons learnedduring application of object-oriented design to a spectralelementFourier NavierStokes solver.

Hugh BlackburnDepartment of Mechanical and Aerospace EngineeringMonash Universityhugh.blackburn@monash.edu

MS103

Architecting Spectral/HP Element Codes for Mod-ern Hardware

Complex finite element software is necessary to meet thedemands of some of today’s most challenging computa-tional problems. The design of software is therefore moreimportant than ever to ensure correctness of the result andmanageability and sustainability of the implementation.We illustrate the approach taken within the Nektar++spectral/hp element framework to compartmentalise codeto align with the mathematical description and produce a

software solution which retains performance and platformportability.

Chris Cantwell, David MoxeyImperial College Londonc.cantwell@imperial.ac.uk, d.moxey@imperial.ac.uk

Mike KirbyUniversity of UtahSchool of Computingkirby@cs.utah.edu

Spencer SherwinImperial College Londons.sherwin@imperial.ac.uk

MS103

High order DG Methods on Pyramidal Elements

High order time-explicit nodal discontinuous Galerkin (dG)methods have grown in popularity over the past decade forreasons both mathematical and computational in nature.Optimized Lagrange interpolation nodes and sharp traceinequalities with explicit constants allow for explicit ex-pressions for optimal CFL and penalty constants. Finally,the computational structure of dG methods on simplicesand hexahedra allows for efficient implementation on ac-celerators and graphics processing units. In this talk, wepresent extensions of these aspects of dG methods to highorder pyramidal elements.

Jesse ChanRice Universityjesse.chan@caam.rice.edu

MS103

What Makes Computational Open Source LibrariesSuccessful?

While software is the backbone of scientific computing, werarely publish information on best practices for writinglarge-scale, open source scientific software. In this talk,we discuss our observations for success for computationallibraries. In particular, we talk about the roles of code,documentation, community, project management, testing,and licenses. The talk is based on our experience maintain-ing the finite element library deal.II (see www.dealii.org).

Timo HeisterClemson UniversityMathematical Sciencesheister@clemson.edu

Wolfgang BangerthTexas A&M Universitybangerth@math.tamu.edu

MS104

Distributed Optimization in Directed Graphs:Push-Sum Based Algorithms

We consider distributed optimization by a collection ofnodes, each having access to its own convex function, whosecollective goal is to minimize the sum of the functions.The communications between nodes are described by atime-varying sequence of directed graphs, which is uni-formly strongly connected. For such communications, as-

94 CS15 Abstracts

suming that every node knows its outdegree, we develop abroadcast-based algorithm, termed the subgradient-push,which steers every node to an optimal value under astandard assumption of subgradient boundedness. Thesubgradient-push requires no knowledge of either the num-ber of agents or the graph sequence to implement. Ouranalysis shows that the subgradient-push algorithm con-verges at a rate of O(ln t/t). The proportionality constantin the convergence rate depends on the initial values at thenodes, the subgradient norms and, more interestingly, onboth the speed of the network information diffusion andthe imbalances of influence among the nodes.

Angelia NedichIndustrial and Enterprise Systems EngineeringUniversity of Illinois at Urbana-Champaignangelia@illinois.edu

Alexander OlshevskyUniversity of Illinois at Urbana-Champaignaolshev2@illinois.edu

MS104

Blessing of Scalability: A Tractable Dual Decom-position l-0 Approach for Large Graph Estimation

Estimating the topology of graphical models has been acritical problem in high-dimensional statistics. In large-scale graphs, the prior knowledge can be formulated as atotal sparsity budget constraints. This induces a huge non-convex/combinatorial optimization problem involving l-0constraint. An interesting observation is: as the graph sizeincreases, the associated optimization problem becomes in-creasingly convex. This motives the use of the distributeddual decomposition method for estimating the graph topol-ogy. By relating the duality gap with certain Kullback-Leibler divergence associated with the graph estimationproblem, we show that the estimator obtained by dualdecomposition achieves asymptotically optimal statisticalrate.

Mengdi WangDepartment of Operations Research and FinancialEngineeringPrinceton Universitymengdiw@princeton.edu

MS104

On the O(1/k) Convergence of Asynchronous Dis-tributed Alternating Direction Method of Multi-pliers

We consider a network of agents that are cooperativelysolving a global optimization problem, where the objectivefunction is the sum of privately known local objective func-tions of the agents and the decision variables are coupledvia linear constraints. Recent literature focused on specialcases of this formulation and studied their distributed solu-tion through either subgradient based methods with O(1/v k) rate of convergence (where k is the iteration number)or Alternating Direction Method of Multipliers (ADMM)based methods, which require a synchronous implementa-tion and a globally known order on the agents. In thispaper, we present a novel asynchronous ADMM based dis-tributed method for the general formulation and show thatit converges at the rate O(1/k).

Ermin WeiMIT

erminwei@mit.edu

Asuman OzdaglarMassachusetts Institute of Technologyasuman@mit.edu

MS104

Distributed Optimization in Undirected Graphs:Gradient and EXTRA Algorithms

Decentralized optimization meets the future needs frommobile computing, self-driving cars, cognitive radios, andcollaborative data mining, just to name a few. It allowsoptimization problems in a self-organizing network to besolved without a central computer. Compared to standarddistributed computing with a central controller, a decen-tralized approach tolerates certain failed nodes or links, hasbetter load balance, and allows each node to keep its dataprivate during the computation. The setting of this talk isthe same as the previous talk but assumes an undirectedgraph, which is more computationally friendly. We analyzeexisting first-order algorithms and their convergence ratesand solution accuracies.

Wotao YinDepartment of MathematicsUniversity of California at Los Angeleswotaoyin@math.ucla.edu

Qing Ling, Kun YuanUniversity of Science and Technology of ChinaDepartment of Automationqingling@mail.ustc.edu.cn, kunyuan@mail.ustc.edu.cn

MS105

Advanced Discretizations And Multigrid MethodsFor The Energy Minimization of Liquid CrystalEquilibrium Configurations

Abstract not available at time of publication.

David EmersonTufts Universitytba@siam.org

MS105

A Parallel Volume Integral Equation Stokes Solverfor Flows in Complex Geometries

Abstract not available at time of publication.

Dhairya MalhotraUniversity of Texas at Austintba@siam.org

MS105

Uncertainty Quantification in Control Problems forFlocking Models

Abstract not available at time of publication.

Mattia ZanellaUniversity of Ferraratba@siam.org

MS106

Polynomial Approximation of Random PDEs by

CS15 Abstracts 95

Discrete Least Squares

We consider global polynomial approximation of theparameter-to-solution map for PDEs with random inputparameters. The polynomial approximation is obtained bya discrete least squares approach based on noise-free point-wise evaluations of the map. We present results concerningthe stability and optimality of the method for random aswell as low discrepancy sequences of points, and various un-derlying probability measures and show high dimensionalnumerical tests supporting the theory.

Fabio NobileEPFL, Switzerlandfabio.nobile@epfl.ch

Raul F. TemponeMathematics, Computational Sciences & EngineeringKing Abdullah University of Science and Technologyraul.tempone@kaust.edu.sa

Giovanni MiglioratiCSQI-MATHICSE, EPFLgiovanni.migliorati@epfl.ch

MS106

Combining Sparsity and Smoothness for FunctionInterpolation

Functions of interest are often smooth and sparse in somesense. Classical linear interpolation methods are effectiveunder strong regularity assumptions, but cannot incorpo-rate nonlinear sparsity structure. At the same time, non-linear methods such as L1 minimization can reconstructsparse functions from very few samples, but do not neces-sarily encourage smoothness. Here we show that weightedL1 minimization effectively merges the two approaches,promoting both sparsity and smoothness in reconstruction.More precisely, we provide specific choices of weights in theL1 objective to achieve rates for functions with coefficientsequences in weighted Lp spaces, p <= 1. We consider theimplications of these results in particular for the multivari-ate setting.

Rachel WardDepartment of MathematicsUniversity of Texas at Austinrward@math.utexas.edu

Holger RauhutAachen Universityrauhut@mathc.rwth-aachen.de

MS106

Quasi-optimal Polynomial Approximation of PDEswith Linear and Nonlinear Stochastic Coefficients

Abstract not available at time of publication.

Clayton G. WebsterOak Ridge National Laboratorywebstercg@ornl.gov

Hoang A. TranOak Ridge National LaboratoryComputer Science and Mathematics Divisiontranha@ornl.gov

Guannan Zhang

Oak Ridge National Laboratoryzhangg@ornl.gov

Ronald DeVoreDepartment of MathematicsTexas A&M Universityrdevore@math.tamu.edu

MS107

Runtime Systems for Fault Tolerant Computing

Since the number of hardware components is expected togrow by one or two orders of magnitude and the circuits’features will also decrease, reliability is expected to be acritical challenge for exascale computing. Specifically, ex-ascale machines are expected to suffer hard faults, i. e.,crashes, soft faults, i. e. silent data corruptions, plus per-formance slowdowns due to unexpected behavior of somehardware components. In this context, a runtime systemable to tolerate the latency due to recovery mechanismsby overlapping them with algorithmic computations is re-quired. Such system must dynamically adapt the workloaddepending on the hardware status and the prevalence offaults. In this talk, we will describe the general featuresthat this kind of runtime software such have.

Marc CasasBarcelona Supercomputing Centermarc.casas@bsc.es

MS107

Fenix: A Framework for Online Failure Recoveryfor Scientific Simulations Towards Exascale

In this talk we present Fenix, a framework for enabling re-covery from process/node/blade/cabinet failures for MPI-based parallel applications in an online and transparentmanner. Fenix provides mechanisms for transparently cap-turing failures, fixing failed communicators, restoring ap-plication state, and returning execution control back tothe application. It relies on application-driven, diskless,implicitly coordinated checkpointing. Using the S3D com-bustion simulation we experimentally demonstrate Fenixsability to tolerate high failure rates with low overhead.

Marc GamellNSF Cloud and Autonomic Computing Center, RutgersDiscoveryInformatics Institute, Rutgers Universitymgamell@cac.rutgers.edu

Daniel KatzComputation Institute, University of ChicagoArgonne National Laboratory, Chicagod.katz@ieee.org

Keita Teranishi, Hemanth Kolla, Jacqueline ChenSandia National Laboratoriesknteran@sandia.gov, hnkolla@sandia.gov,jhchen@sandia.gov

Scott KlaskyOak Ridge National LaboratoryOak Ridge, TNklasky@ornl.gov

Manish ParasharRutgers Discovery Informatics Institute

96 CS15 Abstracts

Department of Computer Scienceparasparashar@rutgers.edu

MS107

DHARMA: Distributed asyncHronous AdaptiveResilient Management of Applications

DHARMA (Distributed asyncHronous Adaptive ResilientManagement of Applications) is a new many-task program-ming model designed with resilience as a primary con-cern. It is a data-flow paradigm that emphasizes over-decomposition of work and exploits both task- and data-parallelism. These qualities enable dynamic and adaptableexecution; yet introduce significant bookkeeping challengesto adequately address faults. In this talk we present anoverview of DHARMAs runtime, discuss key design deci-sions, and present recent empirical results.

Hemanth Kolla, Janine C. Bennett, Jeremiah WilkeSandia National Laboratorieshnkolla@sandia.gov, jcbenne@sandia.gov,jjwilke@sandia.gov

Nicole SlattengrenSandia National Labsnlslatt@sandia.gov

Keita Teranishi, John FlorenSandia National Laboratoriesknteran@sandia.gov, jfflore@sandia.gov

MS107

Understanding the Impact of Transient Faults atthe Application Level in HPC

As new generations of microprocessors are created, softerror rates increase as a consequence of technology scal-ing and reduced energy consumption. Addressing the softerror problem has been identified as key to achieve exas-cale computing. In this talk, we will present our work onunderstanding the resilience problem with an application-level perspective: how they affect different components ofHPC applications? and what mitigation strategies can bedesigned to overcome the problem?

Ignacio LagunaLawrence Livermore National Laboratoryilaguna@llnl.gov

MS108

Numerical Solution of PDEs Posed on Graphs

There is currently considerable interest in a class of models(known as Quantum Graphs) which can be described interms of PDEs posed on large and possibly complex graphs.Such models have found applications in quantum chemistryand solid state physics. The discretization of PDEs posedon graphs using finite element methods and implicit timestepping techniques leads to large, sparse systems of linearequations. This talk will address iterative methods andpreconditioning techniques for solving these systems. Thisis joint work with Mario Arioli.

Michele BenziDepartment of Mathematics and Computer ScienceEmory University

benzi@mathcs.emory.edu

MS108

The Solution of Lyapunov Equations with Nonnor-mal Coefficients

Applications in control require solution of the Lyapunovequation AX + XAT = −BBT . When A is stable and Bhas low rank, the singular values of X often decay rapidly.Existing bounds on those singular values predict slow decaywhen A is far from normal. In contrast, we show that ifthe numerical range of A extends far into the right halfplane, there must be a large difference between the extremesingular values of X.

Mark EmbreeDepartment of MathematicsVirginia Techembree@vt.edu

Jonathan BakerDepartment of Computational and Applied MathematicsRice Universityjpb7@rice.edu

John SabinoThe Boeing Companyjohn-paul.n.sabino@boeing.com

MS108

Indefinite Preconditioning of the Coupled Stokes-Darcy System

We propose the use of an indefinite (constraint) precondi-tioner for the iterative solution of the linear system arisingfrom the finite element discretization of coupled Stokes-Darcy flow. We provide spectral and field-of-value boundsfor the preconditioned system which are independent of theunderlying mesh size. We present numerical results show-ing that the indefinite preconditioner outperforms bothstandard block diagonal and block triangular precondition-ers both with respect to iteration count and CPU times.

Scott LadenheimTemple Universitysaladenh@temple.edu

Prince ChidyagwaiLoyola University MarylandDepartment of Mathematics and Statisticspchidyagwai@loyola.edu

Daniel B. SzyldTemple UniversityDepartment of Mathematicsszyld@temple.edu

MS108

Exploiting Tropical Algebra in the Construction ofPreconditioners

Recently it has been shown that tropical algebra can beusefully applied in numerical linear algebra, for example toapproximate eigenvalues and singular values. The value oftropical algebra is often greater for unstructured matriceswith entries that vary widely in magnitude, i.e., problemsthat are usually considered difficult. In this talk we show

CS15 Abstracts 97

how tropical algebra can be used to understand and de-sign effective incomplete factorization preconditioners forKrylov subspace methods for solving linear systems.

James HookSchool of MathematicsUniversity of Manchesterjames.hook@manchester.ac.uk

Jennifer PestanaMathematical Institute, Oxford University, UKjennifer.pestana@manchester.ac.uk

Francoise TisseurUniversity of ManchesterDepartment of Mathematicsftisseur@maths.manchester.ac.uk

MS109

Error Decomposition and Adaptivity for Re-sponse Surface Approximations with Applicationto Bayesian Inference

We extend our work on error decomposition and adaptiverefinement for response surfaces to focus on the develop-ment of a surrogate model for use in Bayesian inference.Estimation and adaptivity are driven by a quantity of in-terest. The desired tolerance in the error of the posteriordistribution is used to establish a threshold for the accuracyof the surrogate model. Particular focus is paid to accurateestimation of evidence to facilitate model selection.

Corey M. Bryant, Serge PrudhommeICESThe University of Texas at Austincorey.m.bryant@gmail.com, serge@ices.utexas.edu

Todd OliverPECOS/ICES, The University of Texas at Austinoliver@ices.utexas.edu

Tim WildeyOptimization and Uncertainty Quantification Dept.Sandia National Laboratoriestmwilde@sandia.gov

MS109

A Scalable Measure-Theoretic Approach to theStochastic Inverse Problem for Groundwater Con-tamination

We compute approximate solutions to inverse problemsfor determining parameters in groundwater contaminanttransport models with stochastic data on output quanti-ties. We utilize a measure-theoretic inverse framework toperform uncertainty quantification and estimation for theseparameters. The inverse of the map from parameters todata defines a type of generalized contour map. Adjointproblems which are useful in determining a posteriori errorestimates are developed and solved numerically.

Steven MattisUniversity of Texas at Austinsteve.a.mattis@gmail.com

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austin

clint@ices.utexas.edu

Troy ButlerUniversity of Colorado Denvertroy.butler@ucdenver.edu

MS109

Quantifying Error in An Inadequate Model forFlow in a Porous Media

High fidelity models are prohibitively expensive to solve.For porous media flow, these are the Navier-Stokes equa-tions at the pore-scale. To avoid the cost, we usually makesimplifying assumptions leading to a cheaper inadequatemodel. We first give an overview of a general validationframework for these inadequate models. Then we give anexplicit formulation of a model inadequacy for a porous me-dia flow problem and explore how this inadequacy affectsposterior uncertainty.

Teresa PortoneICESUT Austinportone@ices.utexas.edu

Damon McdougallInstitute for Computational Engineering SciencesThe University of Texas at Austindamon@ices.utexas.edu

Todd OliverPECOS/ICES, The University of Texas at Austinoliver@ices.utexas.edu

Robert D. MoserUniversity of Texas at Austinrmoser@ices.utexas.edu

MS109

A Scalable Computational Framework for Estimat-ing Model Discrepancy

In this talk we will focus on devising a scalable computa-tional framework for the estimation of model discrepanciesin uncertainty quantification problems. We will answerquestions like how do we include the choice of model selec-tion in our parameter space, how does our data influencemodel selection, etc. We will answer this in the context ofa measure theoretic framework for stochastic inverse prob-lems.

Nishant PandaColorado State Universitynishant.panda@gmail.com

MS110

Nested Iteration and Adaptive Finite Elements forIce Sheet Models

This talk describes a First-order System Least-squares(FOSLS) formulation of the nonlinear Stokes flow used tomodel glaciers and ice sheets. A Nested Iteration (NI),Newton-FOSLS-AMG approach is used in which the ma-jority of the work is done on coarse grids. A reformula-tion is described that avoids the difficulty of infinite viscos-ity in regions where ice is undergoing small deformations.Numerical tests are presented demonstrating good per-formance of the NI-Newton-FOSLS-AMG approach with

98 CS15 Abstracts

adaptive mesh refinement.

Jeffery M. AllenUniversity of Colorado at Boulderjeffery.allen@colorado.edu

Thomas ManteuffelUniversity of Coloradotmanteuf@colorado.edu

Harihar RajaramUniversity of ColoradoDept. Civil Engineeringhari@colorado.edu

MS110

Parametric Mixed Finite Elements for Two-PhaseFlow Interface Problems

Optimal order convergence of a first-order system leastsquares method using lowest-order Raviart-Thomas ele-ments is presented for domains with curved boundaries.Parametric Raviart-Thomas elements are introduced in or-der to retain the optimal order of convergence in the higher-order case. In particular, an estimate for the normal flux ofthe Raviart-Thomas elements on interpolated boundariesis derived. As an application, boundary values of forces areestimated in the Stokes problem.

Fleurianne BertrandUniversity of Duisburg-Essenfleurianne.bertrand@uni-due.de

Gerhard StarkeUniversity of Duisburg-EssenFakultat fur Mathematikgerhard.starke@uni-due.de

Steffen MunzenmaierGottfried Wilhelm Leibniz University of Hannoversteffen.muenzenmaier@uni-due.de

MS110

Hybrid FOSLS/ll* for Nonlinear Systems of PDEs

This talk presents the extension of Hybrid FOSLS/LL∗ tononlinear systems of PDEs. Hybrid FOSLS/LL∗ combinesthe best features of FOSLS and FOSLL∗. It controls boththe Operator Norm and the L2 norm, approximately min-imizing the Graph Norm of the error. It retains a locallysharp and asymptotically accurate a posterior error esti-mator that can be used with nested iteration and adaptivemesh refinement. The efficacy of this method is demon-strated on Navier/Stokes equation and Stokes equationwith nonlinear viscosity, as used in ice sheet modeling.

Thomas ManteuffelUniversity of Coloradotmanteuf@colorado.edu

Kuo LiuDepartment of Applied MathematicsUniversity of Colorado at Boulderliukuo99@gmail.com

Lei TangDepartment of Applied MathematicsUniversity of Colorado-Boulder

l6tang@gmail.com

John RugeUniversity of Colorado at Boulderruge@colorado.edu

Chad WestphalWabash Collegewestphac@wabash.edu

MS110

A Least Squares Finite Element Method for Cou-pled Surface/Subsurface Flows

A coupled surface/subsurface flow is presented in this talk.The surface flow is modeled by shallow water equationsand the subsurface flow by a generalized Darcy’s law forthe variably saturated case. Coupling is done along aninterface and continuity of pressure and continuity of fluxis enforced. A least squares finite element method for thespatial discretization is utilized and numerical experimentsusing adaptive refinement strategies will be examined.

Steffen MunzenmaierGottfried Wilhelm Leibniz University of Hannoversteffen.muenzenmaier@uni-due.de

MS111

Least Squares Shadowing for Adjoint Calculationof Chaotic and Turbulent Pdes

The adjoint method is an invaluable tool for scientific re-search and engineering design. However, it has been shownthat the traditional adjoint method diverges and producesthe wrong gradient for chaotic and turbulent PDEs. Forthese cases, a new approach, Least Squares Shadowing(LSS) has shown promising results. This talk discusses themethod and its properties, including sources of error andconvergence rates of the adjoint field. Applications includ-ing isotropic homogeneous turbulence are also presented.

Patrick BloniganMITblonigan@mit.edu

Qiqi WangMassachusetts Institute of Technologyqiqi@mit.edu

MS111

Actuator and Sensor Placement for ControllingHigh-Speed Jet Noise

The loudest source of high-speed jet noise, such as found onnaval tactical fighters, appears to be unsteady wavepack-ets that are acoustically efficient but relatively weak com-pared to the main jet turbulence. These wavepackets canbe usefully described by linear dynamics and connected totransient growth mechanisms. Through a component-wisestructural sensitivity analysis of the turbulent jet base-flow, using both the equilibrium and time-average fields,estimates are given as to what location and kind of actu-ators and sensors are most effective, in a linear feedbackcontext, to control the wavepackets to reduce their noise.Low and high frequency approaches are examined wherethe controlling mechanisms differ: the low-frequency con-trol indirectly targets the slow variation of the mean on

CS15 Abstracts 99

which the wavepackets propagate while the high-frequencycontrol targets the wavepackets themselves. The predictedcontrol strategy is evaluated using direct numerical simu-lations on a series of Mach 1.5 turbulent jets.

Mahesh Natarajan, Daniel J. BodonyUniversity of Illinois at Urbana-ChampaignDepartment of Aerospace Engineeringnataraj2@illinois.edu, bodony@illinois.edu

MS111

Using Imperfect Outputs and Derivatives in Large-scale Optimization

The outputs of interest in many engineering systems aretime averages of chaotic solutions. Relevant examples in-clude the lift and drag on aerodynamic bodies, the energyproduced by a fusion reactor, and the (phase-averaged)pressure in an internal-combustion engine. In practice,these outputs must be approximated over a finite integra-tion period, which leads to noise-like errors in the param-eter space. In addition, gradients of these outputs mustbe approximated using ensemble averages or other regu-larizations. Thus, both the outputs and their derivativescontain errors: they are “imperfect.” In this talk we dis-cuss a novel sampling strategy for gradient-based surrogatemodels that aims to address large-scale optimization prob-lems in the context of imperfect data from computationallyexpensive simulations.

Jason E. HickenRensselaer Polytechnic InstituteAssistant Professorhickej2@rpi.edu

MS111

Parallel Bayesian Optimization of Massively Paral-lel Turbulent Flow Simulations

Abstract not available at time of publication.

Chaitanya TalnikarMITtalnikar@mit.edu

MS112

Software Productivity Application: IntegratedModeling for Fusion Energy

Integrated modeling of plasmas is a key scientific capabilityfor the development of fusion as a power source. We willpresent our experience developing the Integrated PlasmaSimulator (IPS), an environment which enables plasmaphysicists to be highly productive in developing and car-rying out a broad range of coupled simulations, while im-proving supercomputer resource utilization. The designand implementation of the IPS is quite general, and it isalso being used in other domains.

David E. BernholdtOak Ridge National LaboratoryComputer Science and Mathematics Divisionbernholdtde@ornl.gov

Wael R. Elwasif, Donald B. BatchelorOak Ridge National Laboratory

elwasifwr@ornl.gov, batchelordb@ornl.gov

MS112

Software Productivity Community Input: Con-cerns and Priorities

This session will start with an overview and history of thesoftware productivity activities across the scientific com-puting community, followed by an open discussion of re-quirements, forums, and opportunities for further engage-ment.

Jeffrey C. CarverDepartment of Computer ScienceUniversity of Alabamacarver@cs.ua.edu

Michael HerouxSandia National Laboratoriesmaherou@sandia.gov

MS112

Overview: Software Productivity Challenges forExtreme Scale Science

The Department of Energy has initiated research in soft-ware productivity for application development and soft-ware infrastructure for extreme-scale scientific computing.The eventual goal is to enable grand challenge sciencesimulations that can survive and even leverage disruptivechanges in extreme-scale computer architectures, and thusenable new frontiers in modeling, simulation, and analysisof complex multiscale and multiphysics phenomena. Thissession will give an overview of DOE activities, includingworkshops, participating communities, and pilot projects.

Lois Curfman McInnesMathematics and Computer Science DivisionArgonne National Laboratorycurfman@mcs.anl.gov

Hans JohansenLawrence Berkeley National LaboratoryComputational Research Divisionhjohansen@lbl.gov

Michael HerouxSandia National Laboratoriesmaherou@sandia.gov

MS112

Software Productivity Challenges in Environmen-tal Applications

Predictive simulations of environmental applications posesignificant challenges for multiscale multiphysics frame-works. Problem complexity requires flexibility to comparedifferent models or model features, to add new models,and to explore model coupling. We will present our expe-rience in addressing these issues in two open-source codes,Amanzi and the Arctic Terrestrial Simulator. We will dis-cuss the importance and challenge of leveraging existingframeworks and libraries as well as components of estab-lished codes.

David MoultonLos Alamos National LaboratoryApplied Mathematics and Plasma Physics

100 CS15 Abstracts

moulton@lanl.gov

Ethan T. CoonLos Alamos National Laboratoryecoon@lanl.gov

Carl SteefelLawrence Berkeley National Laboratorycisteefel@lbl.gov

MS113

Modeling the Effects of Flow on AnticoagulantTherapy

Warfarin is a common anticoagulant used to treat bloodclots. The success of anticoagulation treatment dependson in vivo dynamics that cannot be captured clinically.We combine computational models of warfarin dynamicsand injury-initiated coagulation to determine the impactof blood flow and platelet dynamics on therapeutic out-comes. We highlight the differences between clinical as-sessment and in vivo measures of warfarin effectiveness.Results indicate that blood flow is a significant determi-nant of treatment success.

Erica J. GrahamNorth Carolina State UniversityDepartment of Mathematicsejgraha2@ncsu.edu

Lisette dePillisHarvey Mudd Collegedepillis@hmc.edu

Kaitlyn HoodUCLAektuley1@gmail.com

Yanping MaLoyola Marymount Universityma@math.psu.edu

Julie SimonsTulane UniversityDepartment of Mathematicsjsimons@tulane.edu

Ami RadunskayaPomona CollegeMathematics Departmentaer04747@pomona.edu

MS113

Navier Slip Condition for Viscous Fluids on aRough Boundary

We study the effect of surface roughness on fluid flow overa solid surface. We are able to derive asymptotically aneffective slip boundary condition (Navier slip condition) asa corrector to the no-slip condition on the surface.

Silvia Jimenez BolanosDepartment of MathematicsColgate Universitysjimenez@colgate.edu

Bogdan M. VernescuWorcester Polytechnic Inst

Dept of Mathematical Sciencesvernescu@wpi.edu

MS113

Taming Targeted Drug Delivery: a Mathemati-cal Model of Triggered Drug Delivery Across theBlood-Brain Barrier

The blood-brain barrier is necessary to protect the brainfrom microscopic pathogens and toxic molecules. How-ever, this protective mechanism also poses a challenge tothe delivery of pharmaceutical agents to the brain. Sono-sensitive nanoparticles containing drug show promise as away to overcome this challenge. Here we propose a sched-ule for the treatment of disorders of the brain based ona mathematical model of the circulation, triggered releaseand transport of encapsulated drugs.

Ami RadunskayaPomona CollegeMathematics Departmentaer04747@pomona.edu

MS113

Cooperative Swimming in Viscous Environments

Flagellated organisms exhibit different swimming behav-iors, depending on their local environment. We considerthe cooperative nature of swimming in populations in vis-cous environments, in an effort to understand sperm trans-port. Our approach is a numerical model that relies uponthe method of regularized Stokeslets and is robust to three-dimensional effects. We investigate surface interactions aswell as measures of cooperativity to elucidate why spermhave such a large variation in behavior across species.

Julie Simons, Lisa J. FauciTulane UniversityDepartment of Mathematicsjsimons@tulane.edu, fauci@tulane.edu

Ricardo CortezTulane UniversityMathematics Departmentrcortez@tulane.edu

MS114

A Study of the Entanglement in Polymer Melts

Polymer melts are dense systems of macromolecules. Insuch dense systems the conformational freedom and mo-tion of a chain is significantly affected by entanglementwith other chains which generates obstacles of topologicalorigin to its movement. In this talk we will discuss meth-ods by which one may quantify and extract entanglementinformation from a polymer melt configuration using toolsfrom knot theory. A classical measure of entanglement isthe Gauss linking integral which is an integer topologicalinvariant in the case of pairs of disjoint oriented closedchains in 3-space. For pairs of open chains, we will seethat the Gauss linking integral can be applied to calculatean average linking number. In order to measure the en-tanglement between two oriented closed or open chains ina system with three-dimensional periodic boundary condi-tions (PBC) we use the Gauss linking number to define theperiodic linking number. Using this measure of linking toassess the extend of entanglement in a polymer melt westudy the effect of CReTA (Contour Reduction Topolog-

CS15 Abstracts 101

ical Analysis) algorithm on the entanglement of polyethy-lene chains. Our results show that the new linking measureis consistent for the original and reduced systems.

Eleni PanagiotouUniversity of California Santa Barbaralnpanagiotou@yahoo.com

MS114

A Fast Explicit Operator Splitting Method for aMulti-scale Underground Oil Recovery Model

In this talk, we propose a fast splitting method to solve aMulti-scale underground oil recovery model which includesa third order mixed derivatives term resulting from thedynamic effects in the pressure difference between the twophases. The method splits the original equation into twoequations, one with flux term and one with diffusion termso that the classical numerical methods can be applied im-mediately. Two different spatial discretizations, second-order Godunov-type central-upwind scheme and WENO5scheme, are used to demonstrate that higher order methodprovides more accurate approximation of solutions. Thevarious numerical examples in both one and two dimen-sions show that the solutions may have many different satu-ration profiles depending on the initial conditions, diffusionparameter, and the third-order mixed derivatives parame-ter. The results are consistant with the study of travelingwave solutions and their bifurcation diagram. This is jointwork with C.-Y. Kao, A. Kurganov, Z.-L. Qu.

Ying WangUniversity of Oklahomawang@ou.edu

MS114

Computational Study of Dynamics and Transportin Vortex-Dipole Flows

A finite number of dipole interactions in free space arestudied numerically in order to see how they give rise toa collective fluid flow pattern that is widely seen in oceancurrents and clouds. The classical Lamb Dipole is usedas our vortex unit. The computation is validated by com-paring results with analytic solutions of a free-translatingLamb Dipole. The results have two ingredients. First,the intra- and inner-dipole kinematic pressure fields showdistinct features and they relate the phenomenon of nomass exchange in dipoles interactions. Second, a generalrule of the ultimate vortical flow pattern is observed basedon dipoles interactions in three setups : head on collision,head-end marching, parallel marching.

Ling XuGeorgia State Universityxulingsue@gmail.com

MS114

A Stabilized Explicit Scheme for Coupling Fluid-structure Interactions

We develop a new stabilized explicit coupling partitionedscheme for the fluid-structure interaction problem, wherethe pressure and velocity are decoupled. Proper penaltyterms are applied to control the variations at the interface.Using energy stability analysis, we show that the scheme isstable independent of the fluid-structure density ratio. Nu-merical examples are provided to show that although thepenalty terms degrade the time accuracy, optimal accuracy

is recovered by performing defect-correction subiterations.

Yue YuBrown Universityyuy214@lehigh.edu

MS115

Reaction-diffusion and Electrical Signaling in Neu-rons (Rdesigneur): a System for Multiscale Mod-eling in MOOSE

MOOSE, the Multiscale Object-Oriented Simulation En-vironment, and Rdesigneur support coupled stochasticreaction-diffusion signaling embedded in electrical neuronalmodels. Rdesigneur coordinates loading of electrical andchemical models using standards like NeuroML and SBML.It then populates the complex neuronal geometry with thechemical models, and defines the interfaces between theelectrical and chemical signaling. A set of modular, in-terchangeable numerical engines plug in to the system tocarry out computations at the chosen level of detail.

Upinder Bhalla

National Center for Biological Sciences (NCBS),Bangalorebahlla@ncbs.res.in

MS115

Interactive, Distributed Spatial Stochastic Simula-tion with PyURDME and MOLNs

Computational experiments have lead to new biological in-sights, but the complexity of managing the required dis-tributed computation environments presents a barrier tothe adoption. To address this need, we present MOLNs,a cloud computing appliance for distributed simulationof stochastic reaction-diffusion models. The appliance isbased on IPython and a newly developed, spatial model-ing and simulation package, PyURDME. MOLNs providesan interactive programming platform for development ofsharable and reproducible distributed parallel computa-tional experiments.

Brian DrawertUniversity of California Santa Barbarabdrawert@cs.ucsb.edu

MS115

Gepetto/OpenWorm

Abstract not available at time of publication.

Stephen LarsonOpenWorm.org, MetaCellstephen@openworm.org

MS115

Stochastic Simulation at Your Service

We present StochSS: Stochastic Simulation as-a-Service,an integrated development environment for simulation ofbiological systems with models ranging from ODE to spa-tial stochastic, where a user can build a simple model on alaptop and scale it up to increasing levels of complexity, de-ploying computing resources from the cloud with the pushof a button when they are needed. StochSS is available for

102 CS15 Abstracts

download at www.stochss.org.

Linda R. PetzoldUniversity of California, Santa Barbarapetzold@engineering.ucsb.edu

MS116

Convergence of Inverse Problems using ReducedOrder Models

Inversion requires the repeated solution of expensive for-ward problems and the computation of Jacobians. In re-cent work, we have successfully used reduced order modelsto make nonlinear inversion cheaper. Our approach workswell in practice but does not guarantee convergence. I willdiscuss the solution of a tomography problem using modelreduction and an approach to guarantee convergence.

Eric De SturlerVirginia Techsturler@vt.edu

MS116

From Data to Prediction Via Reduced Parameter-to-Observable Maps: Applications to Antarctic IceSheet Flow

Here we consider the following question: given a large-scalemodel containing uncertain parameters, (possibly) noisyobservational data, and a prediction quantity of interest,how do we construct efficient and scalable algorithms to (1)infer the model parameters from the data, (2) quantify theuncertainty in the inferred parameters, and (3) propagatethe resulting uncertain parameters through the model toissue predictions with quantified uncertainties? We presentefficient and scalable algorithms for this end-to-end, data-to-prediction process under the Gaussian approximationand in the context of modeling the flow of the Antarcticice sheet. We demonstrate that the work required is inde-pendent of the parameter and data dimensions. The key toachieving this is to exploit the fact that, despite their largesize, the observational data typically provide only sparseinformation on model parameters.

Omar GhattasThe University of Texas at Austinomar@ices.utexas.edu

Toby IsaacICESThe University of Texas at Austintisaac@ices.utexas.edu

Noemi PetraUniversity of California, Mercednpetra@ucmerced.edu

Georg StadlerCourant Institute for Mathematical SciencesNew York Universitystadler@cims.nyu.edu

MS116

Combined State and Parameter Reduction for theInversion of Functional Neuroimaging Data

The evaluation of functional neuroimaging data such asEEG and fMRI requires the solution of large-scale inverse

problems constrained by dynamical systems with high-dimensional state and parameter spaces. To acceleratethe inversion, model order reduction can be employed torestrict the optimization to the dominant parameter sub-space and the evaluation of the model to the dominantstate subspace. With this combined state and parame-ter reduction of the underlying model, the inversion be-comes less computationally costly. Two distinct methodsfor the combined reduction of states and parameters arepresented. First, a gramian-based approach, which usesempirical gramians to reduce the state and parameter di-mension based upon the associated controllability and ob-servability. Second, an optimization-based approach thatuses a data-driven greedy approach to assemble the reducedorder model. Both methods are tested and compared on adynamic causal model of a neuronal network.

Christian HimpeInstitute for Computational und Applied MathematicsUniverstiy of Muensterchristian.himpe@uni-muenster.de

Mario OhlbergerUniversitat MunsterInstitut fur Numerische und Angewandte Mathematikmario.ohlberger@uni-muenster.de

MS117

Imaging Biomarkers in Biopharmaceutical Indus-try

Increasingly biopharmaceutical industry is using imagingfor understanding disease and for assessment of therapeuticeffects in all stages of drug development. Different imag-ing modalities can visualize tissue or organ characteristicsmodulated by disease progression and/or therapy. Imagingenables development of predictive disease-based biomark-ers that are translatable between preclinical and clinicalstages of drug development by extracting and mining rel-evant quantitative information from qualitative imagingdata in reliable, efficient and objective manner.

Belma DogdasMerckbelma.dogdas@merck.com

MS117

Simulation-Based Analysis of Complex DecisionOptions in Pharmaceutical Research and Develop-ment

I will present a multi-method modeling and simulationframework for decision analysis in dynamic resource-constrained situations under uncertainty. The frameworkwas developed for, and applied to, nonlinear problems ofstrategic planning, portfolio management, asset valuation,process optimization, and what-if scenario analysis in thecontext of pharmaceutical research and development, andcan be applied to a broader class of real world problems.

Otto RitterIndependent Consultantotto.ritter@gmail.com

MS117

Imaging Genomics for Pharmaceutical Applica-

CS15 Abstracts 103

tions

Imaging Genomics is an emerging field that integratesimaging and genomic data for identifying high-confidencegenesets that relate to a phenotypic response measuredfrom imaging. This talk will explore the use of Imaginggenomics for improved diagnosis, patient stratification andassessment of therapeutic response in oncology. Analysistechniques described will encompass the areas of machinelearning, image processing, and statistics to extract mean-ingful information from high-dimensional, multi-modalitydata for applications in drug discovery and development.

Sangeetha Somayajula, Chandni ValiathanMercksangsom@gmail.com, chandni.valiathan@merck.com;

MS118

Petascale Simulations of Cloud Cavitation Collapse

We present our work on scaling workhorse computationalfluid dynamics kernels and complex applications to thepetascale domain. We show that by extreme algorithmicand code re-engineering we are able to increase sustainedperformance of CFD codes from the traditional single digitregime to a LINPACK like 74%. We employed our codesto study cloud cavitation collapse to unprecedented levelsof fidelity.

Costas BekasIBM Research - ZurichBEK@zurich.ibm.com

MS118

Petascale Simulation of Hurricane Sandy UsingWRF Weather Model on Cray XE6 Blue Waters

The National Center for Atmospheric Research (NCAR)Weather Research and Forecasting (WRF) model has beenemployed on the largest yet storm prediction model usingreal data of over 4 billion points to simulate the landfallof Hurricane Sandy. Using an unprecedented 13,680 nodes(437,760 cores) of the Cray XE6 Blue Waters at NCSA atthe University of Illinois, researchers achieved a sustainedrate of 285 Tflops while simulating an 18-hour forecast.

Pete JohnsenCray Inc.pjj@cray.com

Mark StarkaNCSAm-straka@illinois.edu

Melvyn Shapiro, Alan Norton, Thomas GalarneauNCARmshapiro@ucar.edu, alan@ucar.edu, tomjr@ucar.edu

MS118

Petascale Medical Simulations

We will present the usage of high performance computingsystems for medical applications. The two examples pre-sented are:

• Flow of blood in large arteries with a focus on abdom-inal aortic aneurysms

• Modelling and simulation of bone tissue using directnumerical simulation

We will present methods to integrate simulation into themedical treatment process covering the workflow from CTor MRI based imaging through simulation to visualization.

Michael ReschHLRS, University of Stuttgart, Germanyresch@hlrs.de

Ralf SchneiderHLRSschneider@hlrs.de

MS118

What Are the Priorities Beyond Petascale Com-puting?

Much of the focus in supercomputing has been on floating-point performance since maximizing FLOP/s and GF/Wmeans minimizing time and energy to solution of simula-tions. However, does this apply to low-density problemsand what are the right metrics for these problems? Wediscuss a detailed study of energy and time to solutionperformed on COSMO; a regional model used for climateweather forecasting, and derive effective parameters thatshould be considered in performance optimization.

Thomas C. SchulthessSwiss National Supercomputing Centerschulthess@cscs.ch

MS119

Analysis of a Heterogeneous Multiscale Method forPoroelasticity

In this paper, we develop a highly parallelizable numeri-cal method to solve the heterogeneous linear poroelastic-ity equations in multiple dimensions via operator splittingand a finite-volume based heterogeneous multiscale methodfor the linear elasticity and reaction diffusion equations.We demonstrate convergence both analytically and numer-ically, and analyze its computational complexity on highperformance computers.

Paul M. DelgadoUTEPpmdelgado2@utep.edu

Vinod Kumar, Son Young YiUniversity of Texas at El Pasovkumar@utep.edu, syi@utep.edu

MS119

Experimental Analysis of the Performance of Geo-Claw, AnuGA and SurfWB-UC Numerical Modelsfor the Simulation of Tsunami Inundation Phenom-ena

In this study we test and show the performance of threenumerical codes for modeling tsunami inundation phenom-ena (GeoClaw, AnuGA and SurfWB-UC), by experimen-tally analyzing the numerical convergence to exact analyti-cal solutions of the non-linear shallow water equations, andalso, the speed-up and efficiency of their parallel implemen-tation. This, in order to highlight the complexity of repre-senting tsunami wave inundation in the presence of dry-wet

104 CS15 Abstracts

interfaces and shock-waves under variable bathymetry.

Jose GalazPontificia Universidad Catolica de Chile, CHILEjdgalaz@uc.cl

Rodrigo CienfuegosHydraulic and Environmental Engineeering DepartmentPontificia Universidad Catolica de Chileracienfu@ing.puc.cl

MS119

Stabilization in Relation to Wavenumber in HDGMethods

We study the Hybrid Discontinuous Galerkin (HDG)method for complex wavenumber cases in acoustics andelectromagnetics and show how the HDG stabilization pa-rameter must be chosen in relation to the wavenumber. Weshow that the commonly chosen HDG stabilization param-eter values are not appropriate for all complex wavenum-bers, then discover a constraint on the stabilization pa-rameter, dependent on the wavenumber, that guaranteesunique solvability of both the global and the local HDGproblems. We also perform a dispersion analysis for theHelmholtz case.

Nicole OlivaresPortland State Universitynmo@pdx.edu

Jay GopalakrishnanPortland state universitygjay@pdx.edu

Liang LiUniversity of Electronic Science and Technology of Chinaplum liliang@uestc.edu.cn

Ronan PerrusselUniversite de Toulouse; CNRS;INPT, UPS;Laboratoire Plasma et Conversion d’Energie (LAPLACE)perrussel@laplace.univ-tlse.fr

MS119

Solving the Heat Equation with Wavelets

The numerical solution of parabolic time evolution prob-lems such as the heat equation is required in numerousapplictions. Solving this problem using the boundary ele-ment method (BEM) is an attractive alternative to tradi-tional methods, such as Finite Elements combined with atime-stepping scheme. Using BEM generally leads to fullsystems, so we combine it with a wavelet method. Thisleads to sparse system matrices that can be solved in lin-ear complexity.

Anne ReinarzUniversity of Reading, UKa.reinarz@pgr.reading.ac.uk

Alexey ChernovUniversity of BonnHausdorff Center for Mathematics

a.chernov@reading.ac.uk

MS119

Incompressible Flow and (Stabilised) Mixed FiniteElement Methods on Highly Stretched Meshes

Anisotropic refinement is an interesting concept to resolvelocal features of solutions. Unfortunately, the stability ofa mixed finite element method may depend on the aspectratio and other mesh properties caused by the refinement.We show which part of the pressure space is responsiblefor the deterioration of stability. By imposing a minimalamount of constraints on the pressure, two mixed methodscircumventing the behaviour arise. Numerical experimentsconfirm their stability.

Andreas WachtelUniversity of Strathclyde, UKandreas.wachtel@strath.ac.uk

Mark AinsworthBrown Universitymark.ainsworth@brown.edu

Gabriel R. BarrenecheaUniversity of Strathclydegabriel.barrenechea@strath.ac.uk

MS119

Sublinear Preconditioners for the 2D HelmholtzEquation

We present a new preconditioner for 2D Helmholtz equa-tion in the high frequency regime based on domain de-composition, integral operators and fast algorithms. Thepreconditioner is designed to be seamlessly integrated in ahigh performance computing environment. The algorithmseparates the computation in two parts, one expensive, buthighly parallel, and a second one, sequential but with sub-linear complexity; keeping a sub-linear overhead of commu-nication per solve. We will discuss the new algorithm thesupporting mathematics and prove that the new methodhas sub-linear complexity. Finally, we will demonstrate thesub-linear complexity numerically on examples from geo-physics.

Leonardo Zepeda-NnezMassachusetts Institute of Technologylzepeda@math.mit.edu

Laurent DemanetProfessor of Mathematics, MITlaurent@math.mit.edu

MS120

A Fast Conservative Spectral Solver for the Non-linear Boltzmann Collision Operator

We present a conservative spectral method for the fullynonlinear Boltzmann collision operator based on theweighted convolution structure in Fourier space developedby Gamba and Tharkabhushnanam. The novelty of thisapproach consists of factorizing the convolution weighton quadrature points by exploiting the symmetric na-ture of the particle interaction law. This procedure re-duces the computational cost and storage of the methodto O(M2N4logN) from the O(N6) complexity of the origi-nal spectral method, whereN is the number of velocity grid

CS15 Abstracts 105

points in each velocity dimension and M is the number ofquadrature points in the factorization. We will present nu-merical results that exhibit the efficiency of this approach.

Jeffrey HaackUniversity of Texas at Austinhaack@math.utexas.edu

Jingwei HuThe University of Texas at Austinhu342@purdue.edu

Irene M. GambaDepartment of Mathematics and ICESUniversity of Texasgamba@math.utexas.edu

MS120

Kinetic Equation in a Bounded Domain

Half-space problem is known as the key to understand theboundary layers for kinetic equations (Boltzmann equa-tion, neutron transport equation etc.) in a bounded do-main, where sharp transitions from kinetic to fluid regimepresent. In this talk, I will present a damping-recoveryscheme to obtain the solution in a general setting: theequation is modified by a damping term, and a recoveryprocess is proposed. The damped equation is proved to bewell-posed, and a spectral method is designed to solve it.

Qin LiComputing and Mathematical SciencesCalTechqinli@cms.caltech.edu

MS120

High-Order Semi-Lagrangian DiscontinuousGalerkin Methods for Kinetic Plasma Models

We present a high-order operator split discontuousGalerkin (DG) method for solving the Vlasov-Poisson sys-tem. Our hybrid method relaxes strict CFL limitation byusing semi-Lagrangian techniques, and we permit compli-cated geometries in configuration space with unstructuredgrids. We present 2D-2V results including the formation ofa plasma sheath in the proximity of a cylindrical Langmuirprobe, as well as the simulation of a single-species chargedparticle beam in a particle accelerator.

David C. SealDepartment of MathematicsMichigan State Universityseal@math.msu.edu

James A. RossmanithIowa State UniversityDeparment of Mathematicsrossmani@iastate.edu

Andrew J. ChristliebMichigan State UniverityDepartment of Mathematicsandrewch@math.msu.edu

MS120

A Monte Carlo Method with Negative Particlesfor General Binary Collisions and Application to

Coulomb Collisions

In this work we propose a novel negative particle methodfor the general bilinear collision operators in the spatialhomogeneous case and apply it to the Coulomb collisions.This new method successfully reduces the growth of parti-cle numbers from the numerical time scale to the physicaltime scale for the Coulomb collisions. We also propose aparticle resampling method to reduce the particle numberto further improve the efficiency. Various numerical sim-ulations are performed to demonstrate the high accuracyand efficiency.

Bokai YanDepartment of MathematicsUCLAbyan@math.ucla.edu

Russel CaflischDepartment of MathematicsUniversity of California, Los Angelescaflisch@math.ucla.edu

MS121

OCC-Based Meshing for RGG Applications UsingMeshKit

High fidelity simulations of physical phenomena describedon complex geometries involve efficient generation of opti-mally resolved computational meshes. We present a com-pletely open-source end-to-end workflow focused on nuclearengineering problems that provide components to describethe geometry representation, parallel mesh generation andin-situ visualization. This is made possible with a OCC-based geometry engine used in combination with a wide ar-ray of mesh generation algorithms implemented in MeshKitexposed through a GUI from Kitware called RGGNuclear.

Rajeev JainArgonne National Laboratoryjain@mcs.anl.gov

Jacob BeckerKitwarejacob.becker@kitware.com

Vijay MahadevanArgonne National Laboratorymahadevan@anl.gov

Patrick ShriwiseUniversity of Wisconsin, Madisonshriwise@wisc.edu

Robert O’BaraKitwarebob.obara@kitware.com

Iulian GrindeanuArgonne National Laboratoryiulian@mcs.anl.gov

MS121

High-Order Surface Reconstruction with Appli-cations in Parallel Meshing and Finite ElementSolvers

We present a method for reconstructing high-order surfaces

106 CS15 Abstracts

from a given unstructured surface mesh, based on weightedleast squares polynomial fitting. The method can achievethird and even higher order accuracy. We present the the-oretical framework and compare it with existing methods.We also present its applications in mesh refinement and fi-nite element methods, and show that the meshes adaptedor refined using the proposed method preserve the order ofconvergence of numerical discretizations.

Xiangmin JiaoStony Brook Universityxiangmin.jiao@stonybrook.edu

Navamita RayArgonne National Labratorynray@mcs.anl.gov

Cao Lu, Xinglin ZhaoStony Brook Universityclu@ams.sunysb.edu, xinglin.zhao@stonybrook.edu

MS121

Parallel Mesh Curving and Adaptation with High-Order Surface Continuity for High-Order Finite El-ement Simulations

This talk presents work on developing parallel curvedmeshing techniques for unstructured meshes where high-order surface continuity is maintained for the triangular el-ement faces representing the curved domain surfaces. Op-timal nodal placement methods are studied and appliedto minimize interpolation error. Mesh modification opera-tions are extended to deal with the complexities involvedwith adapting high-order curved meshes. Benefits of us-ing curved meshes with high-order continuity are demon-strated in a set of CFD applications.

Qiukai LuRensselaer Polytechnic Instituteluq3@rpi.edu

Dan A. IbanezRensselaer Polytechnic InstituteSCORECdibanez@scorec.rpi.edu

Mark S. ShephardRensselaer Polytechnic InstituteScientific Computation Research Centershephard@rpi.edu

MS121

Parallel Meshing Technologies for Large ScaleAdaptive Simulations

Scalable parallel simulation workflows require mesh gen-eration and adaptation components to operate in paral-lel and interact with the analysis code using in-memoryinterfaces. Recent developments include improvements inscalability, and the ability to adapt anisotropic boundarylayer elements in both tangential and normal directions.A procedure to distribute the geometric model to avoidmaintaining the entire geometry on each process has beendeveloped. Specific examples of in-memory interfaces withanalysis codes will be presented.

Saurabh TendulkarSimmetrix Inc.saurabh@simmetrix.com

Mark BeallSimmetrix, Inc.mbeall@simmetrix.com

Rocco NastasiaSimmetrix Inc.nastar@simmetrix.com

Mark S. ShephardRensselaer Polytechnic InstituteScientific Computation Research Centershephard@rpi.edu

MS122

Modeling Active Flows and Stress Generation inMicrotubule-Motor Networks

We describe a multi-scale theory for biologically-inspiredsoft active materials composed of microtubules crosslinkedby molecular motors. Brownian dynamics simulations ofmicrotubules with motile crosslinks reveal that activity-generated extensile stresses arise from both polarity sortingand crosslink relaxation. These simulations yield polarity-dependent active stress coefficients for a Doi-Onsager ki-netic theory that captures activity-induced hydrodynamicflows. The model exhibits turbulent-like dynamics, andthe continuous generation and annihilation of disclinationdefects associated with coherent flow structures.

Robert Blackwell, Meredith Betterton, Matthew GlaserUniversity of Coloradorobert.blackwell@colorado.edu,meredith.betterton@colorado.edu,matthew.glaser@colorado.edu

Michael J. ShelleyNew York UniversityCourant Inst of Math Sciencesshelley@cims.nyu.edu

Tony GaoCourant Institute of Mathematical SciencesNew York Universitytgao@cims.nyu.edu

MS122

Computational Models of Cilia and Flagella in aBrinkman Fluid

The interaction between dynamic elastic structures andtheir surrounding fluid is important for sperm navigationand cilia beating within airways. We study a generalizedEuler elastica immersed in a Brinkman fluid, a viscous fluidfilled with a network of proteins. Regularized Greens func-tions for Brinkman flow are used to investigate emergentdynamics with preferred kinematics. Results are presentedfor swimming speeds, synchronization, and efficiency offlagella with planar waveforms in a Brinkman fluid.

Karin LeidermanApplied MathematicsUC Mercedkleiderman@ucmerced.edu

Sarah D. OlsonWorcester Polytechnic Institute

CS15 Abstracts 107

sdolson@wpi.edu

MS122

Fluid Coupling in Continuum Modeling of Micro-tubule Gliding Assays

Active networks are suspensions of actuated filaments ob-tained by mixing cytoskeletal filaments and motor proteincomplexes. We focus on gliding assays, where the molec-ular motors are anchored to a bottom plate. We presenta continuum macroscopic model including the evolution ofrigid filaments density, bound and free motors densitiesand fluid velocity. We focus on cumulative hydrodynamiceffects and our numerical simulations show the emergenceof ordered subregions.

Tamar ShinarComputer SciencesUC Riversideshinar@cs.ucr.edu

Steven CookUC Riversidescook005@cs.ucr.edu

Christel HoheneggerUniversity of UtahDepartment of Mathematicschoheneg@math.utah.edu

MS122

Accurate Simulations of Complex Fluid Flow inDomains with Smooth Boundaries Using Fft-BasedSpectral Methods

We present a method for simulating complex fluid flow indomains with smooth boundaries using simple FFT-basedspectral methods to advance the stress evolution equation.Dirichlet conditions for the velocity are imposed by solv-ing Stokes’ equations using a novel high-order saddle-pointmethod. Our numerical scheme automatically generatesa smooth extension for the velocity field over the non-physical regions of the computational domain, allowing forstraightforward coupling with the stress equation. We in-vestigate the convergence of channel flow for an Oldroyd-Bfluid to the analytical solution in the limit of vanishingartificial stress-diffusion.

David SteinUniversity of California Davisdbstein@math.ucdavis.edu

Becca ThomasesUniversity of California at Davisthomases@math.ucdavis.edu

MS123

Further Developments in the Flux ReconstructionMethod

While the Flux Reconstruction method can recover thenodal DG method, it also allows a wide number of al-ternatives by different choices of the correction function.The presentation will discuss some alternatives optimizedto improve accuracy or to reduce complexity.

Antony JamesonProfessor, Department of Aeronautics & Astronautics

Stanford Universityjameson@baboon.stanford.edu

MS123

Spectral Difference Method for Large Eddy Simu-lation Using Non-Conforming and Sliding Meshes

Recently, we have developed a simple, efficient, and high-order accurate sliding-mesh interface approach to the spec-tral difference method for 2D CFD simulations. The ex-tension of the sliding interface spectral difference (SSD)method to solving unsteady turbulent flows requires care-ful verification and validation studies. This abstract re-flects two aspects of our research. On the aspect of numer-ical methods, we report the development of the spectraldifference method for a parallel solver of turbulent com-pressible flows on non-conforming and sliding meshes withall hexahedral elements. On the aspect of verification andvalidation, we report Large Eddy Simulation results of aturbulent Taylor Couette flow and compare to publishedDirect Numerical Simulation data.

Bin Zhang, Chunlei LiangGeorge Washington Universitybzh@gwmail.gwu.edu, chliang@gwu.edu

MS123

High-Order Methods for Turbulent Flow Simula-tions on Deforming Domains

We present new high-order accurate methods for movingdomains with large deformations. Unstructured movingmeshes are generated by a sequence of entirely local op-erations. This produces high-quality meshes throughoutthe simulation, and provides a simple description of themesh changes between each timestep. Using this informa-tion we can construct efficient numerical schemes, and weconsider both space-time formulations and ALE/projectionbased methods. We demonstrate our methods on a rangeof problems involving complex domain deformations.

Per-Olof PerssonUniversity of California BerkeleyDept. of Mathematicspersson@berkeley.edu

MS123

On the Utility of High-Order Methods for Unstruc-tured Grids: A Comparison Between PyFR andIndustry Standard Tools

Conventional unstructured computational fluid dynamicssolvers used by industry typically employ second-order ac-curate spatial discretizations on CPUs. In this work weassess the potential accuracy and efficiency benefits of high-order unstructured schemes implemented on GPUs, whencompared to such industry standard tools. We compareaccuracy and efficiency between the two methods for tur-bulent flow computations performed via direct numericalsimulation and large eddy simulation.

Brian C. VermeireImperial College Londonb.vermeire@imperial.ac.uk

Freddie Witherden, Peter E. VincentDepartment of AeronauticsImperial College London

108 CS15 Abstracts

freddie.witherden08@imperial.ac.uk,p.vincent@imperial.ac.uk

MS124

Massively Parallel Phase-Field Simulations usingHPC Framework waLBerla

We present a massively parallel phasefield code, based onthe HPC framework waLBerla, for simulating solidificationprocesses of ternary eutectic systems. Various code opti-mizations are shown, including buffering strategies, vector-ization and load balancing techniques. To reduce the ef-fective domain size, a windowing mechanism is developed,such that only the region around the solidification front hasto be simulated. Our simulations are run on SuperMUC, asupercomputer ranked number 12 in the Top500 list, usingup to 32768 cores.

Martin BauerUniversity of Erlangen-NurembergDepartment of Computer Sciencemartin.bauer@fau.de

Harald KoestlerUniversity Erlangen-Nurnbergharald.koestler@fau.de

Ulrich J. RuedeUniversity of Erlangen-NurembergDepartment of Computer Science (Simulation)ulrich.ruede@fau.de

MS124

Large Scale and Massive Parallel Phase-field Simu-lations of Pattern Formations in Ternary EutecticSystems

Different patterns are forming during directional solidifica-tion of ternary eutectics, depending on the physical param-eters, with significant influence on the mechanical proper-ties of the material. These patterns are studied with athermodynamic consistent phase-field model based on theminimization of the grand potential difference, using themassive parallel framework waLBerla. We show structureformation on large scale domains, which give rise to spi-ral growth and compare them to experiments as well asanalytic solutions.

Johannes Hotzer, Marcus Jainta, Philipp Steinmetz,Britta NestlerKarlsruhe Institute of Technology (KIT)Institute of Applied Materials (IAM-ZBS)johannes.hoetzer@kit.edu, marcus.jainta@kit.edu,philipp.steinmetz@kit.edu, britta.nestler@kit.edu

MS124

Multi-Gpu Phase-Field Lattice Boltzmann Simula-tions for Growth and Moving of Binary Alloy Den-drite

Solidification microstructures are of great significance inmaterials science and engineering. The melt convection al-ways occurs in casting and greatly affects the solidificationmicrostructures. Meanwhile, the dendrite growth simula-tion in melt convection needs much computational cost. Inthis study, we accelerate the simulation by employing thephase-field lattice Boltzmann method and multiple graph-ics processing unit computational scheme. The dendrite

growths accompanying movement and rotation are simu-lated by the GPU accelerated phase-field lattice Boltzmannscheme.

Tomohiro TakakiKyoto Institute of TechnologyMechanical and System Engineeringtakaki@kit.ac.jp

Roberto RojasGraduate School of Science and TechnologyKyoto Institute of Technologyrcrmroberto rojas@hotmail.com

Takashi ShimokawabeGlobal Scientific Information and Computing CenterTokyo Institute of Technologyshimokawabe@sim.gsic.titech.ac.jp

Takayuki AokiTokyo Institute of Technologytaoki@gsic.titech.ac.jp

MS124

Large-scale Multi-Phase-Field Simulation of Ab-normal Polycrystalline Grain Growth using TSUB-AME2.5 GPU-Supercomputer

The multi-phase-field method has attracted attention asa very promising tool for simulating microstructure evo-lutions in polycrystalline materials. We developed amultiple-GPU computing technique that facilitate efficient3D simulations. Using the technique developed, we per-formed large scale 3D multi-phase-field simulations of ab-normal polycrystalline grain growth on a GPU-cluster andon the TSUBAME2.5 supercomputer at the Tokyo Insti-tute of Technology.

Akinori YamanakaTokyo Institute of TechnologyGraduate School of Science and Engineeringa-yamana@cc.tuat.ac.jp

Masashi OkamotoTokyo University of Agriculture and Technology50014643014@st.tuat.ac.jp

Takashi ShimokawabeGlobal Scientific Information and Computing CenterTokyo Institute of Technologyshimokawabe@sim.gsic.titech.ac.jp

Takayuki AokiTokyo Institute of Technologytaoki@gsic.titech.ac.jp

MS125

Discussion on Future Directions of Noisy Networks

The organizers will lead a discussion, with participationfrom the other speakers and attendees, on the current stateof research on analysis of networks with noise and uncer-tainty, and possible future directions. The discussion willfocus on the implications of network noise from a theoret-ical perspective, and its impact in different applications,including the ones presented. A key point will be the inter-play between theory and practice in this emerging subfield

CS15 Abstracts 109

of network science.

Sanjukta BhowmickDepartment of Computer ScienceUniversity of Nebraska, Omahasbhowmick@unomaha.edu

Benjamin A. MillerMIT Lincoln Laboratorybamiller@ll.mit.edu

MS125

Using Consensus to Inform Stochastic Graph Ag-gregation

Learning an appropriate graph representation from noisy,multi-source data is an area of increasing interest. Wepresent a consensus-based framework to improve the stabil-ity and quality of graph representations learned by stochas-tic graph aggregation techniques. Furthermore, we usemetrics of stability to quantify our confidence on whichedges represent noise versus structure. We demonstrate theeffectiveness of our framework using the Locally BoostedGraph Aggregation algorithm on a variety of synthetic andreal datasets.

Layla OesperBrown Universitylayla oesper@brown.edu

Rajmonda CaceresLincoln LaboratoryMassachusetts Institute of Technologyrajmonda.caceres@ll.mit.edu

MS125

Statistical Inference on Errorfully ObservedGraphs

For statistical inference on graphs, the existence of edgesis frequently based on imperfect assessment. Instead ofobserving a graph, for each potential edge we observe a“edge feature’ which is used to assess the presence of anedge. Moreover, we face a quantity/quality trade-off: theproportion of assessed potential edges decreases with theedge features quality. For the stochastic blockmodel, wederive the optimal quantity/quality operating point for aspecific inference task.

Carey PriebeJohns Hopkins Universitycep@jhu.edu

Daniel L. SussmanHarvard Universitydpmcsuss@gmail.com

Minh TangJohns Hopkins Universitymtang10@jhu.edu

Joshua VogelsteinDuke Universityjo.vo@duke.edu

Vince Lyzinski, Donniell Fishkind, Nam Lee, YoungserParkJohns Hopkins University

vincelyzinski@gmail.com, fishkind@ams.jhu.edu,nhlee@jhu.edu, youngser@jhu.edu

Avanti AthreyaJohns Hopkins UniversityDepartment of Applied Mathematics and Statisticsdathrey1@jhu.edu

MS125

Pockets of Instability in Network Centrality Met-rics

We discuss how the sensitivity of centrality metrics alter asincreasingly higher percentage of edges are altered in thenetwork. Ideally the metric should change commensuratelywith the change in network. However, we see that insteadof a monotonic change, there are certain pockets of verticeswhere the centrality values are stable and other pocketswhere they change significantly. We also discuss how thestructure of the network leads to the formation of thesepockets.

Vladimir UfimtsevUniversity of Nebraska, Omahavufimtsev@unomaha.edu

Sanjukta BhowmickDepartment of Computer ScienceUniversity of Nebraska, Omahasbhowmick@unomaha.edu

MS126

Kernel-Based Image Reconstruction

In image reconstruction a central problem is the approxi-mate inversion of certain integral transforms like the Radontransform, the spherical mean transforms, or in a more gen-eral setting the Funk transform. Popular techniques for theapproximate reconstruction are kernel-based interpolationmethods. This methods are easy to implement and fastalgorithms are in many cases available. Nevertheless, themathematical analysis of such methods is quite involved.We will discuss several problems regarding these proce-dures and compare some kernel-based methods for imagereconstruction from spherical mean value data.

Frank FilbirInstitute of Biomathematics and BiometryHelmholtz Center Munichfilbir@helmholtz-muenchen.de

MS126

A Numerical Study of the Accuracy of Divergence-Free Kernel Approximations

We present a numerical study of the accuracy ofdivergence-free radial basis function interpolants in 2D and3D and preliminary numerical results indicating a poly-nomial flat limit (ε → 0). When compared to standardinterpolants, our results indicate that using a divergence-free basis improves accuracy of the derivatives in certaindirections. In this talk, we explore strategies for improvingapproximations in these directions and compare accuracyof methods based on radial kernels and multivariate poly-nomials.

Arthur MitranoArizona State University

110 CS15 Abstracts

arthur.mitrano@asu.edu

MS126

Meshfree Computations with SPH and VortexMethods

We will provide a broad overview of Smoothed ParticleHydrodynamics (SPH) and Vortex Methods. This is fol-lowed by a brief discussion on some of the software toolsthat are being developed in our group. We will then lookat recent comparisons of the vortex method and the SPHfor incompressible fluid flow. This is followed by resultsfrom recent work on using SPH for gas dynamics, floodsimulation, explosions, non-Newtonian fluids and Kelvin-Helmholtz instabilities.

Prabhu RamachandranDepartment of Aerospace EngineeringIndian Institute of Technology, Bombayprabhu@aero.iitb.ac.in

MS126

Reproducing Kernels in Parametric Partial Differ-ential Equations

In this talk, we address the problem of approximating thesolution of a parametric partial differential equation. Thenumber of parameters in the differential equation deter-mines the dimensionality of the reconstruction problem.Without any further information such problems suffer fromthe curse of dimensionality. The physical model expressedin the partial differential equation, however, allows in manypractical situations to identity a smaller set of importantparameters. The identification of these important param-eters build also the basis for many algorithms from ma-chine learning. We will outline this connection in a spe-cific situation using problem adapted reproducing kernels.Further, we will use sampling inequalities to show deter-ministic a priori (often exponential) convergence rates ofa rather large class of regularized reconstruction schemes.This is partly based on joint work with M. Griebel and B.Zwicknagl (both Bonn University).

Christian RiegerUniversitat BonnCollaborative Research Centre 1060rieger@ins.uni-bonn.de

MS127

Recent Developments in Forest-of-octrees AMR

Forest-of-octrees AMR offers both geometric flexibility andparallel scalability and has been used in various finite ele-ment codes for the numerical solution of partial differentialequations. Low and high order discretizations alike are en-abled by parallel node numbering algorithms that encapsu-late the semantics of sharing node values between proces-sors. More general applications, such as semi-Lagrangianand patch-based methods, require additional AMR func-tionalities. In this talk, we present algorithmic conceptsessential for recently developed adaptive simulations.

Carsten BursteddeUniversitat Bonnburstedde@ins.uni-bonn.de

Toby IsaacICES

The University of Texas at Austintisaac@ices.utexas.edu

Omar GhattasThe University of Texas at Austinomar@ices.utexas.edu

Donna CalhounBoise State Universitydonnacalhoun@boisestate.edu

MS127

An Implicit, High-Order Accurate, IncompressibleNavier-Stokes Solver on Overlapping Grids

This talk describes an implicit, high-order accurate methodfor incompressible flow combining compact spatial dis-cretizations with approximate factorization schemes andgeometric multigrid on overlapping grids. Efficient implicittime discretization is achieved via a second order accu-rate approximately factored Crank-Nicolson method thatincorporates the compact spatial approximations into a se-quence of fast banded solves. When used with Overture’shigh-order accurate matrix-free multigrid for the pressureequation, our method provides an efficient high-resolutionsolver for LES applications.

Kyle ChandLawrence Livermore National Laboratorychand1@llnl.gov

MS127

Exploring Astrophysical Flows with High-fidelityLarge-scale Simulations

We present a systematic study of compressible flow prob-lems found in many astrophysical environments using high-fidelity, large-scale and multiphysics numerical simulations.It covers topics like developing numerical models, designingsimulation strategies according to the code scalability, andevaluating simulation results in comparisons with observa-tion results. We will share our user experiences in usingcodes on DOE’s and NSF’s leading supercomputers andour interests in improving the efficiency of parallelizationand memory usage.

Min LongDepartment of PhysicsBoise State Universityminlong@boisestate.edu

MS127

Runtimes and Autotuning and Hybrid, Oh My!Chombo Navigates the Waters of Exascale

Adaptive Mesh Refinement (AMR) applications require along-term sustained investment in software infrastructureto create scalable solvers that are capable of utilizing thefull capabilities of the largest available HPC platforms.The scalable AMR framework Chombo provides an envi-ronment for rapidly assembling portable, high-performanceAMR applications for a broad variety of scientific disci-plines. In this talk, we present several levels of parallelismthat can be exploited by Chombo to achieve scaling be-yond petascale. These levels include threading the loadhandled sequentually by each MPI rank, fine-grain paral-lelism within the dimensional loops, and instruction-levelparallelism models to make use of vector processing within

CS15 Abstracts 111

a larger threading model.

Brian Van StraalenLawrence Berkeley National LaboratoryCompuational Research Divisionbvstraalen@lbl.gov

MS128

Nek5000: An Environment for Scalable AlgorithmDevelopment and Production Simulations

Nek5000 is an open source spectral element code for fluidflow and heat transfer. As Nekton 2.0, it was the first com-mercially available software for distributed memory com-puters and, with excellent strong scaling (to beyond a mil-lion processes) it is being used by hundreds of researchersin a variety of applications such as combustion, vascularflow modeling, stability analysis, and MHD. We discussextensibility, scalability, and performance of Nek5000 inthis context.

Paul F. FischerArgonne National Laboratoryfischer@mcs.anl.gov

MS128

Anisotropic Mesh Adaptation for the Many-coreEra

Computing hardware is currently undergoing a rapid trans-formation from the historical trend of increasingly com-plex single processing units operating at ever increasingclock frequency, towards high numbers of low power pro-cessing units where computing throughput is achieved byincreasing concurrency. The consequence for models is thattheir constituent algorithms must be amenable to paral-lelization, otherwise the (quasi-)serial section will quicklybecome the dominant computational cost. In short, algo-rithms without a high degree of parallelism are potentiallyfacing extinction as the computational environment shifts.Many algorithms that are important for the finite elementmethod, such as matrix-vector multiply, are readily paral-lelizable on many levels and lots of effort is going into opti-mal strategies on a range of different types of architectures.However, other important algorithms, such as mesh adap-tation, have complex data interdependencies and irregulardata access patterns. In such cases the overhead associ-ated with parallelization can easily outweigh the gains. Inthis talk we describe the challenges, and solutions, for par-allelizing anisotropic mesh adaptation. Previous work inthis field has mostly been limited to domain decomposi-tion methods implemented using MPI. As more finite ele-ment codes are capable of running in a mixed MPI-threadparallel mode, mesh it is necessary for mesh adaptation toalso exploit thread level parallelism. We find that domaindecomposition methods are not particularly successful forthread parallelism for this class of problem. Instead, aboarder range of parallelization strategies specifically de-signed for irregular computation must be adopted. Per-formance analysis shows that fast scalable performance isachieved but there are still room for improvement. We willconsider what novel trends in parallel programming modelsand hardware might create new opportunities

Gerard J GormanDepartment of Earth Science and EngineeringImperial College London

g.gorman@imperial.ac.uk

MS128

H-to-P Efficiently: a Nektar++ Update on Com-parisons of Cg and Hdg

Since the inception of discontinuous Galerkin (DG) meth-ods for elliptic problems, there has existed a question ofwhether DG methods can be made more computationallyefficient than continuous Galerkin (CG) methods. Fewerdegrees of freedom, approximation properties for ellipticproblems together with the number of optimization tech-niques, such as static condensation, available within theCG framework made it challenging for DG methods to becompetitive until recently. However, with the introduc-tion of a static-condensation-amenable DG method, thehybridizable discontinuous Galerkin (HDG) method, it hasbecome possible to perform a realistic comparison of CGand HDG methods when applied to elliptic problems. Inthis talk, we focus on embedded manifolds, which are con-sidered a valid approximation for many scientific problemsranging from the shallow water equations to geophysics.We describe a comparison between a CG and an HDGnumerical discretiztion in 2D, 3D and of an embeddedtwo-dimensional manifold using high-order spectral/hp el-ements.

Mike KirbyUniversity of UtahSchool of Computingkirby@cs.utah.edu

MS128

Heterogeneous Computing with a HomogeneousCodebase

It is likely that finite element codes of the future will needto support a variety of hardware platformsincluding bothconventional CPUs and accelerators such as GPUs. How-ever, existing implementation strategies often result in fea-ture disparity and quickly succumb to bit-rot. In this talkI will explain the approach we have taken in PyFR thatpromotes feature and performance parity across platformswith an emphasis on sustainability.

Freddie Witherden, Peter E. VincentDepartment of AeronauticsImperial College Londonfreddie.witherden08@imperial.ac.uk,p.vincent@imperial.ac.uk

MS129

A Comparative Analysis of of Asynchronous ManyTask Programming Models for Next GenerationPlatforms

Next generation platform architectures will require a fun-damental shift in programming models due to a combina-tion of factors including extreme parallelism, data localityissues (for managing both performance and energy usage),and resilience. The asynchronous, many-task programmingmodel is emerging as a leading new paradigm to addressthese issues, with many variants of this new model beingproposed. This talk surveys some of the leading proposedruntimes, highlighting their key design decisions, strengths,and weaknesses.

Janine C. BennettSandia National Laboratories

112 CS15 Abstracts

jcbenne@sandia.gov

H. KollaSNLhnkolla@sandia.gov

Jeremiah Wilke, Keita TeranishiSandia National Laboratoriesjjwilke@sandia.gov, knteran@sandia.gov

Nicole SlattengrenSandia National Labsnlslatt@sandia.gov

Greg Sjaardema, Samuel KnightSandia National Laboratoriesgdsjaar@sandia.gov, sknigh@sandia.gov

MS129

Structured Dagger: Supporting Asynchrony withClarity

Abstract not available at time of publication.

Jonathan LifflanderUniversity of Illinoisjliff2@illinois.edu

MS129

Using Multiple Dags to Ensure Portability andScalability in Large Scale Computations Using Uin-tah

Computational modeling of the hazards posed by thou-sands of explosive devices during a Deflagration to Deto-nation Transition (DDT),requires petascale computing re-sources to resolve the spatial and temporal scales present.The resulting scalable software is now capable of determin-ing how the boosters, which should have just deflagrated,interacted to detonate. Preliminary results of the full scalesimulation are shown and the broader scalability lessonsfor codes at this scale are discussed.

John A. SchmidtSCI InstituteUniversity of Utahjas@sci.utah.edu

MS129

A DAG Approach to Tame Complexity in Multi-physics Software on Heterogeneous Architectures

Abstract Directed acyclic graphs (DAGs) provide an ef-fective abstraction to effectively handle complexity arisingfrom both hardware as well as physics. This talk addressesour usage of DAGs to dynamically assemble algorithms forhighly complex, multiphysics problems. We also discusshow we are using DAGs to deploy these complex simula-tions on hybrid architectures such as CPU-GPU systemswhere overlapping computation with host-device transfersis of critical importance. Finally, we discuss other key as-pects of our DAG approach including automated memoryreuse, thread-pooling, etc.

James C. SutherlandDepartment of Chemical EngineeringThe University of Utahjames.sutherland@chemeng.utah.edu

Abhishek BagusettyChemical EngineeringUniversity of Utahabhishek.bagusetty@utah.edu

MS130

Weno Finite Volume Methods for EmbeddedBoundary Grids

We discuss the discretization of hyperbolic conservationlaws on Cartesian grids with embedded boundaries. Forthe regular part of the mesh (i.e., away from the cut cells),we use a high order accurate WENO finite volume methodwith Runge-Kutta time stepping. The cut cells are up-dated using an appropriate version of the h-box method.

Christiane HelzelDepartment of MathematicsRuhr-University-Bochumchristiane.helzel@rub.de

MS130

Diffusion MRI on a Cartesian Grid with ImmersedInterfaces

Diffusion MRI measures the diffusion of water in biologicaltissue. To simulate the diffusion MRI signal, it is impor-tant to accurately describe the geometry of the biologicalcells and cell membranes. We discretize this problem ona Cartesian grid and model cell membranes by interfacesthat are not necessarily aligned with the computationalgrid. This results in a method that correctly accounts forthe interface surface area, which has a strong influence onsimulation results.

Khieu Van NguyenNeurospin, CEA, Saclay, Francenvkhieu89@gmail.com

Jing-Rebecca LiINRIA Saclayjingrebecca.li@inria.fr

Luisa CiobanuNeurospin, CEA, Saclay, Franceluisa.ciobanu@gmail.com

MS130

High-Order Quadrature on Implicitly Defined Do-mains with Application to a High-Order Embed-ded Boundary Discontinuous Galerkin Method forEvolving Interface Problems

We present a high-order accurate (order 2p) numericalquadrature algorithm for evaluating integrals on implicitly-defined domains - suitable for, e.g., cut-cell finite elementmethods in which the mesh is implicitly generated by em-bedding the domain in a Cartesian grid. The algorithmnaturally lends itself to a class of high-order discontinu-ous Galerkin methods (”tiny” cells are merged with neigh-bours) - we show some examples ranging from Poissonproblems to multiphase incompressible fluid flow.

Robert SayeDept. of MathematicsUniversity of California, Berkeley

CS15 Abstracts 113

rsaye@lbl.gov

MS130

Terrain Following Versus Cut-Cells

A finite volume model is described with the same numericsfor cut-cells and terrain-following layers. The model hascurl-free pressure gradients which eliminate the horizontalpressure gradient error. Some clean comparisons betweencut-cells and terrain-following layers are made and, on testsin which the flow interacts with the orography, the terrain-following layers give better accuracy whereas the cut-cellscan excite the computational mode of the Lorenz grid.

Hilary WellerUniversity of Reading, UKh.weller@reading.ac.uk

James ShawUniversity of Readingj.shaw@student.reading.ac.uk

MS131

Community feedback and discussion

This session will continue to solicit feedback and discussionfrom the CSE community on ”Future Directions in CSEEducation and Research”.

Hans De SterckUniversity of WaterlooApplied Mathematicshdesterck@uwaterloo.ca

Ulrich J. RuedeUniversity of Erlangen-NurembergDepartment of Computer Science (Simulation)ulrich.ruede@fau.de

Lois Curfman McInnesMathematics and Computer Science DivisionArgonne National Laboratorycurfman@mcs.anl.gov

Karen E. WillcoxMassachusetts Institute of Technologykwillcox@MIT.EDU

MS131

The Future of CSE Research

This presentation will give an overview of the main pointsaddressed in the draft white paper on ”Future Directionsin CSE Education and Research”. It will comment on therapid expansion of CSE since the beginning of the 21stcentury and the challenges the CSE field is encounteringin the context of recent disruptive developments that in-clude extreme-scale computing, data-driven discovery, anda comprehensive broadening of the application fields ofCSE. The presentation will focus on the future of CSEresearch and will solicit feedback from the broad CSE com-munity.

Ulrich J. RuedeUniversity of Erlangen-NurembergDepartment of Computer Science (Simulation)ulrich.ruede@fau.de

Lois Curfman McInnesMathematics and Computer Science DivisionArgonne National Laboratorycurfman@mcs.anl.gov

MS131

The Future of CSE Education

This presentation will continue the discussion of the mainideas presented in the draft white paper on ”Future Direc-tions in CSE Education and Research”. It will focus on thefuture of CSE education, including expectations for gradu-ate degree outcomes, workforce development, and changesin educational infrastructure. Feedback will be solicitedfrom the broad CSE community.

Karen E. WillcoxMassachusetts Institute of Technologykwillcox@MIT.EDU

Hans De SterckUniversity of WaterlooApplied Mathematicshdesterck@uwaterloo.ca

MS132

Topological Sensitivity Analysis in Systems Biology

Mathematical models of natural systems are abstractionsof much more complex processes. There are often manypotential models consistent with our existing knowledgeand experimental data, so it is critical to understand theimpact of assumptions inherent to a selected model. Ourmethod evaluates the dependence of inferences on the as-sumed model structure. Failing to consider this structuraluncertainty, as is often done in practice, can give rise tomisleading conclusions.

Ann C. BabtieTheoretical Systems BiologyImperial College Londonann.babtie12@imperial.ac.uk

Paul Kirk, Michael StumpfImperial College LondonTheoretical Systems Biologypaul.kirk06@imperial.ac.uk, m.stumpf@imperial.ac.uk

MS132

Bayesian Updating for Dynamic Systems UsingSubset Simulation (Beck) and Active Model Selec-tion (Busetto)

First part by Prof. Beck: A new approximate Bayesiancomputation algorithm, ABC-SubSim, is presented and ap-plied for Bayesian updating of model parameters. It usesthe Subset Simulation algorithm of Au and Beck (2001), avery efficient multi-level MCMC rare-event sampler. Sec-ond part by Prof. Busetto: A method for active approx-imate inference of nonlinear dynamical systems is intro-duced, and its concrete results are discussed. The methodis computationally efficient and provides formal guaranteesof near-optimal informativeness.

AlbertoGiovanni BusettoUCSBagb@ece.ucsb.edu

114 CS15 Abstracts

James BeckDivision of Engineering and Applied ScienceCalifornia Institute of Technologyjimbeck@caltech.edu

MS132

Bayesian Inference of Chemical Kinetic Modelsfrom Proposed Reactions

We present a new framework for tractable Bayesian infer-ence of chemical kinetic models in case of a large numberof model hypotheses generated from a set of proposed reac-tions. The approach involves imposing point-mass mixturepriors over rate constants and exploring the resulting pos-terior distribution using an adaptive Markov chain MonteCarlo method. We show that further gains in sampling ef-ficiency can be realized by analyzing the chemical networkstructure in order to reduce the space of MCMC explo-ration.

Nikhil Galagali, Youssef M. MarzoukMassachusetts Institute of Technologynikhilg1@mit.edu, ymarz@mit.edu

MS132

Advanced Bayesian Computation for ChallengingProblems in the Sciences and Engineering

Bayesian approaches to Uncertainty Quantification rely onefficient Markov chain Monte Carlo methods especially formodels based on large systems of partial differential equa-tions. This talk will present recent work on exploiting (1)Feynman-Kac identities defining the duality between nu-merical deterministic and stochastic (probabilistic) meth-ods in obtaining solutions of certain classes of partial dif-ferential equations, and (2) surrogate geometric structuresin defining Markov transition kernels on symplectic mani-folds. An illustration with shallow water models for globalclimate models.

Mark GirolamiUniversity College Londonm.girolami@warwick.ac.uk

MS133

Multilevel Simulation of Mean Exit Times

Existing methods achieve ε RMS accuracy for the compu-tation of mean exit times for very general Brownian diffu-sions, at a cost which is O(ε−3) for a large class of SDEs us-ing the Euler-Maruyama discretisation. We present a newmultilevel Monte Carlo method which achieves the sameresult with a cost which is O(ε−2(log |ε|)3). This work re-lies heavily on theoretical results derived by E. Gobet andothers, and is supported by numerical experiments.

Michael B. GilesMathematical InstituteOxford UniversityMike.Giles@maths.ox.ac.uk

Francisco BernalInstituto Superior Tecnico, Portugalfco bernal@hotmail.com

MS133

A Multilevel Stochastic Collocation Method for

Pdes with Random Inputs

By employing a hierarchy of both spatial approximationsand interpolations in stochastic parameter space, we de-velop a multilevel version of stochastic collocation meth-ods for random partial differential equations, leading to asignificant reduction in computational cost. We provide aconvergence and cost analysis of the new algorithm, anddemonstrate the gains possible on a typical random diffu-sion model problem.

Aretha TeckentrupUniversity of Batha.l.teckentrup@bath.ac.uk

Peter JantschUniversity of Tennesseejantsch@math.utk.edu

Max GunzburgerFlorida State UniversitySchool for Computational Sciencesmgunzburger@fsu.edu

Clayton G. WebsterOak Ridge National Laboratorywebstercg@ornl.gov

MS133

Hierarchical Acceleration of Stochastic CollocationMethods for PDEs with Random Input Data

We will present an approach to adaptively accelerate a se-quence of hierarchical interpolants required by a multilevelsparse grid stochastic collocation (aMLSC) method. Tak-ing advantage of the hierarchical structure, we build newiterates and improved pre-conditioners, at each level, by us-ing the interpolant from the previous level. We also providerigorous complexity analysis of the fully discrete problemand demonstrate the increased computational efficiency, aswell as bounds on the total number of iterations used bythe underlying deterministic solver.

Guannan Zhang, Clayton G. WebsterOak Ridge National Laboratoryzhangg@ornl.gov, webstercg@ornl.gov

MS134

The Cost of Reliability: Iterative Linear Solversand Reactive Fault Tolerance

We analyze several soft fault models and reactive ap-proaches that may be used given a restarted solver ornested solver. Assuming some portion of the solver re-quires reliability, we analyze the costs of reliable and unre-liable computations. We evaluate these costs given variousparameters to the solvers’ reactive fault tolerance.

James ElliottNorth Carolina State Universityjjellio3@ncsu.edu

Mark HoemmenSandia National Laboratoriesmhoemme@sandia.gov

Frank MuellerNorth Carolina State University

CS15 Abstracts 115

mueller@cs.ncsu.edu

MS134

Inherent Error Resilience of a Complex Moment-Based Eigensolver

In this talk, we consider error resilience property of a com-plex moment-based parallel eigensolver for solving gener-alized eigenvalue problems. We show that the eigensolverwith sufficient subspace size can achieve high accuracy fortarget eigenpairs, even if soft-errors like bit-flip occur in themost time-consuming part of the eigensolver. This prop-erty provides an inherent error resilience of the eigensolverthat does not require checkpointing and replication tech-niques.

Akira Imakura, Yasunori Futamura, Tetsuya SakuraiDepartment of Computer ScienceUniversity of Tsukubaimakura@cs.tsukuba.ac.jp, futa-mura@mma.cs.tsukuba.ac.jp, sakurai@cs.tsukuba.ac.jp

MS134

Analysis of Krylov Solver Resilience in the Pres-ence of Soft-Faults

Convergence rates of Krylov iterative solvers are consid-ered in the context of soft silent faults encountered in mod-ern supercomputers. We propose an analytic hardware ag-nostic fault model based on selective reliability, that canprovide rigorous answers to important resilience questions.We prove convergence for a class of Krylov methods, wherethe original iteration is coupled with periodic restarts (e.g.,restarted GMRES). In addition, we derive optimal restartstrategy that minimizes the resilience overhead.

Miroslav StoyanovOak Ridge National Labmkstoyanov@gmail.com

Clayton G. WebsterOak Ridge National Laboratorywebstercg@ornl.gov

MS134

On the Reliability of Soft Error Detection in CG-POP

Soft errors that are not detected by hardware mechanismsmay be extremely complex to detect at the software layer.One option is to perform a full duplication of the compu-tation (and data) and check on a regular basis that inter-mediate results are consistent. However, this mechanismmay be prohibitive. In the context of CG solver, the mostprohibitive operation to duplicate is SpMV. To avoid theduplication of this operation, checksum mechanisms maybe employed. In this presentation, we investigate the relia-bility of such an approach in finite precision arithmetic. Weillustrate our discussion with the CGPOP code, a miniappfor performing the CG within the Parallel Ocean Program(POP), which is a candidate for exascale climate simula-tions.

Agullo EmmanuelInriaemmanuel.agullo@inria.fr

Luc Giraud

Inria Bordeaux Sud-OuestJoint Inria-CERFACS lab on HPCluc.giraud@inria.fr

Emrullah Fatih YetkinInriaemrullah-fatih.yetkin@inria.fr

MS135

Model Calibration and Error Propagation forLarge-Eddy Simulation of Turbulent Flows

We hypothesize that turbulence simulations of engineeringapplications can be made affordable on the design time-scale by improving model calibration and error estimation.This study considers a Bayesian calibration approach fol-lowed by forward uncertainty quantification. Model pa-rameters are calibrated with DNS of isotropic turbulenceand are then tested in an LES turbulent channel flow con-figuration. Polynomial Chaos expansions are used for ef-ficient propagation of uncertainties from input model pa-rameters to output quantities of interest.

Myra Blaylock, Cosmin SaftaSandia National Laboratoriesmlblayl@sandia.gov, csafta@sandia.gov

Stefan P. DominoSandia. National Laboratoriesspdomin@sandia.gov

John C. Hewson, Jeremy TempletonSandia National Laboratoriesjchewso@sandia.gov, jatempl@sandia.gov

MS135

Predictive Rans Simulations Via Bayesian Model-Scenario Averaging

The turbulence closure model is the dominant source oferror in Reynolds Averaged Navier-Stokes simulations, yetno reliable estimators exist for this error component. Herewe develop a stochastic, a posteriori error estimate, basedon variability in model closure coefficients across multipleflow scenarios, for multiple closure models. The variabil-ity is estimated using Bayesian Model-Scenario Averaging(BMSA), and used to obtain an stochastic solution esti-mate in an unmeasured (prediction) scenario.

Richard DwightDelft University of Technologyr.p.dwight@tudelft.nl

Wouter EdelingTU Delftw.n.edeling@tudelft.nl

Paola CinnellaENSAM, ParisTechpaola.cinnella@ensam.eu

MS135

Accounting for Model Error in the Calibration ofPhysical Models

It is important to account for model error in the fitting ofphysical models to data. In this talk, we discuss avail-

116 CS15 Abstracts

able Bayesian methods for accounting for model errors,highlighting the calibration of models of physical systems.We introduce a Bayesian calibration framework, relyingon probabilistic embedding of the error within the model,allowing clear disambiguation of measurement errors andmodel structural errors. The method is demonstrated inthe calibration of chemical kinetic rate parameters.

Habib N. NajmSandia National LaboratoriesLivermore, CA, USAhnnajm@sandia.gov

Khachik SargsyanSandia National Laboratoriesksargsy@sandia.gov

Roger GhanemUniversity of Southern CaliforniaAerospace and Mechanical Engineering and CivilEngineeringghanem@usc.edu

MS135

Bayesian Model Calibration Techniques That In-corporate Mixed Effects and Model Discrepancy

Measurement errors, model discrepancies, and variabilitydue to differing experimental conditions can produce un-certainty in model parameters estimated through Bayesianmodel calibration techniques. In many cases, model dis-crepancies and variability among data sets are neglectedduring model calibration. However, this can yield non-physical parameter values and produce prediction inter-vals that are inaccurate in the sense that they do not in-clude the correct percentage of future observations. In thispresentation, we discuss techniques to quantify model dis-crepancies and mixed effects due to multiple data sets ina manner that yields physical parameters and correct pre-diction intervals. We illustrate aspects of the frameworkin the context of distributed models with highly nonlinearparameter dependencies.

Brian WilliamsLos Alamos National Laboratorybrianw@lanl.gov

Kathleen SchmidtNorth Carolina State Universityklschmid@ncsu.edu

Ralph C. SmithNorth Carolina State UnivDept of Mathematics, CRSCrsmith@ncsu.edu

MS136

Resolvent Expansions for Higher-order Simulationsof PDEs

By casting the solution to a PDE in terms of pseudo-differential operators, we leverage the use of resolvent ex-pansions, in combination with successive convolution, toarrive at high order time accurate solutions for both linearand nonlinear PDEs. This class of solvers has the advan-tage that it naturally leads to a line-by-line approach thatis well-suited to multi-core GPU computing. We considerseveral common examples to illustrate our method, such

as the 2D Cahn-Hilliard, and the Fitzhugh-Nagumo equa-tions.

Andrew J. ChristliebMichigan State UniverityDepartment of Mathematicsandrewch@math.msu.edu

Matthew CausleyKettering Universitymatt.causley@gmail.com

Hana ChoMichigan State Universitychohana@math.msu.edu

MS136

Generalized Structure Additive Runge-KuttaMethods

This presentation discusses a general structure of the ad-ditively partitioned Runge-Kutta methods by allowing fordifferent stage values as arguments of different componentsof the right hand side. An order conditions theory is devel-oped for the new family of generalized additive methods,and stability and monotonicity investigations are carriedout. The new family, named GARK, introduces additionalflexibility when compared to traditional partitioned Runge-Kutta methods, and therefore offers additional opportuni-ties for the development of flexible solvers for systems withmultiple scales, or driven by multiple physical processes.

Adrian SanduVirginia Polytechnic Institute andState Universitysandu@cs.vt.edu

Michael GuentherBergische Universitaet Wuppertalguenther@math.uni-wuppertal.de

MS136

Efficient Exponential Integrators: Construction,Analysis and Implementation

We will provide an overview of the latest advances in ex-ponential integrators. In particular, we will discuss the ex-ponential propagation iterative (EPI) methods frameworkand describe different classes of these integrators such asthe unsplit, split, hybrid and implicit-exponential methods.Construction of the exponential methods using both clas-sical and stiff order conditions will be discussed. We willalso present the new software package that provides im-plementation of exponential schemes for serial and parallelcomputing platforms.

Mayya TokmanUniversity of California, MercedSchool of Natural Sciencesmtokman@ucmerced.edu

MS136

K-Methods, An Extension of Exponential andRosenbrock Time Integrators

We present a new class of time integration schemes, socalled K-methods. We discuss the derivation of orderconditions for Rosenbrock-K and exponential-K methods.

CS15 Abstracts 117

These schemes consider the time integration and the ap-proximation of linear system solutions, in the case ofRosenbrock-K, or the approximation of matrix exponentialvector products, in the case of exponential-K, as a singlecomputational process. We also give some numerical re-sults showing favorable scalability properties for parallelimplementations.

Paul Tranquilli, Adrian SanduVirginia Polytechnic Institute andState Universityptranq@vt.edu, sandu@cs.vt.edu

Ross GlandonVirginia Techrossg42@vt.edu

MS137

Quantity-of-Interest Based Least-Squares FiniteElement Methods

We present an approach to augment least-squares finite el-ement formulation with a user-specified quantity of inter-est (QoI). The method inherits the global approximationproperties of the standard least squares formulation withincreased resolution of the QoI. We establish theoreticalproperties such as optimality and enhanced convergenceunder a set of general assumptions. We also present anadaptive approach that results in approximations whichpossess high accuracy in global norms as well as in the QoI.Several numerical experiments are presented to support thetheory and highlight the effectiveness of our methodology.

Jehanzeb H. ChaudhryFlorida State Universityjehanzeb.hameed@gmail.com

Thomas ManteuffelUniversity of Coloradotmanteuf@colorado.edu

Luke OlsonDepartment of Computer ScienceUniversity of Illinois at Urbana-Champaignlukeo@illinois.edu

Eric C. CyrScalable Algorithms DepartmentSandia National Laboratotorieseccyr@sandia.gov

Kuo LiuDepartment of Applied MathematicsUniversity of Colorado at Boulderliukuo99@gmail.com

Lei TangDepartment of Applied MathematicsUniversity of Colorado-Boulderl6tang@gmail.com

MS137

An Energy-Minimization Finite-Element Approachfor the Frank-Oseen Model of Nematic LiquidCrystals

We present an energy-minimization finite-element ap-proach to the computational modeling of equilibrium con-

figurations for nematic liquid crystals with applied electricfields. The method targets minimization of system freeenergy based on the electrically augmented Frank-Oseenfree-energy model. We demonstrate the well-posedness ofthe associated intermediate, discrete, linearization systems.Numerical simulations involving heterogenous constant co-efficients for both classical and complicated boundary con-ditions, relevant in ongoing research, are discussed and sup-port the established theory.

David B. EmersonTufts UniversityDepartment of Mathematicsdavid.emerson@tufts.edu

James H. AdlerTufts Universityjames.adler@tufts.edu

Scott MaclachlanDepartment of MathematicsTufts Universityscott.maclachlan@tufts.edu

Timothy AthertonTufts UniversityDepartment of Physicstimothy.atherton@tufts.edu

MS137

Energy Laws and First-Order System LeastSquares for MHD systems

Energy principles play a crucial role in understanding theinteractions and coupling between different scales or phasesin a physical system. This motivates one to investigatehow well various discretization methods preserve the en-ergy laws associated with PDEs. We discuss this ques-tion in the context of First-Order System Least Squares(FOSLS) finite element method applied to time-dependentheat equation and the equations of magnetohydrodynam-ics (MHD). Our study involves numerical experiments andsome theoretical considerations.

Ilya LashukGeorgia Institute of Technologyilya.lashuk@gmail.com

James H. AdlerTufts Universityjames.adler@tufts.edu

Scott MaclachlanDepartment of MathematicsTufts Universityscott.maclachlan@tufts.edu

Ludmil ZikatanovPennsylvania State Universityludmil@psu.edu

MS137

Nested Iteration and First-Order System LeastSquares for Preconditioning a Two-Fluid Electro-magnetic Plasma Model

A two-fluid plasma (TFP) model is presented both as astand-alone solver and as the preconditioner to a fully im-

118 CS15 Abstracts

plicit particle-in-cell (PIC) simulation. The model cou-ples fluid conservation equations for ions and electrons toMaxwell’s equations. A Darwin approximation of Maxwellis used to eliminate spurious light waves. After scalingand modification, the TFP-Darwin model yields a nonlin-ear, first-order system of equations whose Frechet deriva-tive is shown to be uniformly H1-elliptic. This systemis addressed numerically by nested iteration (NI) and aFirst-Order System Least Squares (FOSLS) discretization.Numerical tests demonstrate the efficacy of this approach,yielding an approximate solution within discretization er-ror in a relatively small number of computational workunits (WU).

Chris LeibsUniversity of Colorado Boulderleibs@colorado.edu

Thomas ManteuffelUniversity of Coloradotmanteuf@colorado.edu

MS138

Hierarchically Accelerated Stochastic Collocationfor Random PDEs

Stochastic collocation methods for partial differential equa-tions with high-dimensional random inputs generate largecollections of linear equations, and solving these linear sys-tems is the dominant cost in the construction of an ap-proximate solution. Interpolation on sequences of nestedcollocation nodes provides a natural multilevel hierarchy ofsample points; thus, in this talk we present an acceleratedmethod which utilizes this hierarchical structure to pro-vide linear solvers with improved initial guesses and strong,cheap preconditioners. For a standard elliptic model prob-lem we derive a priori estimates on the savings and compu-tational cost of constructing an approximate solution usinghierarchical acceleration.

Peter JantschUniversity of Tennesseejantsch@math.utk.edu

Diego Galindo, Clayton G. Webster, Guannan ZhangOak Ridge National Laboratorygalindod@ornl.gov, webstercg@ornl.gov, zhangg@ornl.gov

MS138

Parametric Uncertainty Propagation in ResilientDomain Decomposition Methods

One challenging aspect of extreme scale computing con-cerns combining uncertainty quantification methods withresilient PDE solvers. We present and compare differentapproaches of propagating parametric uncertainty in re-silient domain decomposition methods. In such methods,the PDE is solved on many subdomains whose boundaryconditions become the unknowns of a global problem. Weillustrate the implementation of the algorithms in light ofresults obtained for a diffusion equation with an uncertaindiffusivity field.

Paul MycekDuke Universitypaul.mycek@duke.edu

Olivier P. Le MaitreLIMSI-CNRS

olm@limsi.fr

Francesco Rizzi, Khachik Sargsyan, Karla MorrisSandia National Laboratoriesfnrizzi@sandia.gov, ksargsy@sandia.gov,knmorri@sandia.gov

Bert J. DebusschereEnergy Transportation CenterSandia National Laboratories, Livermore CAbjdebus@sandia.gov

Omar M. KnioDuke Universityomar.knio@duke.edu

MS138

A Multilevel Solution Strategy for the StochasticGalerkin Method for PDEs with Random Coeffi-cients

The stochastic Galerkin method for solving partial differ-ential equations (PDEs) with random coefficients yieldshighly accurate numerical solutions yet can be compu-tationally demanding. In this talk, we present a multi-level approach to alleviate some of the prohibitive com-putational cost in the stochastic Galerkin method. Sim-ilar multilevel methods have been successfully applied toMonte Carlo approaches and stochastic collocation meth-ods. We present numerical results for the proposedmultilevel method compared to the standard single-levelmethod.

Sarah OsbornTexas-Tech Universitysarah.osborn@ttu.edu

Victoria HowleTexas Techvictoria.howle@ttu.edu

Jonathan J. HuSandia National LaboratoriesLivermore, CA 94551jhu@sandia.gov

Eric PhippsSandia National LaboratoriesOptimization and Uncertainty Quantification Departmentetphipp@sandia.gov

MS138

Exploring Embedded Uncertainty QuantificationMethods on Next-Generation Computer Architec-tures

We explore approaches for improving the performance ofuncertainty quantification methods on emerging computa-tional architectures. Our work is motivated by the trendof increasing disparity between floating-point throughputand memory access speed. We describe rearrangements ofclassical uncertainty propagation methods leading to im-proved memory access patterns and increased fine-grainedparallelism. We then measure the resulting performanceimprovements on emerging multicore architectures in thecontext of computing solutions to PDEs with uncertain in-

CS15 Abstracts 119

put data.

Eric PhippsSandia National LaboratoriesOptimization and Uncertainty Quantification Departmentetphipp@sandia.gov

H. Carter EdwardsSandia National Laboratorieshcedwar@sandia.gov

Jonathan J. HuSandia National LaboratoriesLivermore, CA 94551jhu@sandia.gov

MS139

Robust Optimization for Decision Making underUncertainty

We present the derivative free trust-region algorithmNOWPAC for solving nonlinear constrained optimizationproblems. In this context we address optimization prob-lems that are subject to two sources of uncertainties. Firstare uncertainties inherent to the constraints and objectivefunction, yielding problems of robust optimization. Secondare uncertainties stemming from computational inaccura-cies in function evaluations; to detect these situations, weintroduce a noise indication tool. We show results for agroundwater flow application.

Florian Augustin, Youssef M. MarzoukMassachusetts Institute of Technologyfmaugust@mit.edu, ymarz@mit.edu

MS139

Comparison of Laminar Flame Models in the Pres-ence of Uncertainty

In this work, we study one-dimensional and two-dimensional laminar flame models using Bayesian infer-ence. In particular, existing experimental data is used tocalibrate, in the Bayesian sense, parameters in chemical ki-netics mechanisms used in the laminar flame models. Bothkinetics and diffusion models are varied. The evidence iscomputed and the plausibility of the various models as-sessed.

Paul BaumanMechanical and Aerospace EngineeringUniversity at Buffalo, State University of New Yorkpbauman@buffalo.edu

MS139

Liposome Vesicles in the Presence of Uncertainty

Liposome vesicles are artificially created vesicles and forma model system for more complicated biological cells, suchas red blood cells. To date, models of vesicles have beendeterministic in nature. Recent work has demonstratedthat thermal fluctuations and the variability of materialparameters play an important role in vesicle behavior. Thistalk will discuss the application of statistical approaches tovesicle simulations.

David SalacUniversity at Buffalo - SUNY

davidsal@buffalo.edu

MS139

Towards Experimental Design Strategies for Inad-equate Models

Obtaining informative measurements is a fundamentalproblem when inadequate models are used to guide the de-sign of experiments. The focus of this study is to developa basic understanding of the impact that modeling errorshave on experimental design strategies. Through a rigorousmodeling of structural errors, new adaptive experimentaldesign strategies can be obtained by exploiting structuraluncertainty. The feasibility of the proposed methodologyis demonstrated in the context of contaminant dispersionmodels.

Gabriel TerejanuUniversity of South Carolinaterejanu@cse.sc.edu

Xiao LinUniversity of South CarolinaUniversity of South Carolinalin65@email.sc.edu

MS140

A Computational Model of Sperm MotilityThrough Viscoelastic Networks

Elastic polymers and filamentous networks within a fluidenvironment are ubiquitous. Mammalian sperm, for exam-ple, must navigate through the highly heterogeneous envi-ronment of layers of viscoelastic networks. We present adiscrete model of such a network coupled to a Stokes flowusing the method of regularized Stokeslets. The networkconsists of links made of springs and dashpots (typical vis-coelastic elements). The results show the network effectson the swimming patterns of the microorganism.

Jacek WrobelDepartment of Mathematics, Tulane UniversityCenter for Computational Sciencejwrobel@tulane.edu

Ricardo CortezTulane UniversityMathematics Departmentrcortez@tulane.edu

Lisa J. FauciTulane UniversityDepartment of Mathematicsfauci@tulane.edu

MS140

Mathematical Modeling of Blood Clot FormationUnder Flow

Vascular injury triggers two intertwined processes, plateletdeposition and coagulation, and can lead to the forma-tion of a blood clot that may grow to occlude a ves-sel. Formation of the clot involves complex biochemical,biophysical, and biomechanical interactions that are alsodynamic and spatially-distributed, and occur on multi-ple spatial and temporal scales. We previously developeda spatial-temporal mathematical model of these interac-tions and looked at the interplay between physical factors

120 CS15 Abstracts

(flow, transport to the clot, platelet distribution within theblood) and biochemical ones in determining the growth ofthe clot. Recently, we extend this model to include re-duction of the advection and diffusion of the coagulationproteins in regions of the clot with high platelet numberdensity. The effect of this reduction, in conjunction withlimitations on fluid and platelet transport through denseregions of the clot, can be profound. Our results suggest apossible physical mechanism for limiting clot growth.

Karin LeidermanApplied MathematicsUC Mercedkleiderman@ucmerced.edu

MS140

Experiment-Driven Surfactant Spreading Models

Surfactants are chemicals that lower surface tensions. Theyare used in many industrial applications as cleaners or sta-bilizers, but are also present in biological arenas such as thetear film of the eye and in the lungs. Surfactant spread-ing models often rely on an equation of state relating sur-factant concentration to surface tension. To make math-ematical analysis more tractable, models have often em-ployed simple functional relationships. However, to modelan experiment with a given fluid and surfactant, a phys-ically meaningful equation of state can be derived fromexperimentally obtained isotherms. We compare modeland experiment for NBD-PC lipid (surfactant) spreadingon glycerol for an empirically-determined equation of state,and compare those results to simulations with traditionallyemployed functional forms. In particular we compare thetimescales by tracking the leading edge of surfactant, thecentral fluid height and dynamics of the Marangoni ridge.We consider both outward spreading of a disk-shaped re-gion of surfactant and the hole-closure problem in which adisk-shaped surfactant-free region self-heals.

Rachel LevyHarvey Mudd Collegelevy@hmc.edu

MS140

A Multi-Moment Approach to Modeling the Onsetof Vortex Merger

We use a low order model to understand how two co-rotating vortices transition from a quasi-steady distancefrom each other to convective merger. Experiments andcomputations have shown that this rapid phenomena oc-curs after diffusion causes the vortex core size to exceedsome critical fraction of the separation distance. Thismodel was derived from the recently developed Multi-Moment Vortex Method and provides several physical in-sights as well as pins down what causes the very initialonset of convective merger.

David T. UminskyUniversity of San FranciscoDepartment of Mathematicsduminsky@usfca.edu

MS141

Efficient Deflated-Based Preconditioning for theCommunication-Avoiding Conjugate GradientMethod

In this work, we demonstrate that deflation precondition-

ing can be applied in communication-avoiding Lanczos-based Krylov methods. We derive deflated communication-avoiding CG, which is mathematically equivalent to de-flated CG of Saad et al. [SIAM J. Sci. Comput., 21 (2000),pp.1909–1926], but performs asymptotically less commu-nication. Numerical examples and performance modelingreveal complex, problem- and machine-dependent tradeoffsbetween convergence rate and time per iteration. We dis-cuss applications for which speedups can be obtained usingthis approach.

Erin C. Carson, Nicholas KnightUC Berkeleyecc2z@eecs.berkeley.edu, knight@cs.berkeley.edu

James W. DemmelUniversity of CaliforniaDivision of Computer Sciencedemmel@berkeley.edu

MS141

Enlarged Krylov Subspace Methods for ReducingCommunication

In this talk we will describe enlarged Krylov subspacemethods. From a partitioning of the input matrix into tsubdomains, these methods are based on adding t new vec-tors to the Krylov subspace at each iteration, instead of onevector in classic methods. The new enlarged search spacecontains the classical Krylov search space based on the ini-tial residual, and hence the novel methods converge at leastas fast as Classical CG in exact precision arithmetic. Wewill discuss parallel versions that reduce communication,and show that the methods converge at least as fast asClassical CG in exact precision arithmetic. The conver-gence results show that they also converge faster than CGin finite precision arithmetic.

Laura GrigoriINRIAFranceLaura.Grigori@inria.fr

Sophie MoufawadLRI - INRIA Saclay, Francesophie.moufawad@inria.fr

Frederic NatafLaboratoire J.L. Lionsnataf@ann.jussieu.fr

MS141

Preconditioning Communication-Avoiding KrylovMethods

Krylov subspace projections methods are important forsolving large-scale linear system of equations. Recent im-provements in a communication avoiding s-step Krylovmethods are important to the scalability of this approachin future architectures. A key missing piece of theseimprovements are robust preconditioners for the s-stepKrylov methods. We present a preconditioner framework,based on domain decomposition, to precondition s-stepKrylov methods without additional communication. Wewill present results on a hybrid CPU/GPU cluster.

Siva RajamanickamSandia National Laboratories

CS15 Abstracts 121

srajama@sandia.gov

MS141

Hierarchical and Nested Krylov Methods forExtreme-Scale Computing

We present hierarchical Krylov methods and nested Krylovmethods to overcome the scaling difficulties for eigenvalueproblems on extreme-scale computers. The work is inspiredby our previous work for linear systems and the arising ap-plications. We demonstrate the impact at high core countson the target applications. Because these algorithms canbe activated at runtime via the PETSc library, applicationcodes that employ PETSc can easily experiment with suchtechniques.

Hong ZhangMCS, Argonne National Laboratoryhzhang@mcs.anl.gov

Lois Curfman McInnesMathematics and Computer Science DivisionArgonne National Laboratorycurfman@mcs.anl.gov

MS142

Anderson Acceleration: Convergence Theory andNumerical Experience

In this talk I will begin with a description of Andersonacceleration and some motivating applications. This partof the talk should get anyone up-to-speed on the topic ofthe mini symposium I will state some new convergence andclose with a report on numerical experiments.

C.T. Kelley, Alex TothNorth Carolina State UnivDepartment of Mathematicstim kelley@ncsu.edu, artoth@ncsu.edu

MS142

On the Performance of Anderson Acceleration forMultiphysics Problems

Anderson Acceleration (AA) has recently garnered atten-tion as an alternative to Picard and Newton-based nonlin-ear solution algorithms. This talk will discuss the efficiencyand robustness of the method compared to the traditionalsolution techniques. Examples will be drawn from produc-tion simulation codes used for nuclear reactor core simula-tion, magnetohydrodynamics and ice sheet modeling. Wewill additionally discuss augmentations to the general al-gorithm to improve performance.

Roger PawlowskiMultiphysics Simulation Technologies Dept.Sandia National Laboratoriesrppawlo@sandia.gov

Steven HamiltonORNLhamiltonsp@ornl.gov

Mark BerrillOak Ridge National Laboratoryberrillma@ornl.gov

Alexander R. Toth

North Carolina State Universityartoth@ncsu.edu

C.T. KelleyNorth Carolina State UnivDepartment of Mathematicstim kelley@ncsu.edu

Andrew SalingerCSRISandia National Labsagsalin@sandia.gov

MS142

Accelerating the EM Algorithm for Mixture-density Estimation

The EM algorithm is widely used for numerically approx-imating maximum-likelihood estimates in the context ofmissing information. This talk will focus on the EM al-gorithm applied to estimating unknown parameters in a(finite) mixture density, i.e., a probability density function(PDF) associated with a statistical population that is amixture of subpopulations, using “unlabeled” observationson the mixture. In the particular case when the subpopu-lation PDFs are from common parametric families, the EMalgorithm becomes a fixed-point iteration that has a num-ber of appealing properties. However, the convergence ofthe iterates is only linear and may be unacceptably slow ifthe subpopulations in the mixture are not “well-separated”in a certain sense. In this talk, we will review the EM al-gorithm for mixture densities, discuss applying Andersonacceleration to improve the convergence of the iterates, andreport on numerical experiments.

Joshua H. Plasse, Homer F. WalkerWorcester Polytechnic Institutejhplasse@wpi.edu, walker@wpi.edu

MS142

Anderson Acceleration for Parallel Applications

Anderson acceleration has demonstrated significant ben-efits in accelerating fixed point solutions in a number ofapplications. The method, however, adds new synchro-nization points that can slow down its use in parallel. Inthis presentation, we will examine the parallel communica-tion requirements of Anderson acceleration and discuss itsperformance for parallel application. In addition, we willdiscuss use of communication-avoiding ideas within the An-derson acceleration algorithm and show results on modelproblems as well as a large-scale application. This workwas performed under the auspices of the U.S. Departmentof Energy by Lawrence Livermore National Laboratory un-der Contract DE-AC52-07NA27344. Lawrence LivermoreNational Security, LLC.

John LoffeldUniversity of CaliforniaMercedloffeld1@llnl.gov

Carol S. WoodwardLawrence Livermore Nat’l Labwoodward6@llnl.gov

MS143

Solution of the Full Waveform Inversion Problems

122 CS15 Abstracts

via Projection based Reduced Order Models

Often discrete measurements of transfer functions in thetime or frequency domains can be equivalently transformedto projection based ROMs for the underlying PDEs. Weuse such ROMs for the numerical solution of the inverse hy-perbolic problems. Justification of our approach is basedon an intriguing connection of the ROMs with the discreteKrein-Marchenko-Gelfand-Levitan method. We show ap-plications to the time-domain full waveform inversion onan example of Marmousi model of seismic exploration in2D.

Vladimir L. DruskinSchlumberger-Doll Researchdruskin1@slb.com

Alexander V. MamonovUniversity of Texas at Austinmamonov@ices.utexas.edu

Mikhail ZaslavskySchlumberger-Doll Researchmzaslavsky@slb.com

MS143

An Efficient Output Error Bound for Model Or-der Reduction of Parametrized Nonlinear Evolu-tion Equations

We present an efficient a posteriori output error bound formodel order reduction of parametrized (nonlinear) evolu-tion equations. The error bound successfully avoids theaccumulation of the residual in time, which is a commondrawback in the existing error estimation for time-steppingschemes. The proposed error bound is applied to twokinds of parametrized instationary problems arising fromchromatographic separation processes. Numerical experi-ments demonstrate the performance and efficiency of theproposed error bound.

Peter Benner, Lihong FengMax Planck Institute, Magdeburg, Germanybenner@mpi-magdeburg.mpg.de,feng@mpi-magdeburg.mpg.de

Yongjin ZhangMax Planck Institute for Dynamics of ComplexSystems,Germanyzhangy@mpi-magdeburg.mpg.de

MS143

Overlapping Clustering and Ldeim in Model Re-duction for Nonlinear Inversion

Projection-based parametric model reduction is success-fully employed in parameter inversion and optimization.However, efficient reduced model evaluation requires anaffine parametrization of the system matrices. When thesystem matrices do not have this property, Discrete Empir-ical Interpolation Method (DEIM) can produce an approx-imate one. In this talk, we combine overlapping cluster-ing algorithms and Local DEIM to generate a high-fidelityaffine approximation with minimal on-line cost. A numer-ical example arising in diffuse optical tomography is pre-sented.

Alexander GrimmDepartment of Mathematics

Virginia Techalex588@vt.edu

Serkan GugercinVirginia Tech.Department of Mathematicsgugercin@math.vt.edu

Christopher A. BeattieVirginia Polytechnic Institute and State Universitybeattie@vt.edu

Eric De SturlerVirginia Techsturler@vt.edu

Misha E. KilmerTufts Universitymisha.kilmer@tufts.edu

MS143

Efficiencies in Global Basis Approximation forModel Order Reduction in Diffuse Optical Tomog-raphy

We consider the nonlinear inverse problem of reconstruct-ing parametric images of optical properties from diffuseoptical tomographic data. Recent work shows MOR tech-niques have promise in mitigating the computational bot-tleneck associated with solving for the parameters. In thistalk, we give an algorithm for efficiently computing the ap-proximate global basis needed in MOR by utilizing a newinterpretation of the transfer function and by capitalizingon Krylov recycling in a novel way.

Meghan O’ConnellDepartment of MathematicsTufts Universitymeghan.oconnell@tufts.edu

Misha E. KilmerTufts Universitymisha.kilmer@tufts.edu

Eric De SturlerVirginia Techsturler@vt.edu

Serkan GugercinVirginia Tech.Department of Mathematicsgugercin@math.vt.edu

Christopher A. BeattieVirginia Polytechnic Institute and State Universitybeattie@vt.edu

MS144

Methods for Accurate and Efficient Computa-tion of the Proper-Orthogonal-Decomposition withLarge Data Sets

Methods for calculating the proper orthogonal decomposi-tion are investigated with regards to efficiency and accu-racy. The classical direct method, the snapshot method,and two new methods, one called ”the deflation method”and the other called the ”recursive snapshot method”, are

CS15 Abstracts 123

compared. The sensitivity of the eigenvalue spectrum andPOD modes to round-off errors and errors caused by us-ing a reduced number of snapshots is investigated. Errorbounds are given for these error sources.

Brian Helenbrook, Fariddudin BehzadClarkson Universityhelenbrk@clarkson.edu, farid.behzad@gmail.com

MS144

Hierarchical Bayesian Sampling for Image Recon-struction of X-Ray and Proton Radiographs

Reconstructing object densities by pulsing particlesthrough a radially symmetric object and collecting themon a CCD results in an ill-posed Abel inversion problem.We present a Markov Chain Monte Carlo approach for solv-ing Abel inversion, where we not only quantify uncertaintyon the image reconstruction, but also quantify uncertain-ties on the prior image covariance matrix and the precisionparameter from the noise model. The data presented wereobtained from high-energy X-ray and proton radiographyfacilities.

Marylesa HowardNational Security Technologies, LLChowardmm@nv.doe.gov

Michael FowlerMathworksmichael.fowler22@gmail.com

Aaron B. LuttmanNational Security Technologies, LLCluttmaab@nv.doe.gov

Margaret HockColumbia Universitymhock1@slu.edu

MS144

An MCMC Approach to Quantifying Uncertaintiesin Neutron Tomography

Two of the most important properties characterizingpulsed fusion neutron sources are the time profile andthe energy spectrum of the fusion neutrons. In this workwe present a model for neutron creation as a function oftime and energy, along with a Markov Chain Monte Carlomethod for estimating the model parameters from neutrondetector measurements. The formulation is demonstratedon real data from a U.S. Department of Energy DensePlasma Focus fusion reactor.

Aaron B. LuttmanNational Security Technologies, LLCluttmaab@nv.doe.gov

Eric MachorroNational Security Technologiesmachorea@nv.doe.gov

Daniel LoweNational Security Technologies, LLC

lowedr@nv.doe.gov

MS144

Proper Orthogonal Decomposition Based ReducedOrder Modeling for Real Time Monte Carlo Simu-lation

Monte Carlo simulations (MCS) are a powerful tool formodeling radiation transport (RT), but require signifi-cant computing resources to obtain accurate results. Inthis work, we develop a proper orthogonal decomposition(POD) based reduced order modeling (ROM) approach toreduce the number of MC particles that must simulatedto obtain statistically significant results. POD typically isdone in space, but here we use it to generate orthogonalbasis functions to describe the radiation energy spectrum.We apply the POD to generate ROMs for terrestrial radi-ation detection scenarios and present numerical results toshow the improvement in accuracy that can obtained usingthe ROM.

Indika G. Udagedara, Brian HelenbrookClarkson Universityudagedig@clarkson, helenbrk@clarkson.edu

Aaron B. Luttman, Stephen MitchellNational Security Technologies, LLCluttmaab@nv.doe.gov, mitchese@nv.doe.gov

MS145

An Adaptable, Application-Aware Task-CentricRuntime System

Abstract not available at time of publication.

George BosilcaUniversity of Tennessee - Knoxvillebosilca@icl.utk.edu

MS145

Task-Based Parallelization of the Fast MultipoleMethod on NVIDIA GPUs and Multicore Proces-sors

Fast Multipole Methods are a fundamental operation forthe simulation of many physical problems. In this talk, wepresent a new approach for implementing these methodsthat achieves high performance across many different com-puter architectures. Our method consists of expressing theFMM algorithm as a task flow and employing a state-of-the-art runtime system, StarPU, to process the tasks onthe different computing units.

Eric F. DarveStanford UniversityMechanical Engineering Departmentdarve@stanford.edu

Emmanuel Agullo, Berenger Bramas, Olivier CoulaudINRIAemmanuel.agullo@inria.fr, berenger.bramas@inria.fr,olivier.coulaud@inria.fr

Matthias MessnerStanford Universityburgerbua@gmail.com

Toru Takahashi

124 CS15 Abstracts

Nagoya Universityttaka@nuem.nagoya-u.ac.jp

MS145

Sparse Direct Solvers on Top of a Runtime System

To face the advent of multicore processors and the everincreasing complexity of hardware architectures, program-ming models based on DAG parallelism regained popular-ity in the high performance, scientific computing commu-nity. Modern runtime systems offer programming modelsand interfaces that comply with this paradigm and power-ful engines for scheduling the tasks into which the applica-tion is decomposed. These tools have already proved theireffectiveness on a number of dense linear algebra applica-tions. This talk evaluates the usability of runtime systemsfor sparse matrix multifrontal factorizations which consti-tute irregular workloads, with tasks of different granular-ities and characteristics and with a variable memory con-sumption. Experimental results on real-life matrices showthat it is possible to achieve the same efficiency as withan ad hoc scheduler which relies on the knowledge of thealgorithm. This talk also shows that thanks to the effec-tiveness and expressiveness of these programming models,it is possible to implement more complex algorithms thatachieve better performance.

Emmanuel AgulloINRIAemmanuel.agullo@inria.fr

Alfredo ButtariCNRS-IRIT, Francealfredo.buttari@enseeiht.fr

Florent LopezEnseeihtflorent.lopez@enseeiht.fr

Abdou GuermoucheLaBRI-INRIA futursabdou.guermouche@labri.fr

MS145

A Task-Based Sparse Direct Solver Suited for LargeScale Hierarchical/heterogeneous Architectures

We study the benefits and limits of replacing the highlyspecialized internal scheduler of our parallel sparse directsolver PaStiX with two generic runtime systems PARSECand STARPU. The analysis highlights that these generictask-based runtimes achieve comparable results on homo-geneous platforms. Furthermore, they are able to signifi-cantly speed up the solver on heterogeneous environmentsby taking advantage of the accelerators while hiding thecomplexity of their efficient manipulation from the pro-grammer.

Pierre RametLaBRI, Univ Bordeaux, France701868

MS146

Application of Lvy-Flight Firefly Algorithm inSolving Several Engineering Problems

There are a lot of optimization problems in engineeringfield. The problems are generally in nonlinear equations,

multimodal and having a lot of constrains. To solve theproblems we can use metaheuristic algorithm to get solu-tion that is near the optimal solution in reasonable time.In this research, the author solves several engineering prob-lems using Lvy-flights combination with the search strategyvia the FIrefly Algorithm that is first developed by XinSheYang in 2010. Advisor: Kuntjoro Adji Sidarto

Fauziah Andini PutriBandung Institute of Technologyfauziahandini16@gmail.com

MS146

Higher Dimensional Smooth Data Interpolation:Algorithmic Techniques from Computational Ge-ometry

In this paper, we derive a construction for computingsmooth interpolants for a given dataset of 3+ dimensions,and develop an algorithm for implementing our construc-tion. The algorithm builds an n-dimensional cell complexusing Delaunay triangulation, where each cell has an as-sociated interpolation function that satisfies Lipschitz con-tinuity for each internal point. This algorithm is imple-mented as a MATLAB package, and is the first of its kindthat can be used on actual datasets. Advisor: MatthewHirn, cole Normale Suprieure, Dpartement d’Informatique

Ariel Herbert-VossUniversity of Utahariel@sci.utah.edu

MS146

A Bioinformatic Approach to Colorectal CancerResearch

My project involved using the R programming language toaccess metadata concerning colorectal cancer. We used epi-genetic data to look at colon cancer in a new way, and cameup with two novel pathways for its development, withoutever doing a wet lab ourselves. Our results shifted cur-rent paradigms about colon cancer development. Advisor:Timothy Yeatman and Mingli Yang, Gibbs Cancer Center

Nicolas Limogiannis, Nick Napier

Wofford College/Gibbs Cancer Centerlimogiannisna@email.wofford.edu,napiernj@email.wofford.edu

MS146

Interpreting Twitter Data from World Cup Tweets

Cluster analysis is a field of data analysis that extractsunderlying patterns in data. We clustered 30,000 tweetsextracted from Twitter just before the World Cup startedand compared the results of k-means, a commonly usedclustering algorithm, and Non-Negative Matrix Factoriza-tion (NMF). The two algorithms gave similar results, butNMF proved to be faster and provided more easily inter-preted results. Advisor: Carl Meyer, NC State

Carol Sadek, Caley JohnsWofford Collegesadekcw@email.wofford.edu, johnsc@email.wofford.edu

MS146

Valuation of American Options and E. Coli Muta-

CS15 Abstracts 125

tions

Numerical methods for the valuation of American optionshave long been an area of active research. Despite theamount of research in this area, there is not enough at-tention given to potential applications of the optimizednumerical methods in use. Considering the valuation ofAmerican options intrinsic coupling with Brownian Mo-tion, a Levy Process, this should be surprising. An area ofpromise seems to be in biological modeling, particularly E.Coli Mutations. Advisor: Liming Feng, UIUC

James A. StronzUIUCjstronz2@illinois.edu

MS146

The Effects of Chronic Wasting Disease on Penn-sylvania Deer and Coyote Populations

Chronic Wasting Disease (CWD) is prevalent in cervids,which can be transmitted directly and indirectly. Thusfar, CWD results in death, and no treatments exist. Thisdisease has captured the attention of officials and hunters.In this presentation, we focus on the effects of CWD di-rectly on a Pennsylvania deer population and indirectly onthe predatory coyote population. We present a dynamicalsystem describing the relationship between deer and coy-otes and some preliminary results. Advisor: Luis Melara,Shippensburg

Brandon D. ThrushShippensburg Universitybt7856@ship.edu

MS147

Realizability in High-Order Numerical Solutions ofEntropy-Based Moment Closures

Entropy-based moment closures for kinetic equations (col-loquially known as MN models) have attractive theoreticalproperties (hyperbolicity, entropy dissipation, and positiv-ity) but are only defined in the set of realizable momentvectors, that is those which are consistent with a positivedistribution. High-order numerical solutions do not alwaysstay in this set, so we investigate the use of a limiter tohandle nonrealizable moments in the implementation of ahigh-order discontinuous Galerkin method.

Graham AlldredgeRWTH AACHEN Universityalldredge@mathcces.rwth-aachen.de

MS147

Kinetic Theory Molecular Dynamics

Electrons are weakly coupled in hot, dense matter that iscreated in high-energy-density (HED) experiments. Theyare also mildly quantummechanical and the ions associatedwith them are classical and may be strongly coupled. Inaddition, the dynamical evolution of plasmas under thesehot, dense matter conditions involve a variety of transportand energy exchange processes. Quantum kinetic theoryis an ideal tool for treating the electrons but it is not ade-quate for treating the ions. Molecular dynamics is perfectlysuited to describe the classical, strongly coupled ions butnot the electrons. We develop a method that combinesa Wigner kinetic treatment of the electrons with classicalmolecular dynamics for the ions. We refer to this hybrid

method as “kinetic theory molecular dynamics,’ or KTMD.The purpose of this paper is to derive KTMD from firstprinciples and place it on a firm theoretical foundation.The framework that KTMD provides for simulating plas-mas in the hot, dense regime is particularly useful sincecurrent computational methods are generally limited bytheir inability to treat the dynamical quantum evolution ofthe electronic component. Using the N-body quantum vonNeumann equation for the electron-proton plasma, we showhow this can be mapped to a classical Liouville equationfor the ions coupled to a set of quantum kinetic equationsfor the 1-particle and 2-particle distribution functions.

Frank GrazianiLawrence Livermore National Laboratorygraziani1@llnl

MS147

Control Strategies for Multi-Agent Games

We present an optimal control problem for a large systemof interacting agents is considered using a kinetic perspec-tive. As a prototype model we analyze a microscopic modelof opinion formation under constraints. For this problema Boltzmann–type equation based on a model predictivecontrol formulation is introduced and discussed. The rela-tion to meanfield is also explored and discussed. For nu-merical purposes a receding horizon strategy is introducedto embed the minimization of suitable cost functional intobinary particle interactions. The corresponding Fokker-Planck asymptotic limit is also derived and explicit expres-sions of stationary solutions are given. Several numericalresults showing the robustness of the present approach arefinally reported.

Michael HertyRWTH Aachen UniverstiyDepartment of Mathematicsherty@mathc.rwth-aachen.de

MS147

A High-Order / Low-Order Approach to OceanModeling

We examine a high-order/low-order approach for the free-surface ocean equations based on an implicit/explicitmethod. The two dimensional scalar continuity equationis treated implicitly with a preconditioned Jacobian-freeNewton-Krylov method (JFNK) and the remaining threedimensional equations are subcycled explicitly within theJFNK residual evaluation with a method. The methodis second-order accurate and scales algorithmically, withtimesteps much larger than fully explicit methods. More-over, the hierarchical nature of the algorithm lends itselfreadily to emerging architectures.

Chris Newman, Geoff Womeldorff, Dana Knoll, LuisChaconLos Alamos National Laboratorycnewman@lanl.gov, womeld@lanl.gov, nol@lanl.gov, cha-con@lanl.gov

MS148

Parameterized Reduced-Order Models for ShapeOptimization of Flow Domains

The proper orthogonal decomposition is combined withderivatives of flow solutions with respect to geometric pa-rameters to build parametric reduced-order models. The

126 CS15 Abstracts

effectiveness of these models is shown by solving optimalcontrol and shape optimization problems and comparingthe results to those obtained with full-order models.

Jeff BorggaardVirginia TechDepartment of Mathematicsjborggaard@vt.edu

MS148

Aeroelastic Design Optimization with Flutter Con-straints and Local Rom Interpolation

Developing an efficient and fast algorithm in PDE-constrained optimization is an ongoing active researchtopic. One attempt is to replace PDE with a reduced ordermodel (ROM). Unfortunately, ROMs are typically proneto parameter change, which is bad in optimization settingwhere a parameter space has to be explored. One remedyis to construct a database of ROMs and interpolate themfor a parameter point that is not in the database. This ap-proach is applied to a real application of aeroelastic wingoptimization problem with flutter constraints. Detailed ex-planation of how to construct a database and sensitivitiesand numerical results will be illustrated in this talk.

Youngsoo ChoiFarhat Research Group, Stanford Universityyc344@stanford.edu

David Amsallem, Charbel FarhatStanford Universityamsallem@stanford.edu, CFarhat@stanford.edu

MS148

Projection-based ROMs for Parametrized PDE-constrained Optimization and Control Problems

Projection-based ROMs provide efficient strategies totackle parametric optimization and parametrized controlproblems, where parameters are related to control/designvariables, or to relevant features of the state system,respectively. In this talk we show how to constructprojection-based ROMs in order to face the large com-putational costs arising in these cases, by discussing twogeneral paradigms (optimize-then-reduce vs. reduce-then-optimize), and showing their performances by means ofnumerical examples.

Andrea ManzoniEPFL, MATHICSE-CMCSSwitzerlandandrea.manzoni@epfl.ch

MS148

POD-G Reduced Order Models for Prediction andControl of Turbulent Flows

Model reduction has become an active area of scientificand engineering research in the past decade or so due toits ability to reduce the complexity of fluid dynamical sys-tems to enable simulation, optimization design and control.Proper orthogonal decomposition Galerkin (POD-G) is oneof the most commonly used methods to generate reduced-order models for turbulent flow systems. In reduced-ordermodeling, balancing the accuracy and efficiency is crucialfor their success. In this talk, we propose an improvementto POD-G models to address this issue. A rigorous error

analysis based on POD approximation theory and applica-tions in realistic simulation and control problems will alsobe discussed.

S.S. RavindranUniversity of Alabama in Huntsvilleravinds@uah.edu

MS149

Strategies for Reducing Setup Costs in AlgebraicMultigrid

Algebraic multigrid (AMG) preconditioners are often em-ployed in large- scale computer simulations to achieve scal-ability. AMG construction can be costly, sometimes asmuch as the solve itself. We discuss strategies for re-ducing expense through reuse of information from priorsolves. The information type depends on the method.For smoothed aggregation AMG this includes aggregationdata, whereas for energy minimization it includes sparsitypatterns and prior interpolants. We demonstrate the effec-tiveness of such strategies in parallel applications.

Jonathan J. HuSandia National LaboratoriesLivermore, CA 94551jhu@sandia.gov

Andrey ProkopenkoSandia National Laboratoriesaprokop@sandia.gov

MS149

Next Generation Sparse Symmetric Factorization

Sparse direct solvers are important in the solution of scien-tific problems but their parallel implementations typicallyexhibit poor scalability. Reducing synchronization andcommunication along the critical path is crucial to achievegood performance on future architectures. In this context,we are investigating a parallel implementation of sparseCholesky factorization using the Fan-Both approach, andwe will present our findings.

Mathias JacquelinLawrence Berkeley National Labmjacquelin@lbl.gov

Esmond G. NgLawrence Berkeley National Laboratoryegng@lbl.gov

MS149

A Distributed CPU-GPU Sparse Direct Solver

We present the hybrid MPI+OpenMP+CUDA implemen-tation of a distributed memory right-looking sparse LU fac-torization algorithm. The difficulty is that small problemsizes dominate the workload, making efficient GPU utiliza-tion challenging. We find ways to aggregate collections ofsmall BLAS operations into larger ones; to schedule opera-tions to achieve load balance and hide long-latency opera-tions, such as PCIe transfer; and to exploit simultaneouslyall of a nodes available CPU cores and GPUs.

Xiaoye Sherry LiComputational Research DivisionLawrence Berkeley National Laboratory

CS15 Abstracts 127

xsli@lbl.gov

Piyush Sao, Richard VuducGeorgia Institute of Technologypiyush3@gatech.edu, richie@cc.gatech. edu

MS149

New Developments in hypres Interfaces andSolvers

The hypre software library provides high performance pre-conditioners and solvers for the solution of large sparse lin-ear systems on massively parallel computers via conceptualinterfaces, which include a structured, a semi-structured,and a traditional linear-algebra based interface. We willdiscuss new algorithmic developments in hypre’s solvers,as well as our efforts and plans to prepare hypre’s inter-faces and solvers for heterogeneous architectures.

Ulrike Meier YangLawrence Livermore National Laboratoryyang11@llnl.gov

MS150

An Implicit Les Strategy for High Order Discon-tinuous Galerkin Discretizations

Due to their high scale-resolving capabilities per degree offreedom, high order Discontinuous Galerkin methods havebeen shown to be very accurate and effective for implicitLES simulations at moderate Reynolds number, if com-bined with a polynomial de-aliasing strategy for stability.In this work, we present an implicit LES strategy suitablefor high order spectral element methods based on a locallyand temporally adaptive de-aliasing, that ensures stabilitythrough physics-based indicators and models dissipation.

Andrea D. Beck, David FladUniversity of Stuttgartbeck@iag.uni-stuttgart.de, flad@iag.uni-stuttgart.de

Claus-Dieter MunzInstitut fur Aerodynamik und Gasdynamik (IAG)munz@iag.uni-stuttgart.de

MS150

High-Order Finite-Volume Solution of TurbulentAerodynamic Flows

Research in high-order unstructured solvers is encouragedby their accuracy advantages and flexibility for complexgeometries. Traditionally, the finite-volume approach hasbeen employed in computational aerodynamics because ofintrinsic conservative properties. A major step towardsthe adoption of higher-order finite-volume methods in CFDsolvers is turbulence modeling. We describe the integrationof the Spalart-Allmaras model into a higher-order finite-volume solver and the treatments required to solve such amathematically stiff problem on anisotropic meshes.

Alireza JalaliPhD Candidate, University of British Columbiaarjalali@interchange.ubc.ca

Carl Ollivier-GoochUniversity of British Columbia

cfog@mech.ubc.ca

MS150

A Theoretical and Computational Framework forMeasure-Valued Solutions to Conservation Laws

Recent results cast doubts on the appropriateness of theentropy weak solution for nonlinear systems of conserva-tion laws and it has been conjectured that the more gen-eral entropy measure-valued (emv) solutions might be theappropriate notion of solution. We proved that boundedsolutions of an arbitrary high order space-time DG schemecombined with a nonlinear shock-capturing converge toan emv solution. The novelty in our work is that nostreamline-diffusion terms are used for stabilization.

Zakerzadeh MohammadRWTH Aachen Universityzakerzadeh@aices.rwth-aachen.de

Georg MayAICESRWTH Aachenmay@aices.rwth-aachen.de

MS150

Understanding the Role of Spectral Vanishing Vis-cosity in High Reynolds Number Flows

To stabilize high Reynolds number simulations using Con-tinuous Galerkin spectral/hp element discretisations sta-bilization is required, even after the application of de-aliaising techniques, although apparently not in Discon-tinous Galerkin (DG) discretisations. For our complex ge-ometry high Reynolds number simulations we are applyingSpectral Vanishing Viscosity (SVV) for stabilization. Inthis presentation we discuss the dispersion analysis of theSVV approach and demonstrate that appropriate choicesof the SVV parameters recover characteristics observed inDG methods.

Rodrigo Moura, Jean-Eloi Lombard, David Moxey, YanBao, Spencer SherwinImperial College Londonr.moura13@imperial.ac.uk, jean-eloi.lombard12@imperial.ac.uk, d.moxey@imperial.ac.uk,y.bao@imperial.ac.uk, s.sherwin@imperial.ac.uk

MS151

Resolving Uncomfortable Tradeoffs in BuildingFast Boundary-Element Method Solvers: It’s Notthe Hows, It’s the Whys

Fast-multipole methods (FMMs) keep pace with parallelcomputing, so where are the scalable, open-source fastboundary-element method (BEM) libraries? We suggestthat a general BEM requires suitable strategies to accountfor the additional abstraction layer (a fast summation algo-rithm) between elementwise computations and the Kryloviteration. This perspective suggests an extensible archi-tecture for general geometries, basis functions, colloca-tion/Galerkin discretizations, scalar and vector problems,and interfaces to ”downstream” applications, e.g. PDE-constrained optimization and coupling to FEM.

Jaydeep BardhanNortheastern Universityj.bardhan@neu.edu

128 CS15 Abstracts

Matthew G. KnepleyUniversity of Chicagoknepley@ci.uchicago.edu

MS151

BEM++ - Building Blocks for Galerkin BoundaryElement Methods

The BEM++ boundary element library (www.bempp.org)is a versatile framework for the solution of boundary in-tegral equations via Galerkin boundary element methods.The focus on this talk is on the design decisions and chal-lenges of developing BEM++. This includes basic meshrepresentation, assembly of operators, FMM and H-matrixmethods, preconditioning, linear algebra, and user inter-faces in C++ and Python.

Timo Betcke, Simon Arridge, Elwin van’t WoutUniversity College Londont.betcke@ucl.ac.uk, S.Arridge@cs.ucl.ac.uk,e.wout@ucl.ac.uk

MS151

Applications of Accelerated BEM in Aeronautics

Airbus Group Innovations is, inside Airbus Group, an en-tity devoted to research and development for the usage ofAirbus Group divisions (Airbus Civil Aircraft, Airbus De-fence & Space, Airbus Helicopters). The numerical analysisteam has been working for now more than 20 years on in-tegral equations and boundary element methods for wavepropagation simulations, first in electromagnetism, later inacoustics and electrostatics. Since 2000, these BEM toolshave received a multipole algorithm (called Fast MultipleMethod) extension that allows to solve very large prob-lems, with ten of millions of unknowns, in reasonable timeon parallel machines. Recently, H-matrix technics havegiven access to fast direct solvers, able to solve with avery good accuracy problems with millions of unknownswithout the problem induced by iterative resolution (nocontrol on the number of iterations, difficulty to find agood preconditioned, etc.). The resulting software is usedon daily basis in acoustics for installation effects compu-tation, aeroacoustic simulation (in a coupled scheme withother tools), in electromagnetism for antenna siting, elec-tromagnetic compatibility or stealth, and in electrostaticsfor fuel tank modelisation and lightning effects. The aimof this talk is to present a wide view of the realizations, tounderline the recent developments (such as H-matrix) andto present the main perspectives and futures directions ofresearch in a context of different physics and applicationsP

Nolwenn Balin, Benoit LizeAirbusnolwenn.balin@airbus.com, benoit.lize@airbus.com

Guillaume SylvandEADS CCR, Centre de Toulouseguillaume.sylvand@airbus.com

Isabelle TerrasseAirbusisabelle.terrasse@airbus.com

MS151

A Numerical Routine for Fast Spherical Grid Ro-

tations

We present a numerical routine that interpolates functionvalues on rotated spherical grids via hybrid nonuniformFFTs. This routine can be used for evaluating singu-lar integral operators on smooth surfaces that are glob-ally parametrized by spherical coordinates. Problems ofthis type arise, for example, in simulating Stokes flowswith particulate suspensions and in multi-particle scatter-ing calculations. The algorithm has a small complexityconstant, and the cost of applying the quadrature rule isnearly-optimal O(p4 log p) for a spherical harmonic expan-sion of degree p. This is joint work with Zydrunas Gimbu-tas (NIST).

Shravan VeerapaneniDepartment of MathematicsUniversity of Michiganshravan@umich.edu

MS152

Recovery Based a Posteriori Error Estimation forFinite Element Methods

The recovery-based Zienkiewicz-Zhu (ZZ) a posteriori errorestimator has been widely used in the engineering practicedue to the ease of implementation, generality, and accu-racy. However, it is well known that the ZZ estimatoris inefficient for non-smooth problems on relatively coarsemeshes. In this talk, we will discuss three types of recovery-based a posteriori error estimators based on the L2, theequilibrium, and theH(div) recoveries, respectively. Theseestimators are efficient, reliable, or/and robust. Moreover,they preserve the mathematical structure of the underlyingproblem.

Zhiqiang CaiPurdue UniversityDepartment of Mathematicscaiz@purdue.edu

MS152

Robust a-Posteriori Error Estimation for Finite El-ement Approximation to H(curl) Problem

In this talk, we will discuss the recovery-type a posteri-ori error estimation for the conforming finite element for-mulation of the positive definite H(curl) problem. Boththe L2-recovery and H(curl)-recovery are discussed. Theglobal recovery problems are localized through weightedaveraging, and a partition of unity of the magnetizing fieldrespectively.

Shuhao CaoPennsylvania State UniversityDepartment of Mathematicsscao@psu.edu

MS152

Localized H(div) Recovery-Based a Posteriori Er-ror Estimators

In this talk, we present recovery-based error estimators forconforming finite element approximation of second-orderelliptic problem. The flux is recovered in H(div) finite ele-ment subspaces by approximating equilibrium and consti-tutive equations simultaneously in a weighted H(div) norm.A posteriori error estimators are constructed locally on ap-propriate patches of triangular elements. Reliability and

CS15 Abstracts 129

efficiency of these local error estimators will be discussed.Numerical results are provided to demonstrate features ofthese error estimators.

Xu ZhangPurdue Universityxuzhang@purdue.edu

Zhiqiang CaiPurdue UniversityDepartment of Mathematicscaiz@purdue.edu

MS153

Continuum Spine Modeling with Application toOuter Retina Neurocircuitry

The continuum theory for dendritic spines is an exten-sion of classical cable theory for which the distribution ofspines is treated as a continuum. With the continuum the-ory, different spine morphologies, multiple populations ofspines, and distributed physiological properties are repre-sented compactly by relatively few differential equations.In this talk I will present a brief overview of continuumspine theory and discuss how to apply the theory to mod-eling neurocircuitry in the outer retina.

Steven M. BaerArizona State UniversitySchool of Mathematical & Statistical Sciencessteven.baer@asu.edu

MS153

Simulation of the Ephaptic Effect in the Cone-Horizontal Cell Synapse of the Retina

The drift-diffusion (Poisson-Nernst-Planck) model—including a numerical model for cell membranes thatresolves surface charge boundary layers—is applied to thecone-horizontal cell synapse in the outer plexiform layerof the retina in a two-dimensional cross-section geometry.Numerical simulations reproduce the experimental calciumcurrent-voltage curves for the goldfish retina in responseto a bright spot, with and without an illuminated back-ground. The ephaptic (electrical) effect is demonstratedby computing the shift in the IV curve for background offvs. background on.

Carl L. GardnerArizona State UniversitySchool of Mathematical and Statistical Sciencescarl.gardner@asu.edu

MS153

Modeling of Calcium-Induced Calcium Release

Calcium release through coordinated IP3 receptor andryanodine receptor (RyR) openings are important signalingevents in neurons in which Ca2+ release from one channelopens other nearby Ca2+ sensitive channels. This is mod-eled using extensive experimental data to compute how theopen/closed probability of RyR changes with Ca2+ con-centration and with RyR open/closed time. Simulationsshow how neighboring channels are recruited and also giveinsights into how this positive feedback mechanism termi-nates.

Dirk GillespieRush University Medical Center

Department of Molecular Biophysics & Physiologydirk gillespie@rush.edu

MS153

Dendritic Coincidence Detection EnablingWordspotting Computation

Dendritic computation is often ignored when building neu-ron models. However, dendrites have been shown to per-form operations like non-linear filtering, spatial and tem-poral summation of synaptic inputs, coincidence detection,synaptic scaling and sequence detection. We show that anetwork of dendrites and a Winner-Take-all network is sim-ilar to a Hidden Markov Model(HMM) classifier often usedfor speech and pattern-recognition. We have developed amathematical framework for Silicon dendrites, that modelsdeep dendritic trees.

Jennifer HaslerElectrical and Computer EngineeringGeorgia Techjennifer.hasler@ece.gatech.edu

MS154

Fast Spectral PDE Solvers for Complex Structures:the Fourier-Continuation Method

We present fast spectral solvers for time-domain Par-tial Differential Equations. Based on a novel Fourier-Continuation (FC) method for the resolution of the Gibbsphenomenon these methodologies give rise to time-domainsolvers for PDEs for general engineering problems andstructures which enjoy a number of desireable proper-ties, including spectral time evolution essentially free ofpollution or dispersion errors for general PDEs in thetime domain, with conditional/unconditional stability forexplicit/alternating-direction methods. A variety of appli-cations to linear and nonlinear PDE problems, includingthe Maxwell equations, the Navier-Stokes equations, theelastic wave equation demonstrate the significant improve-ments the new algorithms can provide over the accuracyand speed resulting from other approaches.

Oscar P. BrunoCalifornia Institute of Technologyobruno@caltech.edu

MS154

Frame Theoretic Convolutional Gridding

This talk is about reconstructing images from non-uniformFourier data. This problem is relevant in applicationssuch as magnetic resonance imaging (MRI) and syntheticaperture radar (SAR). The non-uniform FFT algorithmprovides a practical way to reconstruct images However,choosing the parameters can be difficult and in some casesthe method may fail to converge. This talk providesa mathematical foundation, through the use of Fourierframes, for reconstructing functions from their non-uniformFourier data. As a result, the parameters for the NFFT canbe chosen to ensure numerical convergence under variousnon-uniform sampling schemes common in MRI and SAR.

Anne GelbArizona State Universityannegelb@asu.edu

Guohui Song

130 CS15 Abstracts

Clarkson Universitygsong@clarkson.edu

MS154

Optimized Fourier Continuation Methods

Fourier continuation/extension (FC) methods, have beenshown to achieve arbitrary orders of accuracy in generatingFourier approximations of smooth but non-periodic func-tions from evenly spaced data. The stability of PDE solversbased on FC methods is heavily dependent on the param-eters of the continuation. Optimized FC methods will bepresented that balance accuracy with sufficient conditionsfor stability within a FC based PDE solver. The inherenttrade-off between accuracy and stability will be discussedin detail.

Mark LyonUniversity of New Hampshiremark.lyon@unh.edu

MS154

A New Radial Basis Functions (RBF)-based FrameMethod to Bypass the Runge Phenomenon

Approximating nonperiodic analytic functions with spec-tral accuracy is not an easy task. RBFs, just like poly-nomials and other pseudospectral methods, are susceptibleto suffer from the Runge phenomenon, spurious oscillationsnear the edges of the domain, and from the ill-conditioningof the method’s associated system. Recently, Adcock etal have introduced a method which combines frames the-ory and Fourier extensions in [Adcock, Huybrechs, Martin-Vacquero, On the numerical stability of Fourier extensions,Found Comp Math 14, 635-687]. The method is not onlyspectrally convergent, it is also free from the Runge phe-nomenon even when the data is equispaced. We will use thefact that pseudospectral methods can be seen as particularcases of RBFs to construct an RBF-based frame methodthat generalized Adcocks Fourier extensions method.

Cecile M. PiretUniversite catholique de Louvaincmpiret@mtu.edu

MS155

Parallel and Adaptive Mantle Convection Simula-tion in Aspect

In this talk, we are presenting the open source mantle con-vection code ASPECT to solve large scale convection prob-lems. The main numerical ingredients are higher order fi-nite elements with adaptive mesh refinement, stabilizationschemes, and linear/nonlinear solvers. The talk will alsocover our software design approach to engineer a flexible,extensible, code with a healthy community that can sup-port the project in the long run. Finally, we will talk aboutexamples and show benchmark results.

Timo HeisterClemson UniversityMathematical Sciencesheister@clemson.edu

Wolfgang BangerthTexas A&M University

bangerth@math.tamu.edu

MS155

Large-Scale Forward and Inverse Numerical Simu-lations of Crustal and Lithospheric-Scale Deforma-tion

Geological processes occur over long timescales and involvenonlinear constitutive relationships. We discuss a parallel3D code to simulate such processes, based on a marker-and-cell technique with a staggered finite difference discretiza-tion and visco-elasto-plastic rheologies. We show a fewexamples of geological modelling applications. In addition,we demonstrate how the forward models can be combinedwith geophysical data and a MC Monte Carlo-based inver-sion approach to constrain the rheology and structure ofmountains belts.

Boris KausJohannes Gutenberg University MainzInstitute of Geoscienceskaus@uni-mainz.de

Anton Popov, Tobias BaumannJohannes Gutenberg University Mainz Institute ofGeosciencespopov@uni-mainz.de, baumann@uni-mainz.de

MS155

HPC Finite Elements for Nonlinear Stokes Flow

Rock deformation over geological time scales can be ex-pressed as a nonlinear, incompressible Stokes problem inwhich the viscosity is highly heterogeneous. Algorithmicand computationally scalable preconditioners are necessaryto achieve high resolution 3D simulations. Here I presenta mixed FE method employing a multilevel preconditionerwhich exploits matrix-free kernels. Trading flops for mem-ory bandwidth, significant speedups compared to precon-ditioners requiring assembled operators are obtained. Per-formance is demonstrated using a simplified model of slabdetachment.

Dave A. MayETH Zurichdave.may@erdw.ethz.ch

Jed BrownMathematics and Computer Science DivisionArgonne National Laboratory and CU Boulderjed@jedbrown.org

MS155

Three-Field Block-Preconditioners for Models ofCoupled Magma/mantle Dynamics

We discuss the iterative solution of a finite element discreti-sation of the magma dynamics equations. These equationsshare features of the Stokes equations, however, Elman-Silvester-Wathen (ESW) preconditioners for the magmadynamics equations are not optimal. By introducing a newfield, the compaction pressure, into the magma dynamicsequations, we have developed a new three-field precondi-tioner which is optimal in terms of problem size and lesssensitive to physical parameters compared to the ESW pre-conditioners.

Sander Rhebergen

CS15 Abstracts 131

University of OxfordMathematics Institute and Department of Earth Sciencessander.rhebergen@maths.ox.ac.uk

Garth WellsDepartment of EngineeringUniversity of Cambridgegnw20@cam.ac.uk

Andrew J. WathenOxford UniversityNumerical Analysis Groupwathen@maths.ox.ac.uk

Richard F. KatzUniversity of OxfordRichard.Katz@earth.ox.ac.uk

Laura Alisic, John RudgeBullard LaboratoriesUniversity of Cambridgela339@cam.ac.uk, jfr23@cam.ac.uk

MS156

A Sub Cell Dynamics Based Closure Modelfor Multimaterial Arbitrary Lagrangian EulerianCodes

Arbitrary Lagrangian Eulerian (ALE) codes introduce mul-timaterial cells to represent material interfaces that mayundergo high deformation. A closure model is then re-quired to close the governing equations, which are oth-erwise underdetermined, this defines how volume frac-tions and state variables of individual material componentswithin these multimaterial cells evolve. The requirementsfor these models will be presented and a interface awaresub-scale-dynamics closure model will be described thathas been developed to meet these requirements.

Andrew J. BarlowAtomic Weapons Esatblishment, United KingdomAndy.Barlow@awe.co.uk

MS156

A High-Order/Low-Order Exponentially-Convergent IMC Method

It is well known that standard Monte Carlo converges asthe inverse of the square root of the number of particlehistories executed. We demonstrate that exponential con-vergence is possible using a defect approach in which eachsucceeding Monte Carlo batch estimates only the additiveerror in the solution from previous batches. This solution isobtained by projection of the Monte Carlo solution onto aFEM space. A refinement strategy is required to maintainexponential convergence.

Simon Bolding, Jim E. MorelTexas A&Mbolding@tamu.edu, morel@tamu.edu

Robert B. LowrieLos Alamos National LaboratoryLos Alamos, NM 87545 USA

lowrie@lanl.gov

MS156

Multiphysics Lagrangian/Eulerian Modeling anddeRham Complex Based Algorithms

Multiphysics modeling in an arbitrary La-grangian/Eulerian (ALE) framework leads naturallyto numerical algorithms matching the geometric meaningof the operators in the deRham complex. We discussour experience with this approach relative to solidkinematics, magnetohydrodynamics and full Maxwellhydrodynamic modeling. Sandia National Laboratoriesis a multi-program laboratory managed and operatedby Sandia Corporation, a wholly owned subsidiary ofLockheed Martin Corporation, for the U.S. Department ofEnergy’s National Nuclear Security Administration undercontract DE-AC04-94AL85000.

Allen C. RobinsonSandia National Laboratoriesacrobin@sandia.gov

MS156

Mimetic Finite-Difference Methods

The mimetic finite difference method (J. of Comput. Phys.257(2014)1163) mimics fundamental properties of mathe-matical and physical systems including conservation laws,symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathemati-cal identities of the vector and tensor calculus. We describethe major mimetic ideas and their relevance to academicand real-life problems. The supporting applications includediffusion, electromagnetics, fluid flow, and Lagrangian hy-drodynamics problems on different type of meshes.

Mikhail ShashkovLos Alamos National Laboratoryshashkov@lanl.gov

MS157

Representing Topography in Earth System Modelswith Porous Barriers

The ocean boundary (coasts and sea-floor) is fractal andexhibits features (e.g. ridges and passages) that are criticalto shaping ocean circulation. These features are typicallynot resolvable in contemporary global earth system mod-els. We explore an extension of cut-cells that represents thetopography via porous barriers between cells. We providean algorithm to calculate the porous barrier data and il-lustrate improved fidelity in coarse-resolution models usingthe porous barrier representation of topography.

Alistair AdcroftPrincetonaadcroft@princeton.edu

MS157

A Higher-Order Cut Cell Finite Volume MethodFor Advection-Diffusion

We present a higher-order cut cell algorithm for theadvection-diffusion equation in irregular domains. Thefinite volume operators are constructed using a uniqueweighted least-squares approach, which reduces the sensi-tivity to small cells despite the flux-difference conservation

132 CS15 Abstracts

form. A higher-order RK time discretization treats dif-fusion terms implicitly, so the overall algorithm is limitedonly by the advection term explicit CFL constraint, regard-less of small cells. Accuracy and stability are demonstratedwith several simple tests.

Dharshi DevendranUniversity of Chicagopdevendran@gmail.com

Hans JohansenLawrence Berkeley National LaboratoryComputational Research Divisionhjohansen@lbl.gov

MS157

A Mixed Explicit Implicit Time Stepping Schemefor Cartesian Embedded Boundary Meshes

We present a mixed explicit implicit time stepping schemefor solving the advection equation on Cartesian embeddedboundary meshes. The implicit scheme is used to overcomethe small cell problem and ensure stability at the cut cells.It is coupled to a standard explicit scheme which is usedover most of the mesh. We present a theoretical resultabout the coupling, and show numerical results in one andmore dimensions.

Sandra MayETH Zurichsandra.may@sam.math.ethz.ch

Marsha BergerCourant Institute of Mathematical SciencesNew York Universityberger@cims.nyu.edu

MS157

Inverse Lax-Wendroff Procedure for NumericalBoundary Conditions of Hyperbolic Equations

We develop a high order finite difference numerical bound-ary condition for solving hyperbolic Hamilton-Jacobi equa-tions and conservation laws on a Cartesian mesh. The chal-lenge results from the wide stencil of the interior high orderscheme and the fact that the boundary may not be alignedwith the mesh. Our method is based on an inverse Lax-Wendroff procedure for the inflow boundary conditions.Extensive numerical examples are provided to illustrate itsgood performance of our method. This is a joint work withLing Huang and Mengping Zhang, and with Sirui Tan andFrancois Vilar.

Chi-Wang ShuBrown UniversityDiv of Applied Mathematicsshu@dam.brown.edu

MS158

Sequentially Constrained Monte Carlo

Constraints in the parameter or model space typically makesampling from distributions more complex (although moreinterpretable) than their unconstrained counterparts. Wedefine a Sequentially Constrained Monte Carlo algorithmconnecting a simple distribution, to the target distribu-tion by a path defined by the strictness of constraint en-forcement. We show general applicability by expanding

the usual definition of constraints to include adherence toa theoretical model governed by differential equations.

Dave A. CampbellSimon Fraser Universitydac5@sfu.ca

Shirin GolchiColumbia Universitygolchi.shirin@gmail.com

MS158

On the Use of Particle Based Methods for the RealTime Identification and Control of Nonlinear Dy-namical Systems

The field of structural dynamics is inherently related tothe simulation, identification and control of structural sys-tems. This task is not a straightforward one; firstly, due topotential nonlinear behavior; and secondly, due to uncer-tainties relating to erroneous modeling assumptions, impre-cise sensory information, ageing effects, varying loads, andlack of a priori knowledge of the system itself. This talkdiscusses the implementation of methodologies capable ofsuccessfully simulating such systems by encompassing theaforementioned complexities.

Eleni ChatziInstitute of Structural ENgineeringETH Zurichchatzi@ibk.baug.ethz.ch

MS158

Bayesian Uncertainty Quantification and Prop-agation for Molecular Dynamic Simulations inNanoscale Fluid Mechanics

For five decades, molecular dynamics (MD) simulations, insynergy with experiments, have elucidated critical mecha-nisms in a broad range of physiological systems and tech-nological innovations. However, in nanofluidics, the re-sults of experiments and MD simulations may differ byseveral orders of magnitude. We show that experimen-tal and large scale MD investigations can be consolidatedthrough a Bayesian framework. Our findings indicate thatit is essential to revisit MD simulations in the context ofuncertainty quantification.

Petros KoumoutsakosChair of Computational Science, ETH Zurichpetros@ethz.ch

Panagiotis AngelikopoulosComputational Science, ETH Zurich, Switzerlandpanagiotis.angelikopoulos@mavt.ethz.ch

Costas PapadimitriouUniversity of ThessalyDept. of Mechanical Engineeringcostasp@uth.gr

MS158

Computationally Efficient Tools for Bayesian Un-certainty Quantification and Propagation in Struc-tural Dynamics

Bayesian uncertainty quantification, including Bayesian hi-erarchical modelling, are becoming standard tools in struc-

CS15 Abstracts 133

tural dynamics for model selection, model parameter cali-bration, uncertainty propagation and SHM using vibrationmeasurements. For complex linear/nonlinear models, thecomputations involved in Bayesian asymptotic approxima-tions and MCMC sampling tools may be excessive. Dras-tic reduction in computational effort in model intrusiveand/or non-intrusive schemes is achieved by integratingmodel reduction techniques, adjoint methods, surrogatemodels, parallel computing and highly-parallelizable sam-pling schemes. Acknowledgement: This research has beenimplemented under the ARISTEIA Action of the Opera-tional Programme Education and Lifelong Learning andwas co-funded by the European Social Fund (ESF) andGreek National Resources.

Costas PapadimitriouUniversity of ThessalyDept. of Mechanical Engineeringcostasp@uth.gr

Panagiotis AngelikopoulosComputational Science, ETH Zurich, Switzerlandpanagiotis.angelikopoulos@mavt.ethz.ch

Panagiotis HadjidoukasComputational ScienceETH Zurich, Switzerlandpanagiotis.chatzidoukas@mavt.ethz.ch

Petros KoumoutsakosChair of Computational Science, ETH Zurichpetros@ethz.ch

MS159

H-Matrix Accelerated Second Moment Analysis forPotentials with Rough Correlation

We consider the efficient solution of strongly elliptic poten-tial problems with stochastic Dirichlet data by the bound-ary integral equation method. The computation of the so-lutions two-point correlation is well understood if the two-point correlation of the Dirichlet data is known and suffi-ciently smooth. Unfortunately, the problem becomes muchmore involved in case of rough data. We will show that theconcept of the H-matrix arithmetic provides a powerful toolto cope with this problem. By employing a parametric sur-face representation, we end up with an H-matrix arithmeticbased on balanced cluster trees. This considerably simpli-fies the implementation and improves the performance ofthe H-matrix arithmetic. Numerical experiments are pro-vided to validate and quantify the presented methods andalgorithms.

Helmut Harbrecht, Juergen DoelzUniversitaet BaselDepartement of Mathematics and Computer Sciencehelmut.harbrecht@unibas.ch, juergen.doelz@unibas.ch

Michael PetersUniversity of Baselmichael.peters@unibas.ch

Christoph SchwabETH ZuerichSAM

christoph.schwab@sam.math.ethz.ch

MS159

Adaptive Monte Carlo and Quasi-Monte Carlo In-tegration

Monte Carlo methods are used for computing means ofrandom variables with complex distributions. Both MonteCarlo methods and quasi-Monte Carlo methods are alsoused for computing high dimensional integrals. A keyquestion in these computations is when to stop, while en-suring that the desired accuracy is obtained. Adaptive(quasi-)Monte Carlo algorithms rely on data-based errorbounds to answer this question. This talk describes re-cent work to construct such error bounds and ensure thatthey are trustworthy. We also derive upper bounds onthe computational costs of our adaptive algorithms. Akey idea is to consider cones of random variables or in-tegrands. Our new algorithms have been implementedin the Guaranteed Automatic Integration Library (GAIL)https://code.google.com/p/gail/.

Fred J. HickernellIllinois Institute of TechnologyDepartment of Applied Mathematicshickernell@iit.edu

Lan JiangDpet. of Applied MathematicsIllinois Institute of Technologyljiang14@hawk.iit.edu

Antoni Luıs Jimenez RugamaDepartment of Applied MathematicsIllinois Institute of Technologylluisantoni@gmail.com

MS159

Application of Quasi-Monte Carlo Methods toPDEs with Random Coefficients

PDEs with random coefficients are an important sourceof high dimensional problems. One example is the flowthrough porous medium: because of the near impossibilityof modeling the microscopic channels through which wa-ter can flow in a porous layer, it is common engineeringpractice to model the porous medium as a random per-meability field. The quantity of interest is therefore anexpected value with respect to the random field, leading toa high dimensional integral where the number of variablesis as high as the number of parameters needed to modelthis random field (it can be infinite). In this talk I willexplain how quasi-Monte Carlo (QMC) methods can betailored to a prototype of such integrals. I will discuss thefast construction of higher order QMC methods to improvethe convergence rate and the use of multi-level techniquesto improve the computational cost. The talk will touch ona number of joint works with Ivan Graham and Rob Sche-ichl (Bath), Dirk Nuyens (KU Leuven), Christoph Schwab(ETH Zurich), and Ian Sloan, James Nichols, Josef Dickand Quoc Le Gia (UNSW).

Frances Y. KuoSchool of Mathematics and StatisticsUniversity of New South Wales

134 CS15 Abstracts

f.kuo@unsw.edu.au

MS159

Option Pricing and the Anova Decomposition of aFunction of An Infinite Number of Variables

In this work we consider the ANOVA decomposition of theintegrand in a continuous version of a path-dependent op-tion pricing problem. We show that in the Brownian bridge(or Levy-Ciesielski) formulation, every term in the (in-finite) ANOVA decomposition is smooth. With thisresult we are preparing for an error analysis of the cuba-ture problem for the option pricing problem, in which thediscrete-time problem is approximated by the continuousproblem, and the error analysis then applied to the trun-cated ANOVA expansion, in which every term is smooth.

Ian H. SloanUniversity of New South WalesSchool of Mathematicsi.sloan@unsw.edu.au

Frances Y. KuoSchool of Mathematics and StatisticsUniversity of New South Walesf.kuo@unsw.edu.au

Michael GriebelUniversitat BonnInst fur Angewandte Mathematikgriebel@ins.uni-bonn.de

MS160

Adaptive Determination of Optimal MultilevelMonte Carlo parameters in the Presence of Fail-ures

In the multilevel Monte Carlo (MLMC) method numerousparameters have to be determined. Their choice is crucialfor the work and error of the method. We propose to de-termine the number of samples per level, the finest andcoarsest level by solving an integer optimization problem.Faults influence the MLMC levels to a different extent. Wepresent a fault tolerant MLMC method that adapts to ex-perienced failures without a priori knowledge of the failuredistribution.

Peter ArbenzETH ZurichComputer Science Departmentarbenz@inf.ethz.ch

Stefan PauliETH Zurich Computer Science Departmentstefan.pauli@inf.ethz.ch

MS160

Hierarchical Resilience for Structured AMR

Structured AMR (SAMR) has hierarchy in spatial andtemporal resolution that can be exploited for devising flex-ible and customizable resiliency strategies. We prototypeda hierarchical approach to resilience in Chombo, an SAMRlibrary, using the Global View Resiliency (GVR) librarythat takes differentiated state snapshots for localized re-covery. SAMR is used in various domains, so our strat-egy may benefit those applications, and perhaps an even

broader class of applications with hierarchy.

Anshu DubeyLawrence Berkeley National Laboratoryadubey@lbl.gov

Hajime FujitaDepartment of Computer ScienceUniversity of Chicagohfujita@cs.uchicago.edu

Zachary RubensteinDepartment of Computer Science, The University ofChicagozar1@uchicago.edu

Brian Van StraalenLawrence Berkeley National LaboratoryCompuational Research Divisionbvstraalen@lbl.gov

Andrew A. ChienThe University of ChicagoArgonne National Laboratorachien@cs.uchicago.edu

MS160

Resilience Properties of Gossip-Style Algorithms

Gossip algorithms have interesting resilience propertieswhich can potentially complement and extend state-of-the-art approaches towards algorithmic fault tolerance. We willreview the latest developments in gossip-based all-reduceoperations and some distributed linear algebra kernels builton top of them. Moreover, we will discuss how gossip-based approaches compare to state-of-the-art fault toler-ant algorithms, such as ABFT methods. By combininggossip-based approaches with existing fault tolerant highperformance algorithms, resilience at the algorithmic levelcan potentially be strengthened further.

Wilfried N. GanstererUniversity of ViennaDepartment of Computer Science and BusinessInformaticswilfried.gansterer@univie.ac.at

Gerhard Niederbrucker, Michael Moldaschl, Karl PrikopaUniversity of Viennagerhard.niederbrucker@univie.ac.at,michael.moldaschl@univie.ac.at,karl.prikopa@univie.ac.at

MS160

Spatial Decomposition for Resilient Extreme-ScaleScientific Simulations

We present a probabilistic approach to PDEs, where com-putational results are viewed as data that is used in a re-silient iterative fashion to update information about thesolution until convergence. We rely on a domain decompo-sition method such that the original problem is reduced tosolving the PDE on subdomains with uncertain boundaryconditions. Resilience to both hard and soft errors is in-tegrated within the algorithm. We show promising resultsfor elliptic PDEs.

Francesco Rizzi, Khachik Sargsyan, Karla Morris, Cosmin

CS15 Abstracts 135

SaftaSandia National Laboratoriesfnrizzi@sandia.gov, ksargsy@sandia.gov,knmorri@sandia.gov, csafta@sandia.gov

Paul Mycek, Omar M. KnioDuke Universitypaul.mycek@duke.edu, omar.knio@duke.edu

Olivier LeMaitreLIMSI-CNRSolm@limsi.fr

Habib N. NajmSandia National LaboratoriesLivermore, CA, USAhnnajm@sandia.gov

Bert J. DebusschereEnergy Transportation CenterSandia National Laboratories, Livermore CAbjdebus@sandia.gov

MS161

Uncertainty in Reynolds Stress Closures for Tur-bulent Flow Calculations

Reynolds-averaged Navier-Stokes (RANS) simulations area practical approach for solving complex multi-physics tur-bulent flows, but the underlying assumptions of the turbu-lence models introduce errors and uncertainties in the sim-ulation outcome. We present a framework to characterizethese uncertainty based on perturbations of the eigenval-ues of the anisotropic Reynolds stress tensors which biasthe model towards specific turbulent states. Results arepresented for a broad class of turbulent flows and illustratethe potential for this approach to capture the salient un-certainties introduced by simplified modeling assumptions.

Gianluca IaccarinoStanford UniversityMechanical Engineeringjops@stanford.edu

Michael A. EmoryStanford Universitymemory@stanford.edu

Catherine GorleEMAT, UAcatherine.gorle@ua.ac.be

MS161

Eddy Viscosity Model Selection for Transonic Tur-bulent Flows Using Shrinkage Regression

Linear eddy viscosity models (LEVM), when used in k-epsilon models, often fail to capture complex turbulentphenomena. Our previous work has revealed the structuralshortcomings of LEVMs in simulations of jet-in-crossflowinteractions. We address this issue by calibrating a cubiceddy viscosity model using limited measurements from ajet-in-crossflow experiment. We use shrinkage regressionto identify the terms that need to be retained. Improve-ment over LEVM predictions is quantified and presented.

Sophia Lefantzi

Sandia National Laboratoriesslefant@sandia.gov

Jaideep RaySandia National Laboratories, Livermore, CAjairay@sandia.gov

Srinivasan Arunajatesan, Lawrence DechantSandia National Laboratoriessarunaj@sandia.gov, ljdecha@sandia.gov

MS161

Formulation and Calibration of a Stochastic ModelForm Error Representation for Rans

We develop a stochastic model inadequacy representationfor the RANS equations for wall-bounded flows. The modeltakes the form of a stochastic PDE governing the errorin the Reynolds stress computed according to an eddy-viscosity-based turbulence model. Further, the model isconstructed to conform to available knowledge about theperformance of typical turbulence models—e.g., that themodels are constructed to capture the log layer. We testthe model inadequacy representation using DNS data.

Robert D. MoserUniversity of Texas at Austinrmoser@ices.utexas.edu

Todd OliverPECOS/ICES, The University of Texas at Austinoliver@ices.utexas.edu

Bryan ReuterUniversity of Texas, Austinbryan@ices.utexas.edu

MS161

Estimating a Model Discrepancy Term for theCommunity Land Model Using Latent Heat andRunoff Observations

We estimate three hydrological parameters of the CLM(Community Land Model) using runoff and latent heat fluxmeasurements gathered from sites with a similar hydrolog-ical environment. The estimates are developed as probabil-ity density functions, using a CLM surrogate. Two struc-tural error models were to used represent the discrepancybetween model and data and selected by their ability to re-produce data. The sensitivity of the structural error modelform to the two types of observations is also investigated.

Jaideep RaySandia National Laboratories, Livermore, CAjairay@sandia.gov

Laura SwilerSandia National LaboratoriesAlbuquerque, New Mexico 87185lpswile@sandia.gov

Maoyi Huang, Zhangshuan HouPacific Northwest National Labmaoyi.huang@pnnl.gov, zhangshuan.hou@pnnl.gov

MS162

Optimal Convergence Rates of Co-Simulation Us-

136 CS15 Abstracts

ing Fine Structure Analysis

For coupled systems, where the monolithic simulation isdifficult, co-simulation is an important methodology intime domain. In contrast to coupled ODEs, for coupledDAEs convergence can only be guranteed if certain contrac-tion properties are given. Here, the fine structure analysisis used to verify that the corresponding recursion estimatesare attained upper bounds on the convergence rate. Fur-thermore we verify that numerical convergence might notbe detacted. The relation of iterations and order of thetime integrations is discussed.

Andreas Bartel, Kai GauslingUniversity of Wuppertalbartel@math.uni-wuppertal.de,gausling@math.uni-wuppertal.de

Sebastian SchopsTheorie Elektromagnetischer Felder (TEMF) and GSCETechnische Universitschoeps@gsc.tu-darmstadt.de

MS162

Trigonometric Integration Methods in Circuit Sim-ulation

The numerical calculation of the limit cycle of oscillatorswith resonators exhibiting a high quality factor Q suchas quartz crystals is a difficult task in the time domain.Time domain integration formulas may introduce numeri-cal damping which leads to erroneous limit cycles. A novelclass of adaptive multistep integration formulas is derivedwhich circumvent the aforementioned problems. The re-sults are compared with the well-known Harmonic Balance(HB) technique. Moreover the range of absolute stabilityand error estimates are derived for these methods.

Hans-Georg Brachtendorf, Kai BittnerUniversity of Applied Sciences Upper Austriahans-georg.brachtendorf@fh-hagenberg.at, kai.bittner@fh-hagenberg.at

MS162

Modelling Transmission Power Systems with theImplicit DAE Solver, IDA

The main flow of power on a transmission power systemcan be modeled as a coupled set of differential-algebraicequations. Transmission models of interest, however, in-clude limits on output and internal states as well as limitson state rates of change, deadbands, and positivity con-straints. In this talk, we will outline how we are using ageneral DAE solver package, IDA, for solution of transmis-sion grid models incorporating many of these conditionswithin our simulation. This work was performed under theauspices of the U.S. Department of Energy by LawrenceLivermore National Laboratory under contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC.

Philip TopLawrence Livermore National Laboratorytop1@llnl.gov

Carol S. WoodwardLawrence Livermore Nat’l Labwoodward6@llnl.gov

Alan HindmarshLawrence Livermore National LaboratoryCenter for Applied Scientific Computingalanh@llnl.gov

MS162

Fast Time-Domain Simulation for Reliable FaultDetection

Imperfections in manufacturing processes may cause un-wanted connections (faults) that are added to the nom-inal, ”golden”, design of an electronic circuit. By faultsimulation we simulate all situations: a huge number ofnew connections and each with many different values, upto the regime of large deviations, for the newly added ele-ment. We also consider ”opens” (broken connections). Astrategy is developed to efficiently simulate the faulty so-lutions until their moment of detection. We fully exploitthe hierarchical structure of the circuit. Fast fault simula-tion is achieved in which the golden solution and all faultysolutions are calculated over a same time step.

E. Jan W. ter MatenNXP Semiconductors, Corp IT, DMS-PDM-MathematicsJan.ter.Maten@math.uni-wuppertal.de

Bratislav TasicNXP Semiconductorsbratislav.tasic@nxp.com

Jos J. DohmenNXP Semiconductors, the Netherlandsjos.j.dohmen@nxp.com

Theo G.J. BeelenNXP Semiconductorstheo.g.j.beelen@nxp.com

Rick JanssenNXP Semiconductors, the Netherlandsrick.janssen@nxp.com

Wil SchildersEindhoven University of Technologyw.h.a.schilders@TUE.nl

Michael GuentherBergische Universitaet Wuppertalguenther@math.uni-wuppertal.de

MS163

Sparse QR Factorization on Heterogenous Plat-forms with Multiple GPUs

We present a sparse multifrontal QR Factorization methodon a heterogeneous CPU-GPU platform. Our method isextremely efficient for different sparse matrices sizes andstructures even for matrices that don’t fit in GPU mem-ory. Our method benefits from both the highly parallelgeneral-purpose computing cores available on a single GPUand from multiple GPUs on a single platform. This pre-sentation focuses on parallelism over multiple GPU cores.

Mohamed GadouUniversity of Floridamgadou@cise.ufl.edu

CS15 Abstracts 137

Timothy A. DavisTexas A&MComputer Science and Engineeringdavis@tamu.edu

Sanjay RankaCISE, University of Florida, USAranka@cise.ufl.edu

MS163

Sparse Communication Avoiding Pivoting andGPUs

Modern GPUs provide a window on future hardware plat-forms that we need to design for. In this talk we de-scribe our experience in implementing direct methods forsparse symmetric indefinite matrices in CUDA, a topicthat presents both mathematical and technical challenges.Whilst a number of communication-avoiding methods havebeen developed for dense linear algebra, their applicabilityto sparse linear algebra is limited as they ignore sparsity inselecting pivots, generating significant fill. We will describeheuristics that attempt to manage this complexity througha series of fall-back strategies that in the best case have sim-ilar communication properties to the unpivoted Choleskyfactorization, but for numerically challenging problems de-liver stability on a par with the best existing sparse sym-metric indefinite direct solvers.

Jonathan HoggSTFC Rutherford Appleton Lab, UKjonathan.hogg@stfc.ac.uk

Jennifer ScottRutherford Appleton LaboratoryComputational Science and Engineering Departmentjennifer.scott@stfc.ac.uk

MS163

GLU: LU Re-Factorization on the GPU

In realistic applications we often solve a sequence of similarlinear systems that arise as part of a non-linear iterationprocess. In this talk we focus on the design and implemen-tation of the parallel LU re-factorization on the GPU. Itcan be performed on the linear systems that have the samesparsity pattern, pivoting and reordering to minimize fill-inas the original system. We also discuss batched version ofthe algorithm and present relevant numerical experiments.

Maxim Naumov, Sharan Chetlur, Lung Sheng ChienNVIDIAmaxim.a.naumov@gmail.com, schetlur@nvidia.com,lchien@nvidia.com

MS163

Accelerating the Supernodal Sparse Cholesky Fac-torization on GPUs

Achieving high performance sparse Cholesky factorizationon a GPU is difficult due to irregular computation, limitedGPU memory, and PCIe communication. Previous workshowed how some PCIe communication could be hiddenbehind CPU and GPU computation. This work shows howa larger portion of the factorization can be accelerated onthe GPU, and overall performance substantially improved,by moving entire branches of the elimination tree to the

GPU and greatly reducing the required PCIe communica-tion.

Steven C. RennichNVIDIAsrennich@nvidia.com

Timothy A. DavisTexas A&MComputer Science and Engineeringdavis@tamu.edu

Darko StosicNVIDIAddstosic@bu.edu

MS164

A Fast N-body Algorithm for Kernel Sums in HighDimensions

In computational statistics kernelized methods require therapid evaluation of kernel sums. We present a fast al-gorithm for such sums and introduce novel methods forpruning and for approximating the far field. The schemeis kernel-independent (does not use analytic expansions)and the pruning is combinatorial (not geometric). Its com-plexity depends linearly on the dimension. We present thestructure of the algorithm and experimental results thatdemonstrate is performance. As a highlight, we report re-sults for Gaussian kernel sums for one million points in1000 dimensions and for problems in which the kernel hasvariable bandwidth.

George Biros, Bill MarchUniversity of Texas at Austinbiros@ices.utexas.edu, march@ices.utexas.edu

Bo XiaoSchool of Computational Science and EngineeringGeorgia Institute of Technologyboxiao@gatech.edu

MS164

Information-Theoretic Tools for Uncertainty Quan-tification of High Dimensional Stochastic Models.

We present mathematical tools for deriving optimal, com-putable bounds on sensitivity indices of observables forcomplex stochastic models arising in biology, reaction ki-netics and materials science. The presented technique al-lows for deriving bounds also for path-dependent function-als and risk sensitive functionals. The use of variationalrepresentation of relative entropy also allows for error es-timation and uncertainty quantification of coarse-grainedmodels.

Paul DupuisDivision of Applied MathematicsBrown Universitydupuis@dam.brown.edu

Markos KatsoulakisUniversity of Massachusetts at Amherstmarkos.katsoulakis@gmail.com

Yannis PantazisUniversity of Massachusetts, AmherstDepartment of Mathematics and Statistics

138 CS15 Abstracts

pantazis@math.umass.edu

Petr PlechacUniversity of DelawareDepartment of Mathematical Sciencesplechac@math.udel.edu

MS164

Use of Parallel MCMC Methods with the Commu-nity Land Model

We present the development of a parallel Delayed RejectionAdaptive Metropolis (DRAM) algorithm and its use withthe Community Land Model for Bayesian calibration ofmodel parameters. Bayesian calibration of expensive sim-ulations is often done with emulators because of the com-putational cost of Monte Carlo Markov Chain (MCMC)sampling. In this case, we chose not to use emulators andinstead use a parallel chain scheme directly on CLM toobtain reasonable run times.

Jaideep RaySandia National Laboratories, Livermore, CAjairay@sandia.gov

Laura SwilerSandia National LaboratoriesAlbuquerque, New Mexico 87185lpswile@sandia.gov

Maoyi HuangPacific Northwest National Labmaoyi.huang@pnnl.gov

Jason HouPacific Northwest National Laboratoryzhangshuan.hou@pnnl.gov

MS164

Highly Scalable Hierarchical Sampling Algorithmsfor Gaussian Random Fields

The ability to generate samples of random fields with pre-scribed statistical properties is a key ingredient for manyuncertainty quantification methods. In this talk, we willpresent a highly scalable multilevel hierarchical samplingtechnique that has linear complexity. Samples are gener-ated on a coarse grid using the truncated Karhunen-Loeveexpansion, and then extended to the finer levels by solvinga stochastic partial differential equation. An applicationto Multilevel Monte Carlo simulations of subsurface flowswill be presented to demonstrate the good scalability of ourmethod.

Panayot VassilevskiLawrence Livermore National Laboratoryvassilevski1@llnl.gov

Umberto E. VillaCenter for Advanced Scientific ComputingLawrence Livermore National Laboratoryvilla13@llnl.gov

MS165

Construction of Gaussian Surrogate Process Using

Numerical and Modeling Error Uncertainty

In this talk we will explore the use of adjoint based esti-mates of numerical error (upper bounds where available)in quantities of interest to aid in the construction of moreeffective surrogates. This will complement the vast body ofwork on constructing such surrogates for model parameteruncertainty characterization.

Hossein AghakhaniUniversity at Buffalo, SUNYhaghakha@buffalo.edu

Abani K. PatraSUNY at BuffaloDept of Mechanical Engineeringabani.patra@gmail.com

Elaine SpillerMarquette Universityelaine.spiller@marquette.edu

MS165

Calibration of the Spalart-Allmaras TurbulenceModel for Blunt Body Re-Entry Vehicle Flows Us-ing DNS Data

The Spalart-Allmaras turbulence model is calibrated foruse in predictions of transonic, chemically reacting bound-ary layers with favorable pressure gradients similar to thoseobserved on blunt body re-entry vehicles. The calibrationtakes the form of a Bayesian update for the model pa-rameters. We detail DNS cases specially designed for thiscalibration, uncertainty estimates for the resulting DNSdata, a simple model inadequacy representation used forthe calibration, and the posterior results for the model pa-rameters.

Robert D. MoserUniversity of Texas at Austinrmoser@ices.utexas.edu

Todd OliverPECOS/ICES, The University of Texas at Austinoliver@ices.utexas.edu

Victor TopalianPECOS/ICESThe University of Texas at Austintopalian@ices.utexas.edu

Rhys UlerichThe Univeristy of Texas at Austinrhys.ulerich@gmail.com

MS165

Quantifying the Impact of Numerical Errors Alongwith Other Uncertainties on Probabilistic HazardMapping

A probabilistic hazard map requires: 1) a stochastic sce-nario model – incorporating data and expert opinion – thatdescribes the system’s aleatory variability, and 2) a physi-cal model which lets one explore catastrophic hazards (in-undation by flooding, landslides, tsunamis, etc). Geophys-ical modelers often assume that uncertainty >> numericalerror and ignore impacts of the later. We have devised asurrogate-based strategy using adjoint error estimates to

CS15 Abstracts 139

quantify the effects numerical errors and other uncertain-ties on hazard probabilities.

Elaine SpillerMarquette Universityelaine.spiller@marquette.edu

Hossein AghakhaniUniversity at Buffalo, SUNYhaghakha@buffalo.edu

MS165

Predictive Uncertainty Quantification of An Ablat-ing Entry Vehicle Heatshield

Simulations of hypersonic reacting flow require the integra-tion of a number of complex physical models with uncer-tain parameters, evaluated at conditions for which exper-imental data may be sparse. We discuss calibration andforward propagation of uncertainty in the context of theatmospheric re-entry of a symmetric capsule body with anablating heatshield, focusing on cycles of calibration andprediction for aerothermochemistry, surface ablation, tur-bulence, and other submodels. Multiple years’ results willbe presented.

Roy StognerUniversity of Texas at Austinroystgnr@ices.utexas.edu

MS166

Mathematical Modeling of Gliomas: Implicationsfor Interpreting Therapeutic Efficacy ThroughImaging

Glioblastoma is the most aggressive form of primary braintumor. Traditional clinical images, such as magnetic res-onance images, are limited in their ability to capture thefull extent of the diffuse disease both prior to therapy and,even more, post therapy. In this talk, we will discuss howmathematical modeling can lend insights for interpretingthese images on a patient-specific basis by estimating theextent of the disease not visible on imaging.

Andrea Hawkins-DaarudDepartment of Neurological SurgeryNorthwestern Universityandrea.hawkins-daarud@northwestern.edu

Russell RockneNorthwestern Universityrussell.rockne@northwestern.edu

David CorwinLaunchPad Labdave@launchpadlab.com

Alexander R.A. AndersonMoffitt Cancer Centeralexander.anderson@moffitt.org

Paul KinahanUniversity of Washingtonkinahan@uw.edu

Kristin R. SwansonNorthwestern University

kristin.swanson@northwestern.edu

MS166

Optimization of Computational Simulation Set forQuantification of Hurricane Surge Extreme-ValueStatistics

Extreme-value hurricane flooding statistics are essentialfor effective coastal risk assessment. The joint probabil-ity method is a robust and reliable approach for quantify-ing these statistics and their uncertainty. Yet, the arrayof hurricane possibilities and complexity of physical pro-cesses that must be simulated result in an unmanageablecomputational burden. Here, optimal sampling to reducethis burden is achieved with physics-based, algebraic surgeresponse functions to define continuous probability densityfunctions for hurricane flood elevation.

Jennifer L. IrishVirginia Polytechnic Institute and State Universityjirish@vt.edu

MS166

Hurricane Storm Surge Risk Analysis for the USNorth Atlantic Coast

In this work, we use a physically based assessment to es-timate the risk of hurricane storm surge in NarragansettBay, RI, Jamaica Bay, NY, Atlantic City, NJ, and Norfolk,VA. Using a novel approach to risk analysis, we estimatestorm surge recurrence intervals for the current and futureclimate by forcing a hydrodynamic model with thousandsof synthetic hurricanes generated using data from obser-vations and global climate models. Our results have beenused to inform a multi-institutional, interdisciplinary re-search effort to develop “Structures of Coastal Resilience.”

Talea Mayo, Ning LinPrinceton Universitytmayo@princeton.edu, nlin@princeton.edu

MS166

Representing model inadequacy: A stochastic op-erator approach

We investigate model form uncertainty for a reaction mech-anism model in hydrocarbon combustion. In a typi-cal reaction, the complete mechanism is either not well-understood, or too complex to effectively use as part of alarger combustion problem, necessitating a reduced model.To account for the discrepancy between the full model andits reduced version, we propose an additive, linear, prob-abilistic formulation. This representation is encoded in arandom matrix, whose entries are calibrated using a hier-archical Bayesian scheme. In particular, this formulationis designed to respect certain physical constraints, but alsobe flexible enough to apply to multiple reactions.

Rebecca MorrisonUT Austinrebeccam@ices.utexas.edu

Robert D. MoserUniversity of Texas at Austin

140 CS15 Abstracts

rmoser@ices.utexas.edu

MS167

Adaptive Reconnection-Based Arbitrary La-grangian Eulerian Method

We describe a new h-adaptive ReALE (A-ReALE) method.The adaptive rezone of A-ReALE is proposed based onthe equidistribution principle of centroidal Voronoi tes-sellations (CVTs). In the rezone phase, we introduce aquadtree based initialization to determine the initial guessof the cell generators. A new CVT is generated by mini-mizing the mesh energy of the Voronoi tessellation. For 2Dexamples of time-dependent simulations, A-ReALE showsbetter mesh convergence than ReALE.

Wurigen BoCCS-2, LANLwbo@lanl.gov

Misha ShashkovLos Alamos National Laboratorymisha@t7.lanl.gov

MS167

Multimaterial Simulation in Reale Framework

In the ReALE method presented here, connectivity of themesh is allowed to change during the reconnection phase.The main idea is to define a new grid using specific move-ment of generators and formalism of Voronoi diagrams.This method leads to general polygonal mesh and allows tofollow Lagrangian features of the mesh much better thanfor standard ALE methods. Furthermore, in the contextof multimaterial computations using ReALE method (asfor standard ALE method), grid and fluid move separately,and mixed cells containing two or more materials could ap-pear. These mixed cells contain material interfaces, whichneed special treatment to be taken into account. This isdone using the Moment of Fluid (MOF) method.

Jerome BreilCELIA, UMR 5107 CNRS, University of Bordeaux andCEA, 351 Cobreil@celia.u-bordeaux1.fr

MS167

Triangular Metric-Based Mesh Adaptation forCompressible Multi-Material Flows in Semi-Lagrangian Coordinates

Lagrangian methods for multi-material flows are very at-tractive (precision, contact discontinuity preservation), butfail to calculate vertexes or shears. Classical remedy is ALEmethod which consists defining a ”smoother” mesh with-out changing its connectivity and the remap the solutionon it. The next step is mesh adaptation to improve robust-ness and precision. In this context, we present a metric-based triangular mesh adaptation method in 2D, using aninterface reconstruction approach to address the numericaldissipation of material interfaces.

Stephane Del Pino, Isabelle MarmajouCEA

stephane.delpino@cea.fr, isabelle.marmajou@cea.fr

MS167

Reconnection ALE in a Massively-Parallel,Staggered-Grid, Multi-Physics Code

The development of Reconnection-based ArbitraryLagrangian-Eulerian (ReALE) methods has focused oncell-centered discretizations for Lagrangian hydrodynam-ics to greatly simplify the conservative remapping offluid variables. Our approach is different, using bothspatially-staggered and subzonal discretizations. Thistalk will focus on the benefits of this discretization in thecontext of multi-physics, the unique challenges it presentsin the context of ReALE, and the novel techniques wehave developed to address these challenges.

David StarinshakLawrence Livermore National Laboratorystarinshak1@llnl.gov

J. Michael Owen, Douglas S. MillerLawrence Livermore Nat. Labmikeowen@llnl.gov, dougmiller@llnl.gov

MS168

Interpolatory Model Reduction for Nonlinear In-version

Model reduction by rational interpolation has been effec-tively used for producing accurate, in some cases, optimalreduced models in a numerically feasible way. In this talk,we will show that interpolatory methods can be also eas-ily employed in nonlinear inversion problems to reduce thecost of the overall inversion process with little loss of ac-curacy. We will present the framework in the applicationsetting of diffuse optical tomography.

Serkan GugercinVirginia Tech.Department of Mathematicsgugercin@math.vt.edu

MS168

Nonlinear Model Order Reduction UsingPod/DEIM 4-D Var with Trust Region Ap-plied to a Spherical Shallow Water EquationsModel

We address a very large-scale optimization problem withPDE constraints governed by a spherical shallow waterequations as proxy for an atmospheric model.( 4-D VAR)MOR with POD/DEIM and trust region model using bothforward and adjoint snapshots opens opportunity of reduc-ing computational cost of 4-D VAR data assimilation. Im-pact of number of POD basis functions, DEIM points alongwith choice of snapshots and optimization algorithm andfinally CPU-speed-up will be investigated.

Ionel M. NavonFlorida State UniversityDepartment of Scientific Computinginavon@fsu.edu

Fangxin FangDepartment of Earth Science and EngineeringImperial College London, U.K.f.fang@imperial.ac.uk

CS15 Abstracts 141

Juan DuIAP, Academia Sinica, Beijing, Chinadujuan10@mail.iap.ac.cn

MS168

Reduced Order Modelling for Fluid-Structure In-teraction Problems

We present some advances in Reduced Order Modelling ap-plied to fluid structure interaction problems, modelled asinverse problems within a parametric setting. Special at-tention is devoted to the coupling between fluid and struc-ture through the interface in order to apply reduced com-putational models to fluid and structure and manage theinterface deformation with efficient algorithms. A specialemphasis is devoted to the coupling between optimizationand fluid-structure interaction problems.

Francesco BallarinPolitecnico di Milano, Italyfrancesco.ballarin@polimi.it

Gianluigi RozzaSISSA, International School for Advanced StudiesTrieste, Italygianluigi.rozza@sissa.it

MS168

Aposteriori Error Estimates and Adaptive Re-duced Order Modeling Data Assimilation

We will develop goal-oriented aposteriori estimators of theerror in the strong constraint reduced order 4DVar solu-tion. Specifically we will formulate goals as functions thatdepend on the analysis obtained by minimizing a standarddata assimilation cost function. The novel framework willbe used to guide an adaptive efficient choice of snapshots,location of discrete empirical interpolation points (DEIM)and matrix DEIM indexes leading to suboptimal reducedsolutions that approximate well the full data assimilationanalyses.

Razvan StefanescuVirginia Techrstefane@vt.edu

Adrian SanduVirginia Polytechnic Institute andState Universitysandu@cs.vt.edu

MS169

Numerical Stability Issues in H2 approximationMethods

We discuss the fine details of numerical implementation ofthe IRKA and the VF algorithms for H2 rational approx-imations of linear systems, i.e. turning the methods intoreliable mathematical software. Our thesis is that such fi-nal step is by no means simple or routine task, even withthe state of the art numerical software packages. We tacklethe problems of the underlying Cauchy and Vandermondestructures, moment matching, as well as convergence issuesin the appropriate function spaces.

Zlatko DrmacUniversity of ZagrebDepartment of Mathematics

drmac@math.hr

Christopher A. BeattieVirginia Polytechnic Institute and State Universitybeattie@vt.edu

Serkan GugercinVirginia Tech.Department of Mathematicsgugercin@math.vt.edu

MS169

Certified Reduced Basis Model Reduction forMaxwell’s Equations

The Reduced Basis Method generates low-order models forthe efficient evaluation of parametrized PDEs in many-query and real-time contexts. The approximation qualityis certified by using rigorous error estimators. We apply theReduced Basis Method to systems of Maxwell’s equationsarising from electrical circuits. Using microstrip models,the input-output behaviour of interconnect structures isapproximated for a certain frequency range, parametrizedgeometry like distance between microstrips and materialcoefficients.

Martin W. HessMax-Planck-Institute for Dynamics of Complex TechnicalSystems Magdeburghessm@mpi-magdeburg.mpg.de

Peter BennerMax Planck Institute, Magdeburg, Germanybenner@mpi-magdeburg.mpg.de

MS169

Parameter Estimation for Inverse Problems

As mathematical models continue to grow in size and com-plexity, the efficiency of the numerical methods used tosolve their corresponding inverse problems becomes in-creasingly important. With differential equation models,for example, avoiding the computation of the forward solu-tion is desirable. Constructing a “nearby” inverse problemavoids this computation to create a numerically robust ap-proach while also providing parameter estimates suitablefor the solution of the original inverse problem.

Justin KruegerDepartment of MathematicsVirginia Techkruegej2@vt.edu

MS169

Stochastic Approach to Nonlinear Inversion Com-bining Simultaneous Random and DeterministicSources

We discuss parametric inversion for diffuse optical tomog-raphy using simultaneous random sources and detectors todrastically reduce the costs of the expensive solution ofmany large linear systems to be solved. Each linear sys-tem corresponds to a solving a 3D PDE. We compare thiswith inversion approaches using reduced order models. Inaddition, we consider methods to improve solution qualityat low cost.

Selin Sariaydin

142 CS15 Abstracts

Department of MathematicsVirginia Techselin@vt.edu

Eric De SturlerVirginia Techsturler@vt.edu

Serkan GugercinVirginia Tech.Department of Mathematicsgugercin@math.vt.edu

Misha E. KilmerTufts Universitymisha.kilmer@tufts.edu

MS170

Using Numerical Optimization Methods for Sam-pling in Inverse Problems

Many solution methods for inverse problems compute themaximum a posteriori (MAP) estimator, or equivalently,the regularized solution, by solving an optimization prob-lem. Uncertainty quantification (UQ), on the other hand,typically requires sampling from the Bayesian posteriordensity function. In this talk, we bring these two ideas to-gether and present posterior sampling methods that makeuse of existing algorithms for computing regularized so-lutions/MAP estimators. Theoretically correct samplersfor both linear and nonlinear inverse problems will be pre-sented.

Johnathan M. BardsleyUniversity of Montanabardsleyj@mso.umt.edu

MS170

Point Spread Reconstruction from the Image of aSharp Edge: Computation and Uncertainty Quan-tification

The blurring of an image is often modeled as convolutionwith a point spread function (PSF) specific to the imaginginstrument. We present a method for estimating the PSFthat is suitable for applications where it is possible to imagea sharp edge. In our model, the PSF is a solution to aFredholm integral equation of the first kind, known to beill-posed. We employ optimization and sampling methodsto compute several stable estimates of the solution.

Kevin JoyceUniversity of MontanaDepartment of Mathematical Scienceskevin1.joyce@umontana.edu

Johnathan M. BardsleyUniversity of Montanabardsleyj@mso.umt.edu

Aaron B. LuttmanNational Security Technologies, LLCluttmaab@nv.doe.gov

Peter GolubstovMoscow State University

peter.golubstov@umontana.edu

MS170

Statistical Tests for Total Variation RegularizationParameter Selection

We explore three new algorithms for choice of scaling orregularization parameter in Total Variation denoising. TVregularization is viewed as an M-estimator and it is as-sumed to converge to a well defined limit even if theprobability model is not correctly specified. The Dis-crepancy Principle, a modified version of the χ2 methodfor Tikhonov regularization and an empirically Bayesianapproach are implemented and compared on benchmarkproblems in digital image processing.

Jodi MeadBoise State UniversityDepartment of Mathematicsjmead@boisestate.edu

MS170

Constrained Iterative Solver for Sparse Unmixingand Deblurring of Hyperspectral Images

Spectral unmixing involves the computation of fractionalcontributions of elementary spectra, called endmembers.The forward model involves a linear mixture of endmem-bers, with nonnegative sparse coefficients, and a wave-length dependent blurring operation. The inverse (recon-struction) problem requires solving a large scale, struc-tured, constrained least squares problem. We show thatby exploiting structure of the coefficient matrix, and usingknown properties of the endmembers, iterative methodscan be used to efficiently reconstruct the fractional abun-dance coefficients.

Sebastian BerishaUniversity of Pennsylvaniaberishas@mail.med.upenn.edu

James G. NagyEmory UniversityDepartment of Math and Computer Sciencenagy@mathcs.emory.edu

Robert PlemmonsWake Forest Universityplemmons@wfu.edu

MS171

Task Based Programming with Pycompss: Lever-aging Python in Parallel Platforms

StarSs is a family of task-based programming models whichis based on the idea of writing sequential code which is ex-ecuted in parallel at runtime taking into account the datadependences between tasks. COMPSs is an instance ofStarSs, which intends to simplify the execution of Java ap-plications in distributed infrastructures, including clustersand Clouds. The talk will focus in PyCOMPSs, a bindingfor the Python language which will enable a larger numberof scientific applications in fields such as lifesciences andin the integration of COMPSs with new Big Data resourcemanagement methodologies developed at BSC.

Rosa M. BadiaBarcelona Supercomputing Center / CSIC

CS15 Abstracts 143

rosa.m.badia@bsc.es

MS171

Coarse Grained Task-Based Parareal Parallel-In-Time Applications in Fusion Energy

Parallelization in the temporal domain has recentlyemerged as a promising approach to utilize the massiveconcurreny at the heart of existing and emerging comput-ing platforms. We present an event-driven task-based for-mulation of the parareal algorithm, implemented using aflexible, lightweight Python framework for coupled simula-tions. We describe recent applications of this frameworkto various problems in fusion modelling and simulation,including turbulance, advanced tokamak scenario analysis,and plasma edge dynamics.

Wael R. ElwasifOak Ridge National Laboratoryelwasifwr@ornl.gov

Debasmita SamaddarCCFEUK Atomic Energy Authoritydsamaddar@alaska.edu

MS171

A Task-Based Computational Astronomy Applica-tion

The European Extremely Large Telescope project is oneof Europe’s highest priorities in ground-based astronomy.The core implementation of the simulation lies in the in-tensive computation of a tomographic reconstructor, whichis used to drive the deformable mirror in real-time fromthe measurements. A new task-based numerical algorithmis proposed to capture the actual experimental noise andto substantially speed up previous implementations by ex-posing more concurrency, while reducing the number offloating-point operations.

Hatem LtaiefExtreme Computing Research CenterKAUSThatem.Ltaief@kaust.edu.sa

MS171

Applications at Airbus Group of a Task-Based H-Matrix Solver

The Boundary Element Method (BEM) requires the solv-ing of large, ill-conditionned, dense linear systems with alarge number of righ-hand sides. A H-Matrix is a hierachi-cal, approximate, data-sparse storage format for matricesthat can be manipulated to produce a fast direct linearsolver. We consider the H-Matrices for the BEM, withapplications to Airbus Group industrial test cases ; andwe present the parallelization of this algorithm in sharedand distributed memory, using the StarPU runtime sys-tem. An almost optimal parallel efficiency is achieved inshared memory, along with promising results in distributedmemory.

Guillaume SylvandEADS CCR, Centre de Toulouseguillaume.sylvand@airbus.com

Benoit Lize

Airbus Group Innovationsbenoit.lize@airbus.com

MS172

Estimation of Unmodeled Gravitational WaveTransients: an Application of Spline Based Regres-sion and Particle Swarm Optimization

Detecting and estimating unmodeled transient gravita-tional wave (GW) signals in noisy data is a major challengein GW data analysis. This paper explores a solution thatcombines spline regression with particle swarm optimiza-tion for knot placement and directional parameter estima-tion. Analyses of data from a network of detectors showfairly good directional estimates, with reasonable fidelityin the reconstruction of both GW polarization waveforms,at a signal to noise ratio capped at 15. Advisor: SoumyaMohanty, U Texas, Brownsville

Calvin LeungHarvey Mudd Collegecleung@g.hmc.edu

MS172

Persistent Random Walk of Microorganisms in aPorous Medium

We develop a persistent random walk model for the mo-tion of swimming cells in an idealized lattice-like porousmedium. The walk is described by a Markov chain in phasespace, tracking both position and velocity. Physical param-eters, including the overall geometry, bulk flow, and scat-tering laws, are incorporated into the memory-dependenttransition amplitudes. We numerically compute first pas-sage times in MATLAB to predict the effects of latticestructure on microbial transport. Advisor: Joern Dunkel(Massachusetts Institute of Technology)

Grace LimCalifornia State Polytechnic University, Pomonagracelim@csupomona.edu

Aden ForrowMITaforrow@mit.edu

MS172

Mean Squared Displacement and Mean First Pas-sage Time in Fluids with Memory

Modeling the motion of passive particles in a viscous fluid iswell studied and understood. Extensions to passive motionin a complex fluid which exhibits both viscous and elasticproperties have been developed in recent years. However,questions remain on the characterization of mean-squaredisplacement and mean first passage for different theoret-ical models. We present a statistically exact covariancebased algorithm implemented in parallel C++ to generateparticle paths to answer these questions. Advisor: Chris-tel Hohenegger, Department of Mathematics, University ofUtah

Michael SenterUniversity of Utah

144 CS15 Abstracts

u0822950@utah.edu

MS172

Pymethyl: A Bioinformatic Approach to Methyla-tion Patterns and their Epigenetic Effects on Riskof Breast Cancer

The study looked at the genomes of two different groupsof parous and nulliparous women and their risk for breastcancer. These genomes were sequenced for their genomicmethylation patterns. The information was then processedby a high throughput, brute force algorithm to look forplaces of hypermethylation within the promoter regions ortranscribable regions of specific genes. This informationhelps us gain information on the epigenetic effects to therisk of breast cancer. Advisor: Jose Russo, Fox ChaseCancer Center Mentor

Cody WatsonWofford Collegewatsonca@email.wofford.edu

MS172

Modeling Bull Sperm Motility Using Image Pro-cessing

We use image processing to determine whether the chemi-cal heparin may change bending in a bull sperm flagellum.Experimental movies for several sperm are analyzed to de-termine sperm location. From this data, curvature of bend-ing and swimming speeds are analyzed. We also computebending forces and resulting fluid flow using the methodof regularized Stokeslets. We conclude that heparin doeschange bending in the neck region as well as changing hy-drodynamic efficiency and energy. Advisor: Sarah D. Ol-son, Worcester Polytechnic Institute

Linan ZhangWorcester Polytechnic Institutelzhang2@WPI.EDU

MS172

Bounds on Electrical Fields in Two-Component In-homogeneous Bodies

We investigate bounds on the maximum value of electricalfield in two-component inhomogeneous bodies. We assumethe conductivities of the inclusions and the surroundingbody are known, with no assumptions on the precise ge-ometry of the inclusions. Results are in terms of valuesof the voltage and current that can be attained from mea-surements on the boundary of the body. This research haspotential applications in preventing electrical breakdown incomposite materials. Advisor: Graeme Milton, Universityof Utah

Zoe Koch, Michael Primrose, Michael ZhaoUniversity of Utahkochzoe@gmail.com, tba, mz84092@gmail.com

MS173

On a New Class of Semi-Lagrangian Schemes forKinetic Equations

In this talk we introduce a new class of semi-Lagrangianschemes for simulating kinetic type equations. In this ap-proach we genealize the fast semi-Lagrangian scheme devel-oped in [J. Comput. Phys., Vol. 255, 2013, pp 680-698] to

the case of high order reconstructions. The first order ac-curate semi-Lagrangian scheme is supplemented with poly-nomial reconstructions of the distribution function and ofthe collisional operator leading to an effective high orderaccurate numerical scheme for all regimes, from extremlyrarefied to highly collisional. The limitation of the recon-structions to avoid spurious oscillations is made a poste-riori using polynomial order decrementation. This later isbased on so-called detection criteria which filter problem-atic cells which need limitation from acceptable cells whichare updated with an optimal accurate scheme.

Giacomo DimarcoUniversita degli Studi di Ferraradmrgcm@unife.it

MS173

Practical Numerical Methods for Solving the Boltz-mann Transport Equation in Nuclear ReactorAnalysis

The numerical solution of the linearized form of the Boltz-mann Transport Equation (BTE), as applied to the trans-port of neutrons within a ”multiplicative” medium, resultsin the characterization of various macroscopic quantitiesof interest such as criticality, power distribution, and com-positional changes in a nuclear reactor. For the purposeof practical reactor analysis and design, various physicalapproximations are introduced in order to reduce the sizeof the neutral-particle phase-space. The goal of this talkis twofold: first, to review current standard numericalmethods used for the solution of BTE, and secondly, topresent recent progress in the spatial discretization of theBTE in the context of lattice physics calculations. TheMethod of Characteristics (MoC), used to solve BTE inlattice physics, has become ubiquitous in design calcula-tions. However, the order of accuracy of this scheme, as afunction of mesh size, remains first-order. In order to relaxthis limitation, a spatially-linear scheme is introduced inthe MoC scheme in order to obtain second-order accuracy.Although general high-order discretizations have been de-rived, the spatially-linear scheme remains an optimal com-promise between run time and storage, for an equal level ofaccuracy. Numerical results will be presented to supportthe conclusions sketched above and realistic numerical sim-ulations will presented and discussed.

Rodolfo FerrerStudsvikrodolfo.ferrer@studsvik.com

MS173

A Deterministic-Particle Transport Solver forScale-Bridging Simulation of Thermal RadiativeTransfer

A high-order, low-order (HOLO) algorithm is a moment-based, scale-bridging algorithm for transport equations.HOLO algorithms have recently made significant efficiencyand accuracy impacts in thermal radiative transfer (TRT)problems. The goal of this work is to develop an efficient,robust, Lagrangian, characteristic-based transport solverfor TRT problems within the context of a HOLO algo-rithm. A preliminary example has shown that a new HOsolver can achieve a factor of 100 reduction in computa-tional effort compared to both Monte Carlo and Sn forand equivalent accuracy.

Hyeongkae Park

CS15 Abstracts 145

Los Alamos National Laboratoryhkpark@lanl.gov

MS173

A Hierarchy of Hybrid Numerical Methods forMulti-Scale Kinetic Equations

In this work, we construct a hierarchy of hybrid numericalmethods for multi-scale kinetic equations based on momentrealizability matrices, a concept introduced by Levermore,Morokoff and Nadiga. Following such a criterion, one canconsider hybrid scheme where the hydrodynamic part isgiven either by the compressible Euler or Navier-Stokesequations, or even with more general models, such as theBurnett or super-Burnett systems. The efficiency of themethod obtained can sometimes match the one of a fluidmethod, with the accuracy of a kinetic one.

Thomas ReyUniversity of Marylandtrey@cscamm.umd.edu

Francis FilbetUniversity of Lyonfilbet@math.univ-lyon1.fr

MS174

HJB-POD Feedback Control for Advection-Diffusion Equations

We present an algorithm for the approximation of aninfinite horizon optimal control problem for advection-diffusion equations. The method is based on the couplingbetween a POD representation of the solution and a Dy-namic Programming approximation scheme for the corre-sponding stationary Hamilton-Jacobi equation. We discussseveral features regarding the selection of the snapshots foradvection dominated terms. Some test problems are pre-sented to illustrate the method.

Alessandro AllaDepartment of MathematicsUniversity of Hamburg, Germanyalessandro.alla@uni-hamburg.de

Michael HinzeUniversitat HamburgDepartment Mathematikmichael.hinze@uni-hamburg.de

MS174

Application of Discrete Empirical InterpolationMethod to Reduced Order Modeling of NonlinearParametric Systems

We study two approaches of applying discrete empirical in-terpolation method (DEIM) in the finite element context,one applied to the assembled and the other to the unassem-bled form of the nonlinearity. We carefully examine howDEIM is applied in each case, and the substantial efficiencygains obtained by the DEIM. In addition, we demonstratehow to apply DEIM to obtain ROMs for a class of param-eterized system that arises, e.g. in shape optimization.

Harbir AntilGeorge Mason UniversityFairfax, VA

hantil@gmu.edu

MS174

Reduced Order Models for Nonlinear PDE-Constrained Optimization Problems in Fluid Dy-namics

We propose a model order reduction framework forparametrized optimization problems constrained by non-linear PDEs. First, we build – by means of either RB-greedy or POD methods – the reduced order model follow-ing a suitable all-at-once optimize-then-reduce paradigm.Then, combining rigorous error bounds with some heuris-tic computational strategies, we provide cheap yet reliablea posteriori error estimates. The methodology is appliedto the boundary optimal control of parametrized Navier-Stokes equations.

Federico NegriMathematics Institute of Computational Science andEng, EPFLfederico.negri@epfl.ch

Andrea ManzoniEPFL, MATHICSE-CMCSSwitzerlandandrea.manzoni@epfl.ch

Alfio QuarteroniEcole Pol. Fed. de LausanneAlfio.Quarteroni@epfl.ch

MS174

Reduced Basis Method for Hamilton-Jacobi-Bellman Equations

We consider the Hamilton-Jacobi-Bellman (HJB) equa-

tion of the form −∂tv + supα

{− a(α;μ)Δv − b(α;μ) ·

∇v − f(α;μ)}

= 0 for numerous different parameters

μ ∈ D ⊂ IRp by applying the Reduced Basis Method. Inour approach, the HJB equation is separated into an equa-tion which determines v and another which yields α. Toobtain an error estimator, we use a space-time formulationof these equations and apply the Brezzi-Rappaz-Raviarttheory for quadratic non-linearities. The implementationshows that this error estimator is efficient for the chosenexamples.

Sebastian SteckInstitute for Numerical AnalysisUniversity of Ulm, Germanysebastian.steck@uni-ulm.de

Karsten UrbanInstitute of Numerical Mathematics, University of Ulmkarsten.urban@uni-ulm.de

MS175

Application of Algebraic Multigrid (PETSc) forBlock Structured Adaptive Mesh Refinement Ap-plications (Chombo)

We report on progress in using algebraic multigrid (AMG)methods in the numerical library PETSc for challeng-ing problems in block structured adaptive mesh refine-ment (BSAMR) applications that use the Chombo library.

146 CS15 Abstracts

Chombo’s built-in geometric multigrid (GMG) solvers arefast for simple operators but for problems with complexgeometry GMG is not effective and AMG is an effectivesolution. We discuss new capabilities in Chombo for con-structing matrices, required for AMG, from BSAMR prob-lems.

Mark AdamsLawrence Berkeley Laboratorymfadams@lbl.gov

MS175

Solvers and Error Control for Atmospheric ColumnPhysics

Atmospheric column physics involves coupling of nons-mooth processes such as phase change and nonlocal/stiffprocesses like radiation and precipitation, along with strictpositivity constraints. The splitting schemes currentlyused by CAM are not convergent in time and have beencalibrated to compensate for systematic numerical errors.In this talk, we investigate the use of more rigorousODE/DAE approaches using PETSc and Sundials on thebasis of accuracy and efficiency.

Jed BrownMathematics and Computer Science DivisionArgonne National Laboratory and CU Boulderjed@jedbrown.org

MS175

FASTMath Unstructured Mesh (MOAB) Solver(PETSc) Interactions

High fidelity applications typically rely on unstructuredmeshes representing complex geometry, and interoperablesolver interfaces are critical for optimal mesh based traver-sal and operator assembly procedures. We present devel-opments on a discretization manager DM implementationthat utilizes array-based mesh database MOAB that ex-poses scalable mesh handling capabilities to simulators, re-sulting in reduced memory and communication overhead.Several scalar and multi-component solver demonstrationsemploying combinations of geometric multigrid and alge-braic preconditioners is discussed.

Vijay Mahadevan, Iulian GrindeanuArgonne National Laboratorymahadevan@anl.gov, iulian@mcs.anl.gov

Barry F. SmithArgonne National LabMCS Divisionbsmith@mcs.anl.gov

MS175

Scalable Adaptive ImEx Integration with ARKodeand HYPRE

Computational science increasingly focuses on simulationsof complex systems, typically involving interacting physicalprocesses and large data/computational requirements. Inthis talk, we consider the solution of a system of interactingadvection-diffusion-reaction equations, decomposing theseinto stiff (reaction-diffusion) and non-stiff (advection) por-tions. For this problem, we apply two open-source solver li-braries within the FASTMath project. The ARKode solver(part of the SUNDIALS library suite) enables high or-

der and stable ImEx simulations, while HYPRE excels atmassively-parallel linear systems and is used to precondi-tion the implicit solves within ARKode.

Daniel R. ReynoldsSouthern Methodist UniversityMathematicsreynolds@smu.edu

MS176

Aerodynamic Simulations Using a High-Order Dis-continuous Galerkin Solver

A parallel high-order Discontinuous Galerkin solver is de-veloped to simulate aerodynamic problems. The solvercapabilities include: mixed hybrid elements, hp-adaption,and an exact linearization used in an implicit precon-ditioned Newton-Krylov solver. Preconditioners includeGauss-Seidel relaxation, line implicit Jacobi, and ILU(0).Flows with strong shocks are simulated on simple geome-tries using a PDE based artificial viscosity. Also, turbulentflows are simulated on 2D airfoils and a full 3D aircraft us-ing the new negative Spalart-Almaras RANS model.

Michael BrazellUniversity of Wyomingmbrazell@uwyo.edu

Dimitri MavriplisDepartment of Mechanical EngineeringUniversity of Wyomingmavripl@uwyo.edu

MS176

Superconvergent HDG Methods with SymmetricStress Approximations for Stokes Flow (and LinearElasticity)

We present an abstract framework to obtain superconver-gence of HDG methods with symmetric stress approxi-mations (HDG-S methods) for the Stokes flow. Several2D methods are constructed based on local enrichment ofthe stress spaces of existing (suboptimal) HDG-S methods.Numerical results are provided to show their superior per-formance. Extension of the results to linear elasticity withsymmetric stress approximations is discussed. And chal-lenges for constructing 3D superconvergent HDG-S meth-ods are addressed.

Bernardo Cockburn, Guosheng FuSchool of MathematicsUniversity of Minnesotacockburn@math.umn.edu, fuxxx165@umn.edu

MS176

Active Fluxes; A New High-Order Paradigm

We consider finite-volume schemes in which the interfacefluxes are independent degrees of freedom, as proposed byvan Leer in 1977. In the semi-discrete limit these aresimilar to, and in some cases identical to, DiscontinuousGalerkin methods, but are naturally fully discrete and inthat case have several advantages, being more accurate,faster and requiring less storage.

Philip L. RoeAnn Arbor

CS15 Abstracts 147

philroe@umich.edu

MS176

Riemann-Solver-Free Space Time DiscontinuousGalerkin Method for General Conservation Laws

We will talk about a Riemann-solver-free space-time dis-continuous Galerkin method for general conservation laws.The method uses staggered space-time mesh to enforcespace-time flux conservation in the DG framework. Theresulting method is of high order and Riemann-solver free.The method is able to solve general conservation laws suchas compressible Euler equations, shallow water equationsand magnetohydrodynamics equations without the need ofany type of Riemann solvers.

Shuang Z. TuJackson State Universityshuangzhang.tu@jsums.edu

MS177

ScalFMM: A Generic Parallel Fast Multipole Li-brary

ScalFMM (Parallel Fast Multipole Library for Large ScaleSimulations) offers all the functionalities needed to performlarge parallel simulations while enabling an easy customiza-tion of the simulation components: kernels, particles andcells. We will present how we use our library on two kindsof application involving boundary integral representationsof physical fields. The first one implements isotropic dislo-cation kernels for Dislocation Dynamics and the second atime dependent kernel for acoustic problems.

Pierre BlanchardInriapierre.blanchard@inria.fr

Berenger Bramas, Olivier CoulaudINRIAberenger.bramas@inria.fr, olivier.coulaud@inria.fr

Eric F. DarveStanford UniversityMechanical Engineering Departmentdarve@stanford.edu

Laurent DupuyCEA-Saclaylaurent.dupuy@cea.fr

Arnaud EtcheverryInriaarnaud.etcheverry@inria.fr

Guillaume SylvandEADS CCR, Centre de Toulouseguillaume.sylvand@airbus.com

MS177

PVFMM: A Parallel Fast Multipole Method forVolume Potentials

PVFMM is a scalable FMM library for computing solu-tions to constant coefficient elliptic PDEs (Poisson, Stokes,Helmholtz) on cubic domain with free-space and periodicboundary conditions. In this talk, we discuss performance

optimizations including distributed and shared memoryparallelism, integration with co-processors, vectorizationand cache optimization. We also integrate our methodwith GMRES in PETSc to compute solutions to variablecoefficient Stokes problems and demonstrate scalability tothousands of compute nodes on TACC’s Stampede super-computer.

Dhairya MalhotraInstitute of Computational Engineering and SciencesThe University of Texas at Austindmalhotra@ices.utexas.edu

George BirosUniversity of Texas at Austinbiros@ices.utexas.edu

MS177

Robust Implementation of Quadrature by Expan-sion (QBX)

QBX is a quadrature scheme for computing singular in-tegrals that arise from the discretization of integral equa-tions. In its standard (global) form, it fails to be robust forclose to touching geometries. In this talk, we introduce alocal variant of QBX. The local variant is computationallymore expensive, and therefore should only be used judi-ciously when needed. We provide details of a robust hybridimplementation of global and local QBX which uses localQBX only in areas of complicated geometry.

Manas RachhCourant InstituteNYUmanasrachh@gmail.com

Leslie GreengardCourant InstituteNew York Universitygreengar@cims.nyu.edu

Michael O’NeilNew York Universityoneil@cims.nyu.edu

Andreas KloecknerDepartment of Computer ScienceUniversity of Illinois at Urbana-Champaignandreask@illinois.edu

MS177

ExaFMM – a Testbed for Comparing Various Im-plementations of the FMM

The software design space for the fast multipole method(FMM) is large, where various schemes exist for partition-ing, communication, tree traversal, and translation opera-tors. The optimal choice is problem and architecture de-pendent, and most FMM codes focus on a specific combina-tion of the two. ExaFMM is a open source FMM code thatprovides the capability to explore this vast design spacewithout sacrificing speed, scalability, or readability.

Rio YokotaKing Abdullah University of Science and Technologyrio.yokota@kaust.edu.sa

David E. Keyes

148 CS15 Abstracts

KAUSTdavid.keyes@kaust.edu.sa

Lorena A. BarbaDepartment of Mechanical and Aerospace EngineeringGeorge Washington Universitylabarba@gwu.edu

MS178

A Posteriori Error Estimation in the MaximumNorm for Finite Element Methods

Adaptive finite element methods are designed to controlthe error in measuring a specific norm or functional of thesolution. In some situations it is of interest to control themaximum error. In this talk we will discuss recent progressin developing a posteriori error estimates in the maximumnorm for elliptic problems, with special focus on singularlyperturbed reaction-diffusion equations. Time allowing, wewill also discuss the sharpness of logarithmic factors whichappear in our estimates.

Alan DemlowTexas A&M Universitydemlow@math.tamu.edu

MS178

Robust Residual-Based a Posteriori Error Estima-tion for Interface Problems: Nonconforming Ele-ments

A robust residual-based a posteriori error estimation forthe non-conforming linear finite element approximation tothe interface problem is studied. We introduce a new anddirect approach, without using the Helmholtz decomposi-tion, to analyze the reliability of the estimator. It is provedthat our estimator is reliable with the constant indepen-dent of the jump of the interfaces, without the assumptionthat the diffusion coefficient is quasi-monotone. Numericalresults are also presented.

Cuiyu HePurdue Universityhe75@math.purdue.edu

Zhiqiang CaiPurdue UniversityDepartment of Mathematicscaiz@purdue.edu

Shun ZhangCity University of Hong Kongshun.zhang@cityu.edu.hk

MS178

A PDE Approach to Fractional Diffusion: a Poste-riori Error Analysis

We derive a computable a posteriori error estimatorfor the α-harmonic extension problem, which localizesthe fractional powers of elliptic operators supplementedwith Dirichlet boundary conditions. The derived estima-tor relies on the solution of small discrete problems onanisotropic cylindrical stars. It exhibits built-in flux equili-bration and is equivalent to the error up to data oscillation.A simple adaptive algorithm is designed and numerical ex-

periments reveal a competitive performance.

Abner J. SalgadoDepartment of MathematicsUniversity of Tennesseeasalgad1@utk.edu

MS178

Robust a Priori and a Posteriori Error Estimatesfor Diffusion Problems with Discontinuous Coeffi-cients

For diffusion problems of discontinuous coefficients, thequasi-monotonicity assumption (QMA) is a very impor-tant condition to guarantee the robustness of problems in-dependent of the coefficients. In this talk, new results ofrobust and optimal a priori and a posteriori error estimatesfor various finite element approximations of the diffusionproblem with discontinuous coefficients with and withoutQMA are discussed. With new tools, we show that Con-forming FEM is only optimal and robust in 2D with lowregularity, while Mixed FEM, Nonconforming FEM, andDGFEM are both robust with respect to coefficients andoptimal with respect to local regularities. For a posteri-ori error estimates, using nodal interpolations in stead ofClement interpolations, we show the robustness of CFEM,MFEM, NFEM, and DGFEM without GMA.

Shun ZhangCity University of Hong Kongshun.zhang@cityu.edu.hk

MS179

Primal-Dual Newton Conjugate Gradients forCompressed Sensing Problems with Coherent andRedundant Dictionaries

Abstract not available at time of publication.

Kimon FountoulakisUniversity of Edinburghk.fountoulakis@sms.ed.ac.uk

MS179

Augmented Lagrangian Methods for Large-ScaleNonlinear Optimization

Abstract not available at time of publication.

Sven LeyfferArgonne National Laboratoryleyffer@mcs.anl.gov

MS179

Column Generation Techniques for Large Mixed-Integer Programs

We study two-stage mixed-integer programs (MIP) thatarise from co-generation in smart buildings. These MIPproblems are beyond the capability of available MIP solversdue to a large number of binary variables in the second-stage problem. We develop a column generation approachthat reduces problem size by building a coarser MIP model.The first-stage solutions are validated using a rolling hori-zon method. We test our approach using data sets fromdifferent types of buildings.

Fu Lin

CS15 Abstracts 149

Mathematics and Computer Science DivisionArgonne National Laboratoryfulin@mcs.anl.gov

MS179

Convexification Methods for Sequential QuadraticProgramming

Abstract not available at time of publication.

Elizabeth WongUniversity of California, San DiegoDepartment of Mathematicselwong@ucsd.edu

MS180

Gaussian-Localized Polynomial Interpolation (Her-mite Function Interpolation) on a Finite Interval:Are Spectrally-Accurate Rbfs Obsolete?

Spectrally-accurate radial basis functions (RBFs) such asGaussians often succeed where polynomial interpolationfails because of the Runge Phenomenon. Why? Compar-ative analysis of RBF and polynomial cardinal functions(nodal bases) shows that RBF cardinals are much morelocalized. This motivated us to abandon RBFs in favorof Gaussian-mollified polynomial cardinal functions: muchmore accurate, cheaper to construct and much better con-ditioned than RBFs. Using potential theory, we prove anexponential, geometric rate of convergence. On a uniformgrid, the Runge Phenomenon is not completely annulled,but the Runge Zone is an order of magnitude smaller thanfor polynomial interpolation. Applications to solving dif-ferential equations, especially in complicated geometry, arein progress. A note was published as “Hermite FunctionInterpolation ..., Appl. Math. Letters, 26, 10, 995-997(2013).

John P. BoydUniversity of MichiganAnn Arbor, MI 48109-2143 USAjpboyd@umich.edu

MS180

Automatic Multivariate Approximation

Fully automatic one-dimensional approximation can be im-plemented successfully using Chebyshev polynomial expan-sions, as demonstrated in the Chebfun software project. Inhigher dimensions, dimensionality and geometry are majornew challenges. One proposal for automatic approximationin two and three dimensions using partition of unity, spec-tral methods, and radial basis functions will be presented.

Tobin DriscollUniversity of DelawareMathematical Sciencesdriscoll@udel.edu

MS180

A Windowed Fourier Method for Computations onthe Sphere

A spectral method based on windowed Fourier approxima-tions for computations on the sphere is presented. It relieson domain decomposition, such as in the cubed sphere,and is suitable for adaptive and parallel implementation.

One of the advantages of this approach is that computa-tions can be carried out using fast Fourier transforms ona nearly uniform grid. Approximations are obtained onoverlapping domains and a global solution is obtained byweighted average.

Rodrigo B. PlatteArizona State Universityrbp@asu.edu

MS180

A Fast and Well-Conditioned Spectral Method

We describe a spectral method for the solution of linear or-dinary differential equations that leads to well-conditionedmatrices that are banded except for a few rows. We ex-tend this to a spectral method for the solution of linearpartial differential equations using low rank approximationand generalized Sylvester matrix equations. Techniquesfrom automatic differentiation and preconditioning are em-ployed to develop an automatic, adaptive, and spectrallyaccurate solver.

Alex TownsendOxford Universitytownsend@maths.ox.ac.uk

MS181

Recent Advances in Numerical Modelling ofThermo-Chemically Coupled Two-Phase Flow

Many processes in geodynamics involve a significantamount of active magmatism. Recent advances in compu-tational magma dynamics have allowed formulating a novelmulti-component two-phase flow model including a realis-tic visco-plastic rheology for host rock deformation and abasic thermodynamic disequilibrium model describing thesimplified petrology of a multi-phase silicate material. Themodel has been implemented numerically using a parallelfinite-difference method in 2-D for the use in studies ofvolatiles (H2O, CO2) in magmatic systems.

Tobias KellerUniversity of OxfordDepartment of Earth Sciencestobias.keller@earth.ox.ac.uk

MS181

Scalable Nonlinear Solvers for Magma Dynamics

We present new nonlinear solvers for magma dynamicsproblems based upon the nonlinear preconditioning frame-work in PETSc. We demonstrate their effectiveness onmodel problems, and examine a possible direction for con-vergence analysis.

Matthew G. KnepleyUniversity of Chicagoknepley@ci.uchicago.edu

Richard F. KatzUniversity of OxfordRichard.Katz@earth.ox.ac.uk

MS181

Multi-Scale Modelling of Granular Avalanches

It is important to be able to predict the distance to which a

150 CS15 Abstracts

hazardous natural flows travel. In dense flows the large par-ticles segregate to the surface, where they are transportedto the margins forming bouldery flow fronts. In naturalflows these bouldery margins experience a much greaterfrictional force, leading to frontal fingering instabilities. Amultiscale model for this fingering instability is comparedin terms of cost and accuracy to full-scale discrete particlesimulations.

Anthony R. ThorntonUniversity of TwenteMulti-scale mechanics groupa.r.thornton@utwente.nl

MS182

Domain Specific Languages and Automated CodeGeneration: High Expressiveness and High Perfor-mance

Software should be carefully designed to closely follow themathematical abstractions of the problem domain. Wedemonstrate this principle with FEniCS, which employsa domain-specific language, UFL, that mimics the math-ematics of variational forms for finite element discretisa-tions. By following this principle, we demonstrate howUFL and the FEniCS code generation techniques can beused to automatically derive extremely high-performancecode for adjoints of PDEs, for use in sensitivity analysis,optimisation, and inverse problems.

Patrick E. FarrellDepartment of MathematicsUniversity of Oxfordpatrick.farrell@maths.ox.ac.uk

MS182

Moose: An Open Source Platform For Rapid De-velopment of Multiphysics Simulation Tools

Many physical phenomena can be modeled with systems ofpartial differential equations. Some examples include nu-clear reactors, geothermal flow, microstructural evolution,and fluid-structure interaction. Solving systems of non-linear equations has typically been achieved with customsoftware or by combining existing simulation tools. Theopen-source Multiphysics Object-Oriented Simulation En-vironment (MOOSE; mooseframework.org) employs a dif-ferent approach: it provides a generic, common platformfor solving multiphysics problems. This technique allowsscientists and engineers to focus on the physics while theframework manages the task of parallel, nonlinear solverdevelopment. A discussion of the platforms capabilitiesand software development model will be followed by sev-eral example applications in nuclear physics, geophysics,chemistry, and material science.

Derek R. GastonIdaho National Laboratoryfriedmud@gmail.com

Cody PermannCenter for Advanced Modeling and SimulationIdaho National Laboratorycody.permann@inl.gov

David Andrs, John Peterson, Andrew SlaughterIdaho National Laboratorydavid.andrs@inl.gov, jw.peterson@inl.gov, an-

drew.slaughter@inl.gov

MS182

Project Jupyter: a Language-Independent Archi-tecture for Cse, from Interactive Computing to Re-producible Publications

Project Jupyter is the evolution of the IPython interac-tive computing system into language-agnostic componentsto support all aspects of computational research. Jupyterabstracts the basic elements of interactive computing intoopenly documented file formats and protocols. Using these,”Jupyter kernels” can execute code in any language andcommunicate with clients that range from simple termi-nals to the rich web-based Jupyter Notebook that supportscode, results, rich media, text and mathematics.

Fernando PerezHelen Wills Neuroscience InstituteUniversity of California, BerkeleyFernando.Perez@berkeley.edu

MS183

Bayesian Global Optimization of Expensive Func-tions with Low-Dimensional Noise

Motivated by the design of cardiovascular bypass graftsusing computationally-expensive physics-based stochasticsimulators, we consider optimizing an objective functionthat is an integral of some expensive-to-compute functionover a low-dimensional space. While such problems canbe solved using an optimization solver for expensive deter-ministic functions, or for expensive noisy functions, neitheruses the low-dimensional structure of the noise. We providea new Bayesian global optimization method that exploitsthis problem structure to improve performance.

Jing XieCornell Universityjx66@cornell.edu

Sethuraman SankaranHeartflow, Inc.ssankaran@heartflow.com

Abhay RamachandraDepartment of Mechanical and Aerospace EngineeringUniversity of California, San Diegoabbangal@ucsd.edu

Saleh ElmohamedCornell Universityelmohamed@cornell.edu

Alison MarsdenDepartment of Mechanical and Aerospace EngineeringUniversity of California, San Diegoamarsden@ucsd.edu

Peter I. FrazierCornell Universitypf98@cornell.edu

MS183

Modeling An Augmented Lagrangian for Improved

CS15 Abstracts 151

Blackbox Constrained Optimization

We propose a combination of response surface modeling,expected improvement, and the augmented Lagrangian nu-merical optimization framework, allowing the statisticalmodel to think globally and the augmented Lagrangian toact locally. We focus on problems where the constraintsare the primary bottleneck, requiring expensive simulationto evaluate and substantial modeling effort to map out. Inthat context, our hybridization presents a simple yet ef-fective solution that allows existing objective-oriented sta-tistical approaches, like those based on Gaussian processsurrogates and expected improvement heuristics, to be ap-plied to the constrained setting with minor modification.

Robert GramacyUniversity of Chicagorbgramacy@chicagobooth.edu

Genetha GraySandia National Laboratoriesgagray@sandia.gov

Sebastien Le DigabelGERAD - Polytechnique MontrealSebastien.Le.Digabel@gerad.ca

Herbert LeeUC Santa Cruzherbie@soe.ucsc.edu

Pritam RanjanAcadia Universitypritam.ranjan@acadiau.ca

Garth WellsDepartment of EngineeringUniversity of Cambridgegnw20@cam.ac.uk

Stefan WildArgonne National Laboratorywild@mcs.anl.gov

MS183

Topology Optimization of a Permanent-MagnetSynchronous Machine under Uncertainties

The modeling and simulation of a permanent-magnet syn-chronous machine requires the application of Maxwell’sequations. Within a two-dimensional finite element model,the shapes of rotor poles, which are represented by zero-level sets, are optimized by a redistribution of an iron and amagnetic material using an iterative process. More specif-ically, we consider a stochastic problem, where randomfields due to unknown variations of material properties aretaken into account to model the propagation of uncertain-ties. Furthermore, in a robust optimization formulation,a multi-objective functional, which includes the mean andthe standard deviation, is minimized subject to constraints.For this purpose, we apply methods dedicated to stochas-tic problems such as e.g. polynomial chaos expansions.Finally, the results of numerical simulations show that theproposed methods are robust and efficient.

Roland PulchUniversity of Greifswaldpulchr@uni-greifswald.de

Piotr PutekBergische Universitat Wuppertalputek@math.uni-wuppertal.de

MS183

A Model and Variance Reduction Method for Com-puting Statistical Outputs of Stochastic Partial Dif-ferential Equations

We present a model and variance reduction method forcomputing statistical outputs of stochastic PDEs. We com-bine the hybridizable discontinuous Galerkin (HDG) andthe reduced basis discretization of elliptic PDEs with amultilevel variance reduction method, exploiting the sta-tistical correlation among the HDG and reduced basis ap-proximations to accelerate the convergence of Monte Carlosimulations. We develop a posteriori error estimates forthe statistical outputs, and propose an optimal selection ofmultilevel structure.

Ferran Vidal-Codina, Cuong Nguyen, Jaime PeraireMassachusetts Institute of Technologyfvidal@mit.edu, cuongng@mit.edu, peraire@MIT.EDU

Michael B. GilesMathematical InstituteOxford UniversityMike.Giles@maths.ox.ac.uk

MS184

Accurate All-Electron Electronic Structure Theoryfor Large Systems

This contribution focuses on algorithmic developments to-wards efficient, accurate all-electron methods for com-putational simulations of materials and nanostructuresfrom first principles. We demonstrate (i) accurate nu-meric atom-centered basis sets for ground-state densityfunctional theory as well as perturbative methods suchas GW or RPA, (ii) the open-source, massively paral-lel eigenvalue solver library ELPA and developments con-nected to it, essential for parallel scalability towards sys-tem sizes of ∼1000s of atoms, (iii) first steps towardsa mixed, load-balanced CPU-GPU implementation realspace integrals required in electronic structure theory.The methods described are implemented in the general-purpose all-electron electronic structure code FHI-aims[http://aims.fhi-berlin.mpg.de]

Volker BlumDuke Universityvolker.blum@duke.edu

MS184

Enabling Large-Scale Hybrid Density FunctionalTheory Calculations

Hybrid density functional theory (DFT), in conjunctionwith a treatment of van der Waals/dispersion interactions,provides a substantial improvement over popular DFTfunctionals based on the generalized gradient approxima-tion, in the modeling of condensed-phase molecular sys-tems such as liquid water, albeit with a prohibitively largecomputational cost. In this work, we will demonstrate hownovel theoretical and algorithmic developments, coupledwith efficient utilization of supercomputer architectures,enable large-scale hybrid DFT calculations on condensed-

152 CS15 Abstracts

phase molecular systems of interest.

Robert A. DiStasio, Jr.Princeton Universitydistasio@princeton.edu

MS184

Finite Elements for Large, Accurate Quantum Me-chanical Materials Calculations: from Classical toEnriched to Discontinuous

We discuss recent developments in finite-element (FE)based methods for the solution of the Kohn-Sham equa-tions that have made possible smaller basis sets andlarger calculations than possible by current state-of-the-artplanewave (PW) based methods, in some cases by an orderof magnitude or more. We begin with classical FE basedapproaches, then discuss recent enriched partition-of-unityFE (PUFE) methods, which build known atomic physicsinto the basis while retaining strict locality and system-atic improvability. By incorporating known physics, thesebases can achieve the required accuracies with an orderof magnitude fewer degrees of freedom (DOF) than tradi-tional PW based methods. However, with such enrichmentcomes more expensive quadrature and some degree of ill-conditioning. By incorporating not only local-atomic butalso environmental physics into the basis, recent Discontin-uous Galerkin (DG) based approaches can achieve largerreductions in DOFs still, while retaining strict locality andsystematic improvability. Most notably, the DG formu-lation allows for orthonormality as well, alleviating con-ditioning issues and allowing for the solution of standardrather than generalized discrete eigenproblems in the crit-ical N3 scaling step of the Kohn-Sham solution. Accuratequantum mechanical forces and molecular dynamics havebeen demonstrated. Incorporation of Pole Expansion andSelected Inversion (PEXSI) has been undertaken to elim-inate the need for diagonalization entirely. We concludewith an outlook and applications interests going forward.

John PaskLawrence Livemore National Labpask1@llnl.gov

MS184

Enabling Large Scale LAPW DFT Calculations bya Scalable Iterative Eigensolver

In LAPW-based methods a sequence of dense generalizedeigenvalue problems appears. Traditionally these prob-lems were solved using direct eigensolvers from standardlibraries like ScaLAPACK. We developed a subspace it-eration method pre-conditioned with Chebyshev polyno-mials of optimal degree (ChFSI). This algorithm is con-sistently competitive with direct eigensolvers and greatlyenhance performance and scalability. ChFSI is included inthe FLEUR software and improves its scaling behaviourfor calculations of large physical systems on modern super-computers.

Daniel WortmannInstitute for Asvanced SimulationForschungszentrum Juelichd.wortmann@fz-juelich.de

Edoardo A. Di NapoliJuelich Supercomputing Centree.di.napoli@fz-juelich.de

Mario BerljafaSchool of MathematicsThe University of Manchesterm.berljafa@maths.man.ac.uk

MS185

Solving Optimal Feedback Control Problems forPartial Differential Equations Using AdaptiveSparse Grids

An approach to solve finite time horizon optimal feedbackcontrol problems for partial differential equations usingadaptive sparse grids is proposed. A semi-discrete optimalcontrol problem is introduced and the feedback control isderived from the corresponding value function. The valuefunction can be characterized as the solution of an evo-lutionary Hamilton-Jacobi Bellman (HJB) equation whichis defined over a state space whose dimension is equal tothe dimension of the underlying semi-discrete system. Be-sides a low dimensional semi-discretization it is importantto solve the HJB equation efficiently to address the curseof dimensionality. We propose to apply a semi-Lagrangianscheme using spatially adaptive sparse grids. Sparse gridsallow the discretization of the high(er) dimensional valuefunctions arising in the numerical scheme since the curse ofdimensionality of full grid methods arises to a much smallerextent. For additional efficiency an adaptive grid refine-ment procedure is explored. We present several numericalexamples studying the effect of the parameters character-izing the sparse grid on the accuracy of the value functionand optimal trajectories. Furthermore we analyze the be-haviour of the trajectories in case of noise.

Jochen GarckeUniversity of Bonngarcke@ins.uni-bonn.de

Axel KronerRICAM, Austriaaxel.kroener@ricam.oeaw.ac.at

MS185

Dimension-Independent, Likelihood-InformedMcmc Sampling Algorithms for Bayesian InverseProblems

Many Bayesian inference problems require exploring theposterior distribution of high-dimensional parameters,which in principle can be described as functions. By ex-ploiting the intrinsic low dimensionality of the likelihoodfunction, we introduce a suite of MCMC samplers thatcan adapt to the complex structure of the posterior dis-tribution, yet are well-defined on function space. Posteriorsampling in nonlinear inverse problems arising from variouspartial differential equations and also a stochastic differen-tial equation are used to demonstrate the efficiency of thesedimension-independent likelihood-informed samplers.

Kody LawSRI UQ Center, CEMSE, KAUSTkodylaw@gmail.com

Tiangang Cui, Youssef M. MarzoukMassachusetts Institute of Technologytcui@mit.edu, ymarz@mit.edu

MS185

Numerical Solution of Elliptic Diffusion Problems

CS15 Abstracts 153

on Random Domains

In this talk, we provide regularity results for the solution toelliptic diffusion problems on random domains. Especially,based on the decay of the Karhunen-Loeve expansion ofthe domain perturbation field, we establish rates of de-cay which imply the tractability of the Quasi-Monte Carlomethod. By taking into account only univariate deriva-tives, the regularity results can considerably be sharpenedin order to show also the applicability of the stochasticcollocation method and related rates of convergence. Wemoreover employ parametric finite elements to computethe solution of the diffusion problem on each particularrealization of the domain generated by the perturbationfield. This simplifies the implementation and yields a non-intrusive approach. The theoretical findings are comple-mented by numerical examples.

Michael PetersUniversity of Baselmichael.peters@unibas.ch

Helmut HarbrechtUniversitaet BaselDepartement of Mathematics and Computer Sciencehelmut.harbrecht@unibas.ch

MS185

Data and Uncertainties: Representation of High-Dimensional Dependencies Using Adaptive SparseGrids

Wherever simulations depend on parameters, high-dimensional problems arise, and the representation of high-dimensional dependencies based on data and/or uncertain-ties is required. Where the dependencies are non-smooth,adaptive refinement and basis functions with local sup-port are able to avoid Gibbs phenomenon. Sparse grids,together with suitable refinement strategies, provide sucha hierarchical and incremental approach. We will discusssome of their properties and give best practice examples.Examples stem from uncertainty quantification, data min-ing, and density estimation.

Dirk PflugerUniversity of StuttgartDirk.Pflueger@ipvs.uni-stuttgart.de

Fabian FranzelinUniversitat Stuttgartfabian.franzelin@ipvs.uni-stuttgart.de

MS186

Incorporating Error Detection and Recovery intoHierarchically Semi-Separable Matrix Operations

Hierarchically semi-separable (HSS) matrix factorizationsare promising components for high-performance linearsolvers. To construct a fault-tolerant HSS solver, we haveidentified several checksum relationships that are preservedduring HSS matrix-vector multiplication. Whenever thesechecksum assertions fail, the Containment Domains libraryrestores the faulty arrays and re-executes the necessary re-gion of the code. The timing profile of our algorithm isused to parametrize a Markov model and determine theoptimal granularity of the checksum tests.

Brian AustinNERSC

Lawrence Berkeley National Laboratorybaustin@lbl.gov

Alex Druinsky, Xiaoye Sherry LiComputational Research DivisionLawrence Berkeley National Laboratoryadruinsky@lbl.gov, xsli@lbl.gov

Osni A. MarquesLawrence Berkeley National LaboratoryBerkeley, CAoamarques@lbl.gov

Eric RomanLawrence Berkeley National Laboratoryeroman@lbl.gov

MS186

Parallel Spectral Element-Based AgglomerationAlgebraic Multigrid for Porous Media Flow

We present an element based algebraic multigrid strat-egy for scalable parallel simulation of porous media flow.Coarse basis functions in the multigrid algorithm areadapted to the high contrast coefficients by solving sparseor dense local eigenvalue problems. An advantage of theapproach is that setup and application are based on sparsematrix-vector and matrix-matrix products, so that any re-silient implementations of these components will be inher-ited by the entire algorithm.

Andrew T. BarkerCenter for Applied Scientific ComputingLawrence Livermore National Laboratorybarker29@llnl.gov

Delyan KalchevUniversity of Coloradodelyank@gmail.com

Panayot VassilevskiLawrence Livermore National Laboratoryvassilevski1@llnl.gov

Umberto E. VillaCenter for Advanced Scientific ComputingLawrence Livermore National Laboratoryvilla13@llnl.gov

MS186

Attaining High Arithmetic Intensity in Finite-volume Methods through High-order Quadratures

Finite-volume discretizations in production codes are typ-ically only second-order accurate, resulting in methodswith low arithmetic intensity. The widening performancegap between processor and memory motivates developingschemes that do more work for less data motion. Wepresent an arithmetic intensity analysis for finite-volumemethods with high-order flux approximations. The modelsuggests the flops-to-byte ratio of the methods increasesrapidly with order of accuracy. We also discuss perfor-mance measurements of the methods on current multicorehardware. This work was performed under the auspices ofthe U.S. Department of Energy by Lawrence Livermore Na-tional Laboratory under Contract DE-AC52-07NA27344.

154 CS15 Abstracts

Lawrence Livermore National Security, LLC.

John LoffeldUniversity of CaliforniaMercedloffeld1@llnl.gov

Jeffrey A. HittingerCenter for Applied Scientific ComputingLawrence Livermore National Laboratoryhittinger1@llnl.gov

MS186

Controlling Numerical Error in Particle-In-CellSimulations of Collisionless Dark Matter

Particle-in-cell (PIC) methods are commonly used to sim-ulate the gravitational evolution of collisionless dark mat-ter in cosmological settings. However, such methods areknown to be prone to numerical error on scales below themean inter-particle separation. An understanding of theseerrors is crucial, both for correctly interpreting simulationresults, and for designing higher-order PIC methods. Wediscuss the use of two techniques: regularization and adap-tive phase-space remapping, to improve the accuracy ofcosmological PIC simulations.

Andrew MyersComputational Research DivisionLawrence Berkeley National Laboratoryatmyers2@gmail.com

Brian Van StraalenLawrence Berkeley National LaboratoryCompuational Research Divisionbvstraalen@lbl.gov

Colella PhillipLBNLpcolella@lbl.gov

MS187

Accelerating the Solution of Inverse Problems Us-ing Reduced-Order Models

Inverse problems are a special class of PDE-constrainedoptimization problems for which model parameters are es-timated. This inverse problem often needs to be solvedin real-time based on measurements obtained on the field.The computational complexity associated with the opti-mization problem of interest generally prevents its fast so-lution. To accelerate its solution, a strategy based on adatabase of pre-computed reduced-order model is here cho-sen. Special attention will be given to the training of such adatabase in the case of high-dimensional parameter spaces.

David AmsallemStanford Universityamsallem@stanford.edu

MS187

Reduced Basis Method for Uncertainty Quantifica-tion Problems: A Recent Update

In this talk, we present a recent update of the developmentand application of reduced basis method for forward andinverse uncertainty quantification (UQ) problems. Specifictopics include reduced basis method for time-dependent

Bayesian inverse problem, time-dependent optimal controlproblems, convergence of reduced basis method for high-dimensional or possibly infinite-dimensional problems, etc.

Peng ChenETH Zurichpeng.chen@sam.math.ethz.ch

Gianluigi RozzaSISSA, International School for Advanced StudiesTrieste, Italygianluigi.rozza@sissa.it

MS187

Recent Advances in Reduced Order Modellingin Computational Fluid Dynamics within EU-MORNET COST Activities

We provide some recent updates about reduced order mod-elling techniques in computational fluid dynamics with aspecial focus on flow instabilities and bifurcations for timedependent non-linear flows. A special attention is devotedto parameter sampling techniques and approximation sta-bility. A posteriori error bounds are recalled. A cardio-vascular application is presented as benchmark example.This work wants to provide a general overview on somerecent tasks of the EU-MORNET COST activities (Euro-pean Union MOdel Reduction NETwork, Cooperation inScience and Technology).

Gianluigi RozzaSISSA, International School for Advanced StudiesTrieste, Italygianluigi.rozza@sissa.it

Giuseppe PittonSISSA, International School for Advanced Studies TriesteItalygpitton@sissa.it

Annalisa QuainiDepartment of Mathematics, University of Houstonquaini@math.uh.edu

MS187

A Minimum-residual Mixed Reduced BasisMethod: Exact Residual Certification and Simul-taneous Finite-element Reduced-basis AdaptiveRefinement

We present a reduced basis method for parametrized PDEscertified by a dual-norm bound of the residual computednot in the typical finite-element “truth’ space but rather inan infinite-dimensional function space. The bound, whichadmits an efficient offline-online decomposition, builds on aminimum-residual mixed finite-element method and an as-sociated reduced-basis approximation. The method, com-bined with a spatio-parameter adaptation strategy, yieldsan online system that meets any user-specified residual tol-erance for any parameter value.

Masayuki YanoMassachusetts Institute of Technologymyano@mit.edu

MS188

A New Look at Global Error Estimation in Differ-

CS15 Abstracts 155

ential Equations

Global error represents the actual discretization error re-sulting after solving a system of differential equations. Iwill introduce new time-stepping methods with built-inglobal error estimates for ordinary and differential alge-braic equations. Calculating and controlling a posteriorierrors is an expensive process, and therefore in practiceonly the (local) error from one step to the next is used toestimate the global errors. However, local error estimationis not always suitable and may lead to error underestima-tion. I will review several strategies for a posteriori errorestimation and discuss new approaches that generalizes theclassical strategies.

Emil M. ConstantinescuArgonne National LaboratoryMathematics and Computer Science Divisionemconsta@mcs.anl.gov

MS188

On the Construction of Robust Additive Runge-Kutta Methods

Space discretization of some PDEs gives rise to systems ofODEs in additive form whose terms have different stiffnessproperties. Sometimes, the solution to these PDEs havequalitative properties which are relevant in the context ofthe problem. In these cases, it is convenient to preserve nu-merically these properties. In this talk we show how robustschemes can be constructed for this class of problems. Wewill also show their performance on nontrivial problems.

Inmaculada HiguerasDepartamento de Ingenieria Matematica e InformaticaUniversidad Publica de Navarrahigueras@unavarra.es

MS189

A Sparse Multiresolution Regression Frameworkfor Uncertainty Quantification

A novel nonintrusive, i.e., sampling-based, framework ispresented for approximating stochastic solutions of inter-est admitting sparse multiresolution expansions. The co-efficients of such expansions are computed via greedy ap-proximation techniques that require a number of solutionrealizations smaller than the cardinality of the multireso-lution basis. The effect of various random sampling strate-gies is investigated. The proposed methodology is verifiedon a number of benchmark problems involving nonsmoothstochastic responses.

Daniele E. SchiavazziUniversity of California, San Diegodschiavazzi@ucsd.edu

Alireza DoostanDepartment of Aerospace Engineering SciencesUniversity of Colorado, BoulderAlireza.Doostan@Colorado.EDU

Gianluca IaccarinoStanford UniversityMechanical Engineering

jops@stanford.edu

MS189

Adaptive Compressive Sensing Method for Uncer-tainty Quantification

The standard generalized polynomial chaos (gPC) methodin uncertainty quantification (UQ) selects basis functionsbased on the randomness of the input. However, this maynot be an efficient way. We propose a new method toconstruct the basis functions based on the output of thesystem. With the new gPC expansion, the system has asparser representation, hence sparse recovery approaches,e.g., compressive sensing technique, can be more effective.

Xiu YangPacific Northwest National Laboratoryxiu.yang@pnnl.gov

Xiaoliang WanLouisiana State UniversityDepartment of Mathematicsxlwan@math.lsu.edu

Huan Lei, Guang LinPacific Northwest National Laboratoryhuan.lei@pnnl.gov, guang.lin@pnnl.gov

George E. KarniadakisBrown UniversityDivision of Applied Mathematicsgeorge karniadakis@brown.edu

MS189

Stochastic Collocation Methods Via L1 Minimiza-tion

In this talk, we discuss the stochastic collocation meth-ods via L1 minimization. The motivation it to constructpolynomial approximations for parametric functions. Twosampling strategies, that is, the random sampling and thedeterministic sampling methods will be introduced. Weshall also discuss how to handle derivative information inthis framework.

Tao ZhouInstitute of Computational Mathematics, AMSSChinese Academy of Sciencestzhou@lsec.cc.ac.cn

Ling GuoDepartment of Mathematics, Shanghai NormalUniversity, Chinalguo@shnu.edu.cn

Dongbin XiuPurdue Universitydxiu@purdue.edu

MS190

Development of a Time-Dependent Ice Flow ModelAdjoint and Its Applications

The adjoint approach is quite popular in fitting glacial iceflow models to observations. For the most part, however,the approaches are time-independent. As remote sensingdata becomes more frequent and more complete, it is fair to

156 CS15 Abstracts

expect that time-dependent models of ice dynamics mightbe constrained with transient data, providing better cap-ture of transient state, and a better representation of un-known properties, such as bed topography or sub-ice shelfmelt.

Daniel GoldbergUniversity of Edinburghdan.goldberg@ed.ac.uk

Patrick HeimbachMassachusetts Institute of Technologyheimbach@mit.edu

MS190

Parallel 4D Variational Data Assimilation

A parallel algorithm to solve the inverse problem associatedwith the 4D Var Data assimilation problem is described.The inverse problem is solved in the variational framework.The optimization required to evaluate the analysis is per-formed using augmented Lagrangian technique. The eval-uation of the cost function and the derivative informationrequired to perform the optimization is computed in par-allel using forward and adjoint sensitivity analysis.

Vishwas Hebbur Venkata Subba RaoVirginia Polytechnic Institute and State Universityvisrao@vt.edu

Adrian SanduVirginia Polytechnic Institute andState Universitysandu@cs.vt.edu

MS190

An Adjoint Based Analysis of the Physical Driversof Uncertainty in Air-Sea Exchange and OceanDraw Down of Co2

We describe the use of an innovative adjoint approach toquantify and attribute uncertainty in model estimate of air-sea CO2 exchange. The adjoint approach provides a com-putationally efficient way to capture spatio-temporal vari-ability in the sensitivity of net air-sea exchange to physicalprocesses represented in a model. In this study we focus ondiapycnal mixing in the upper ocean, which can vary widelyin space and time. The processes by which the ocean re-sponds to disequilibrium with atmospheric CO2 are keyattributes of the Earth system decadal-centenial-millenialresponse to changes in CO2 emissions. The study providesquantitative insight into where and how diapycnal mixingprocesses contribute to that response. The study makesextensive use of the open-source automatic differentiationtool, OpenAD.

Chris HillEarth, Atmospheric and Physical SciencesM.I.T.cnh@mit.edu

Oliver JahnMITjahn@mit.edu

Jean UtkeArgonne National Laboratory

utke@mcs.anl.gov

MS190

Improving the Efficiency of the Adjoint of Fixed-Point Iterations

Reverse mode automatic differentiation (AD) computes theadjoints of codes precisely and efficiently. The reversemode employs checkpointing to store data between its for-ward and the reverse computational sweeps. When thecode contains fixed point iterations, unecessary checkpoint-ing can result in excessive memory or disk usage. Refor-mulating the adjoint of the fixed point iteration, drasticallyreduces the usage. An implementation of the reformulationand its use in an ice sheet model will be presented.

Sri Hari Krishn NarayananArgonne National Laboratorysnarayan@mcs.anl.gov

Daniel GoldbergUniversity of Edinburghdan.goldberg@ed.ac.uk

Paul D. HovlandArgonne National LaboratoryMCS Division, 221/C236hovland@mcs.anl.gov

MS191

Multivariate Weighted Least-squares using MonteCarlo Samples

We propose and analyze an algorithm for computingpolynomial discrete least-squares approximations to high-dimensional parameterized systems. Our sample grid fordiscrete least-squares is generated using Monte Carlo sam-ples, and we show that our method exhibits several asymp-totically optimal properties. Stability and accuracy can beestablished when the number of samples scales log-linearlywith the dimension of the approximation space. This anal-ysis relies on results from the fields of orthogonal polyno-mial and pluripotential theory. Our method is straight-forward and efficient to apply, addresses approximationsfor general random variables with bounded and unboundedrange, and easily extends to cases of epistemic uncertaintywhen the distribution of the parametric random variableis not known. We validate the algorithm on several low-and high-dimensional examples that are common in theuncertainty quantification community.

Akil NarayanUniversity of Massachusetts Dartmouthakil.narayan@umassd.edu

MS191

Title Not Available at Time of Publication

Abstract not available at time of publication.

Raul F. TemponeMathematics, Computational Sciences & EngineeringKing Abdullah University of Science and Technologyraul.tempone@kaust.edu.sa

MS191

Local Polynomial Chaos Methods for High Dimen-

CS15 Abstracts 157

sional SPDE

We present a localized polynomial chaos expansion forPDE with random inputs. We focus on problems withinput random fields of short correlation length, resultingin high dimensional random inputs. The local polynomialchaos method employs a domain decomposition techniqueto approximate the stochastic solution locally and indepen-dently with very low dimensions and then obtains the cor-rect global solution via sampling. The drastic dimensionalreduction makes the method highly efficient for practicalproblems.

Yi ChenPurdue Universitychen411@purdue.edu

John D. JakemanSandia National Labsjdjakem@sandia.gov

Xueyu Zhu, Dongbin XiuUniversity of Utahxzhu@sci.utah.edu, dongbin.xiu@utah.edu

MS191

Uncertainty Propagation Using Infinite Mixture ofGaussian Processes and Variational Bayesian Infer-ence

Uncertainty propagation (UP) is a very challenging mathe-matical and computational problem. Among other things,UPs difficulty is due to the limited number of model eval-uations, the curse of dimensionality, discontinuities, andmultivariate responses with non-trivial correlations. In or-der to deal with all these problems simultaneously, we de-velop an infinite mixture of multi-output Gaussian processmodel. We train the model using variational Bayesian in-ference and we obtain highly competing results in porousflow problems.

Peng Chen, Nicholas ZabarasCornell Universitypc423@cornell.edu, nzabaras@gmail.com

Ilias BilionisPurdue Universityebilionis@gmail.com

MS192

The Collective Impact of Social Factors and Inter-ventions on the Dynamics of Reported Narcotic-Related Criminal Cases in the Community Areasof Chicago

Abstract not available at time of publication.

Maryam KhanSAL Mathematical Computational Modeling ScienceCenterArizona State Universitymaryam.khan.1@asu.edu

MS192

An Effective Community-based Approach to Miti-gate Sybil Attacks in Online Social Networks

The popularity of online social networks (OSNs) has re-

sulted in increasing Sybil attacks where an adversary forgesmany fake identities (called Sybils) to disrupt or control thenormal functioning of the system. Proposed attack miti-gation schemes primarily work by computing the landingprobability or statistical distribution of the visiting fre-quency of short random walks and are dependent on ac-curate trusted nodes identification. In this talk, we willpresent SybilExposer, an algorithmic framework which ad-dresses these limitations. Our experiments on several largegraphs validate the effectiveness of SybilExposer.

Satyajayant MisraDepartment of Computer ScienceNew Mexico State Universitymisra@cs.nmsu.edu

MS192

The Dynamics of Co-Evolution of Health Behaviorsin College Population

Abstract not available at time of publication.

Anuj MubayiArizona State Universityanuj.mubayi@asu.edu

MS192

Analysis of Information Diffusion on Social Net-works

Abstract not available at time of publication.

Daniel RomeroSchool of InformationUniversity of Michigandrom@umich.edu

MS193

Fluctuating Hydrodynamics of Suspensions ofRigid Particles

We develop a computational method for fluid-structurecoupling at small Reynolds numbers that consistently in-cludes the effects of thermal fluctuations. This is impor-tant in problems involving Brownian rigid and semi-rigidstructures immersed in a fluid. We couple an immersed-boundary Lagrangian representation of rigid bodies to afluctuating finite-volume fluid solver. We handle com-plex rigid (e.g., synthetic nanorods) and semi-rigid (e.g.,short DNA segments) bodies by composing each structurefrom a collection of spherical particles constrained to move(semi)rigidly. The underlying fluctuating hydrodynamicsformulation automatically ensures the correct translationaland rotational Brownian motion.

Aleksandar DonevCourant Institute of Mathematical SciencesNew York Universityaleks.donev@nyu.edu

MS193

Boltzmann’s State of Motion: PhenomenologicalModeling of Chemical and Ecological Systems

We carry out a mathematical analysis, a la Helmholtz’sand Boltzmann’s 1884 studies of monocyclic Newtonianmechanics, for chemical reaction and ecological systemscontaining oscillatory dynamics. One of the important

158 CS15 Abstracts

features of the systems considered, absent in the classicalmechanical model, is a natural stochastic dynamic formu-lation of which the deterministic differential equation isthe infinite population limit. We separate the conserveddynamics from the dissipative models and show how theconservation law along a single trajectory can be extendedto incorporate both variations in model parameters and inthe initial conditions: Helmholtz’s theorem establishes abroadly valid conservation law in a class of chemical andecological dynamics. Further analysis identifies an entireorbit as a stationary behavior, and establishes the notionof an “equation of behavioral state’. Studies of the stochas-tic dynamics shows the conserved dynamics as the robust,fast cyclic underlying behavior. The mathematical narra-tive provides a novel way of capturing long-term dynamicalbehavior with an emergent conservative motion.

Yian MaUniversity of Washingtonyianma@uw.edu

Hong QianDepartment of Applied MathematicsUniversity of Washingtonhqian@u.washington.edu

MS193

A Nano Pore-Scale Model for the NanostructuredCathode of Lithium-Oxygen Batteries

We propose a nano pore-scale model that bridges the gapbetween continuum models and atomistic models to studythe impact of cathode microstructure and rate-dependentmorphology of Li2O2 on the discharge performance of Li-O2 batteries. The model captures the micro-scale resolvednanostructure of cathode with varying porosities, pore sizedistributions and surface-to-volume ratios, the diffusion-limited transport of oxygen across the porous structure ofthe cathode, and the morphology of Li2O2 growth at dif-ferent current densities.

Wenxiao PanPacific Northwest National Laboratorywenxiao.pan@pnnl.gov

MS193

SPH Model for Landau-Lifshitz Navier-Stokes andAdvection-Diffusion Equations

We propose a novel Smoothed Particle Hydrodynamics(SPH) discretization of the fully-coupled Landau-Lifshitz-Navier-Stokes (LLNS) and advection-diffusion equations.The accuracy of the SPH solution is demonstrated by test-ing the scaling of velocity variance and self-diffusion co-efficient with kinetic temperature and particle mass, thespatial covariance of pressure and velocity fluctuations, theso-called giant fluctuations of the front between light andheavy fluids with and without gravity, and the effect ofthermal fluctuation on the Rayleigh-Taylor instability.

Alexander TartakovskyPacific Northwest National Laboratoryalexandre.tartakovsky@pnnl.gov

Jannes KordillaGeoscientific CentreUniversity of Goettingenjkordil@gwdg.de

Wenxiao PanPacific Northwest National Laboratorywenxiao.pan@pnnl.gov

MS194

Computing Exactly and Eficiently Arbitrarily-High-Order Response Sensitivities to Model Pa-rameters

This work presents a new methodology for computing ex-actly and (most) efficiently response sensitivities, of arbi-trarily high-order, to model parameters. This new methodgeneralizes the adjoint method for sensitivity analysis ofnonlinear systems originated by Cacuci (1981), requiringat most O(NK-1) large-scale adjoint computations per re-sponse to obtain exact Kth-order sensitivities for a sys-tem with N parameters. In contradistinction, conventionalmethods require O(NK) large-scale computations to obtainapproximate values for the Kth-order sensitivities.

Dan G. CacuciUniversity of South Carolinacacuci@cec.sc.edu

MS194

Toward New Applications of the Adjoint Tools in4D-Var Data Assimilation

The development of efficient methodologies to assess andimprove the information content (’value’) of high-resolutionatmospheric measurements is an imperative task. Thistalk presents recent advances in the adjoint-based evalua-tion of the model forecast sensitivity to observations, errorcovariance parameter specification, and impact estimationin a four-dimensional variational data assimilation system.The practical significance and further research directionsare discussed together with preliminary experiments andthe current status of implementation at numerical weatherprediction centers.

Dacian N. DaescuPortland State UniversityDepartment of Mathematics and Statisticsdaescu@pdx.edu

Ricardo TodlingNASA/GSFC Global Modeling and Assimilation Officericardo.todling@nasa.gov

Rolf LanglandNaval Research LaboratoryMonterey, CArolf.langland@nrlmry.navy.mil

Austin HudsonPortland State UniversityPortland, OR, USAhudsonaustins@gmail.com

MS194

Dealing with Nonsmoothness in Data Assimilation

The theory of adjoints and their use in inverse problemsusually assumes that the state equations and error normsare smooth. In practice this assumption may be violatedthrough the use of nonsmooth norms or due to nonsmoothmodification of the state equations, e.g. the use of fluxlimiters in spatial discretizations. We analyze the theoret-

CS15 Abstracts 159

ical and practical effects and discuss suitable algorithmicmodifications.

Andreas GriewankHU Berlin, Germanygriewank@math.hu-berlin.de

MS194

Second Order Analysis in Variational Data Assim-ilation

The problem of Variational Data Assimilation, consideredin the framework of Optimal Control Theory, leads to anOptimality System containing all the available information: model, data and statistics, its solution gives a neces-sary condition for optimality. Introducing a second orderadjoint a second order analysis can be carried out withimportant applications such as: -Improvement of the opti-mization algorithms - Sensitivity Analysis - Estimation ofa posteriori statistics on the solution. Theory and applica-tions will be presented.

Francois-Xavier L. Le-DimetUniversity Joseph Fourierledimet@imag.fr

M Yousuff HussainiFlorida State Universitymyh@csit.fsu.edu

Ha Tran ThuVietnamese Academy of Sciencesfxld@yahoo.com

MS195

Data-Driven Model for Solar Irradiation Based onSatellite Observations

We construct a data-driven model for solar irradiationbased on satellite observations. The model yields prob-abilistic estimates of the irradiation field every thirtyminutes starting from two consecutive satellite measure-ments.The probabilistic nature of the model captures pre-diction uncertainties and can therefore be used by solarenergy producers to quantify the operation risks. The dy-namics are represented in a nonlinear, nonparameteric wayby a recursive Gaussian process. The predictions of themodel are compared with observed satellite data as well aswith a similar model that uses only ground observations atthe prediction site. We conclude that using satellite data inan area including the prediction site significantly improvesthe prediction compared with models using only groundobservation site data.

Ilias BilionisPurdue Universityebilionis@gmail.com

Emil M. Constantinescu, Mihai AnitescuArgonne National LaboratoryMathematics and Computer Science Divisionemconsta@mcs.anl.gov, anitescu@mcs.anl.gov

MS195

Two-Stage Adaptive Robust Unit CommitmentUsing Scenarios Induced Uncertainty Set

In this talk, we propose a new robust optimization frame-

work for unit commitment under uncertainty. We presenta new type of uncertainty set induced by correlated sce-nario samples to capture spatial-temporal correlations ofthe uncertainties. Furthermore, for large-scale problems,we propose an efficient approximation of the Scenarios In-duced Uncertainty (SIU) set using Principal ComponentAnalysis. Computational results demonstrate the economicbenefits of using SIU sets and the efficacy of the proposedsolution approach.

Richard L. ChenSandia National LaboratoriesLivermore, CArlchen@sandia.gov

Cosmin SaftaSandia National Laboratoriescsafta@sandia.gov

Jean-Paul WatsonSandia National LaboratoriesDiscrete Math and Complex Systemsjwatson@sandia.gov

Habib N. NajmSandia National LaboratoriesLivermore, CA, USAhnnajm@sandia.gov

Ali PinarSandia National Labsapinar@sandia.gov

MS195

Economic Impacts of Wind Covariance Estimationon Power Grid Operations

We study the impact of capturing spatiotemporal corre-lations between multiple wind supply points on economicdispatch procedures. Using a simple dispatch model, wefirst show analytically that over/underestimation of corre-lation leads to positive and negative biases of dispatch cost,respectively. A rigorous, large-scale computational studyfor the State of Illinois transmission grid with real topol-ogy and physical constraints reveals similar conclusions.For this study, we use the Rao-Blackwell-Ledoit-Wolf es-timator to approximate the wind covariance matrix froma small number of wind samples generated with the nu-merical weather prediction model WRF and we use thecovariance information to generate a large number of windscenarios. The resulting stochastic dispatch problems aresolved by using the interior-point solver PIPS-IPM on theBlueGene/Q (Mira) supercomputer at Argonne NationalLaboratory. We find that strong and persistent biases re-sult from neglecting correlation information and indicateto the need to design a market that coordinates weatherforecasts and uncertainty characterizations.

Cosmin G. PetraArgonne National LaboratoryMathematics and Computer Science Divisionpetra@mcs.anl.gov

Victor ZavalaArgonne National Laboratoryvzavala@mcs.anl.gov

Elias Nino-RuizVirginia Polytechnic Institute and State University

160 CS15 Abstracts

enino@vt.edu

Mihai AnitescuArgonne National LaboratoryMathematics and Computer Science Divisionanitescu@mcs.anl.gov

MS195

An Efficient Approach for Stochastic Optimizationof Electricity Grid Operations

Stochastic unit commitment optimization problems typi-cally handle uncertainties in forecast demand by consider-ing a finite number of random realizations from a stochas-tic process model for uncertain loads. In this paper wepropose a more efficient approach using Polynomial Chaosrepresentations valid over the range of the forecast uncer-tainty. We demonstrate the approach for several powergrid models with and without transmission constraints.

Cosmin SaftaSandia National Laboratoriescsafta@sandia.gov

Habib N. NajmSandia National LaboratoriesLivermore, CA, USAhnnajm@sandia.gov

Richard L. ChenSandia National LaboratoriesLivermore, CArlchen@sandia.gov

Ali PinarSandia National Labsapinar@sandia.gov

Jean-Paul WatsonSandia National LaboratoriesDiscrete Math and Complex Systemsjwatson@sandia.gov

MS196

On the Coupling of Far-Field Wind-Wave Simula-tion and Near-Field Free-Surface Flow Simulation

We develop a computational framework for simulating in acoupled manner the interaction of large-scale ocean wavesand winds with the presence of complex floating structures.We employ an efficient large-scale model to develop offshorewind and wave environmental conditions, which are thenincorporated to a high resolution two-phase flow solverwith fluid-structure interaction (FSI). The far-field/near-field coupling algorithm is validated under several test casesinvolving simple wave trains as well as three-dimensionaldirectional waves.

Antoni E. CaldererSaint Anthony Falls Lab, Civil Engineering departmentUniversity of Minnesotacald0075@umn.edu

Xin GuoUC Berkeleyxinguo@ieor.berkeley.edu

Fotis Sotiropoulos

Saint Anthony Falls Lab, Civil Engineering departmentUniversity of Minnesotafotis@umn.edu

Lian ShenUniversity of Minnesotashen@umn.edu

MS196

Topological Change with a Cut Cell based SharpInterface Method for Multi-phase Flows

In the conservative, consistent, all-speed, sharp-interfacemethod presented by Chang, Deng & Theofanous 2013, afree interface is represented by cut faces and evolved withthe help of a level set function. It shows good performanceon simulating multi-phase flow problems with clear inter-faces, but cannot deal with topological change. By switch-ing between this cut cell/level set mixed method and apure level set method, topological change can be realizedsmoothly.

Xiao-Long DengBeijing Computational Science Research Centerxiaolong.deng@csrc.ac.cn

MS196

High Resolution PDE Solvers on Octree Grids andParallel Architectures

Abstract not available at time of publication.

Frederic G. GibouUC Santa Barbarafgibou@engineering.ucsb.edu

MS196

A Second Order Virtual Node Algorithm forNavierStokes Flow Problems with InterfacialForces and Discontinuous Material Properties

We present a numerical method for the solution of theNavier-Stokes equations in three dimensions that handlesinterfacial discontinuities due to singular forces and discon-tinuous fluid properties such as viscosity and density. Wediscretize the equations using an embedded approach on auniform MAC grid to yield discretely divergence-free ve-locities that are second order accurate. The method leadsto a discrete, symmetric KKT system for velocities, pres-sures, and Lagrange multipliers. We also present a novelsimplification to the standard combination of the secondorder semi-Lagrangian and BDF schemes for discretizingthe inertial terms. Numerical results indicate second orderspatial accuracy for the velocities (L∞ and L2) and firstorder for the pressure (in L∞, second order in L2).

Joseph TeranUCLAjteran@math.ucla.edu

MS197

Asynchronous Preconditioning on Accelerators

This talk focuses on how preconditioners can be con-structed using asynchronous algorithms. Such algorithmsare fine-grained and can tolerate memory latency, makingthem suitable for modern architectures, particularly ac-celerators. Preconditioners including incomplete factoriza-

CS15 Abstracts 161

tions and sparse approximate inverses may be constructedthis way. We discuss convergence of various types of asyn-chronous algorithms applied to constructing precondition-ers, necessary implementation differences on GPUs and In-tel Xeon Phi, and inner-outer asynchronous iterations de-signed to reduce communication volume from low levels ofthe memory hierarchy.

Edmond ChowSchool of Computational Science and EngineeringGeorgia Institute of Technologyechow@cc.gatech.edu

MS197

Overview and Contrast of Modern Computer Ar-chitectures Including the Intel Phi

State-of-the-art distributed-memory clusters today containmulti-core CPUs with 8 to 12 cores, massively parallelGPUs with thousands of computational cores, and many-core accelerators such as the 60-core Intel Phi, connectedby high-performance networks such as InfiniBand intercon-nect. This talk will give an overview of their features, showsample code how to use GPUs and the Intel Phi processorin hybrid mode, and contrast performance results for basictest problems.

Jonathan Graf, Samuel Khuvis, Xuan HuangDepartment of Mathematics and StatisticsUniversity of Maryland, Baltimore Countyjongraf1@umbc.edu, khsa1@umbc.edu, hu6@umbc.edu

Matthias K. GobbertUniversity of Maryland, Baltimore CountyDepartment of Mathematics and Statisticsgobbert@umbc.edu

MS197

Offloading Computational Kernels in Long-TimeSimulations to the Intel Phi

Simulating calcium waves in a heart cell requires both finemeshes and large final times to match laboratory exper-iments. This is a perfect example of a problem that canprofit from offloading numerical kernels to accelerators suchas the 60-core Intel Phi processor on each hybrid computenode, combined with pooling memory from several nodesto allow for the desired spatial resolutions. We report re-sults for special-purpose code for this problem.

Samuel Khuvis, Xuan Huang, Jonathan GrafDepartment of Mathematics and StatisticsUniversity of Maryland, Baltimore Countykhsa1@umbc.edu, hu6@umbc.edu, jongraf1@umbc.edu

Matthias K. GobbertUniversity of Maryland, Baltimore CountyDepartment of Mathematics and Statisticsgobbert@umbc.edu

MS197

The HPCG Benchmark Using Intel Phi Accelera-tors

The High Performance Preconditioned CG (HPCG)Benchmark, developed by Sandia National Laboratories,uses a preconditioned conjugate gradient method to solvethe Poisson equation, since this may be more relevant to

many applications than the LINPACK benchmark. Afterintroducing this new benchmark that reported rankings forthe first time in June 2014 we show its implementation andperformance on CPUs only and on hybrid nodes with IntelPhi accelerators, connected by a QDR InfiniBand intercon-nect.

Adam Cunningham, Gerald Payton, Jack SlettebakUniversity of Maryland, Baltimore Countycunning5@umbc.edu, gpayton1@umbc.edu,slet1@umbc.edu

Jordi Wolfson-PouDepartment of PhysicsUniversity of California, Santa Cruzjswolfso@ucsc.edu

MS198

Creating the Largest Decoys Database to ImproveScoring Functions Using Machine Learning

In the protein structure prediction field it is absolutely vi-tal to develop reliable scoring functions that will allow re-searchers to efficiently identify the very best models outof hundreds of thousands and sometimes even millions ofpredictions. Such scoring functions have proven to be dif-ficult to produce. The protein folding community believesthat machine learning techniques will advance the capa-bilities of scoring functions. Datasets of computationallygenerated models known as decoys are used to train andtest the scoring functions that are created. While thereare decoys datasets available to perform these tests, thesedatasets are very small in comparison to the amount ofprotein models that are created during the Critical As-sessment of protein Structure Prediction (CASP) competi-tions. Larger datasets are essential to create more accuratescoring functions. The WeFold collaboration mediated bythe homonymous gateway gathers an enormous amount ofmodels, which are shared by its users. We are creatingthe largest database of decoys to make available to themachine learning community. The database does not onlystore models, but also numerical features that describe im-portant characteristics of protein models. MongoDB is be-ing used to store all of this information and an interface isbeing created to integrate MongoDB with the WeFold gate-way. Users will be able to submit queries to the databaseand download all models created by all groups, all mod-els created by specific groups, specific features for specificmodels, and even more. Speakers: Ricardo Ferreira andChristopher Cook

Ricardo Ferreira, Christopher CookMountain View Community Collegeri.ferreira2020@gmail.com, cc112591@gmail.com

MS198

WeFold: a Collaborative and Educational Experi-ment

Determining protein structure is key to advances in sci-ence and medicine. To advance this field a social-mediabased consortium of labs worldwide was created to bringtogether researchers from all walks and disciplines. Re-cently, the project added an educational component bybringing a group of students and faculty under one roofto discuss protein folding. We will discuss the results ofWeFold both as a new way to conduct research and engagestudents to learn computational science. Speakers: Silvia

162 CS15 Abstracts

Crivelli, John Hatherill, and Jesse Fox.

Silvia N. CrivelliLawrence Berkeley National Laboratorysncrivelli@lbl.gov

John HatherillDel Mar Community Collegejhatherill@delmar.edu

Jesse FoxMountain View Community Collegejfox@dcccd.edu

MS198

Reducing the Data Complexity with Filtering andClustering

Wefold maintains hundreds of thousands of models ob-tained from participants like Foldit. Model computation istime intensive due to NP complete nature, thus this teamsought smaller accurate protein conformation datasets.Preliminary results from our filter concluded the filtrationachieved a decrease in set size with an accuracy increase.However, this set retains unworkable complexity. Differentparallel clustering algorithms and metrics were analyzed tofind accurate clusters and representatives to finally reducethe set. Speakers: Davis, Ogden, and Raiyyani

Rachel A. DavisDrake Universityrachel.davis@drake.edu

Jennifer OgdenSaint Mary’s College of Californiajennogden95@gmail.com

Rehan RaiyyaniUniversity of California, San Diegorehan.raiyyani@gmail.com

MS198

The Maintenance of the WeFold Gateway forCASP11

The protein structure prediction and refinement methodsgenerated by the WeFold community in the context of theCASP11 competition were executed as pipelines of com-ponents contributed by different labs. Twenty labs world-wide including more than 100 researchers participated inthis collaboration. Because of deadlines to submit predic-tions to the competition, it was important to facilitate theexecution of the pipelines. I will discuss the maintenanceof the WeFold gateway as well as the results achieved.

Anthony LopezDel Mar Community Collegelopez52891@yahoo.com

MS199

An Implcit, Conservative Vlasov-Darwin PicSolver in Multiple Dimensions

We propose a new, implicit 2D-3V particle-in-cell algo-rithm for non-radiative, electromagnetic kinetic plasmasimulations. Local charge, global energy, and canonicalmomentum are exactly conserved. The Darwin-Vlasovequations are discretized with particles on a grid, using

a time-centered, implicit scheme, which is converged non-linearly. The nonlinear solver is accelerated by a moment-based preconditioner. We demonstrate the properties ofthe algorithm with several verification examples, includ-ing a Weibel instability and a Kinetic Alfven wave ion-ionstreaming instability.

Guangye Chen, Luis ChaconLos Alamos National Laboratorygchen@lanl.gov, chacon@lanl.gov

MS199

A Moment Model for the Vlasov Fokker PlanckEquation

We present a moment method based on spherical harmon-ics for the Vlasov equation coupled with some common col-lision operators. A transformation in phase space is usedto enable the moments to give a perturbation around theequilibrium solution in phase space. Furthermore, we givenumerical results which show the difference between us-ing/not using a transformation in phase space.

Charles K. Garrett, Cory HauckOak Ridge National Laboratorygarrettck@ornl.gov, hauckc@ornl.gov

MS199

Modeling Non-Ideal Plasmas: a Hyrbid Quan-tum Hydrodynamics and Molecular Dynamics Ap-proach

Abstract not available at time of publication.

Michael MurilloLos Alamos National Laboratorymurillo@lanl.gov

MS199

iFP: An Optimal, Fully Conservative, Fully Im-plicit, Vlasov-Fokker-Planck Solver

We introduce a new, exactly conservative (mass, momen-tum, and energy), and fully nonlinearly implicit solver fora multi-species 1D-2V Vlasov-Rosenbluth-Fokker-Plancksystem. The new solver optimizes mesh resolution require-ments by 1) adapting the velocity-space mesh based on thespecies’ local thermal-velocity, and 2) treating the cross-species collisions exhibiting disparate thermal velocities byan asymptotic formulation. We demonstrate the efficiencyand accuracy properties of the approach with challengingnumerical examples.

William T. Taitano, Luis Chacon, Andrei SimakovLos Alamos National Laboratorytaitano@lanl.gov, chacon@lanl.gov, simakov@lanl.gov

MS200

Current Challenges in Mesh Partitioning forPhysics Simulations

For modern and complex physics simulations on very largedata, achieving a good load balancing of the computationsat every time step is still a hard problem. For mesh basedsimulations, load balancing is achieved by performing meshpartitioning. In this talk, we shall define what can be thegoals of mesh partitioning. We shall also present main

CS15 Abstracts 163

problems we are currently working on at CEA: - Multi cri-teria (re-)partitioning, in order to deal with multi physicssimulations; - Memory constrained (re-)partitioning, tomodel layers of ghost cells which can fill up the availablememory.

Cedric ChevalierFrench Alternative Energies & Atomic EnergyCommission (CEA)cedric.chevalier@cea.fr

MS200

The Zoltan2 Toolkit: Partitioning, Task Place-ment, Coloring, and Ordering

Zoltan2 is a toolkit of partitioning, coloring, and order-ing algorithms for use in parallel scientific applications. Asuccessor to the Zoltan toolkit, Zoltan2 is designed to ad-dress current issues in scientific computing: extreme data-set sizes, parallel computers built of multicore processors,and sustainable software design. Zoltan2 is built on thetemplated software stack in the Trilinos solvers framework,and, thus, provides more seamless integration with Trilinos’data structures. This presentation provides an introduc-tion to the design and capabilities of Zoltan2.

Karen D. DevineSandia National Laboratorieskddevin@sandia.gov

Erik G. BomanSandia National Labs, NMScalable Algorithms Dept.egboman@sandia.gov

Siva Rajamanickam, Lee Ann RiesenSandia National Laboratoriessrajama@sandia.gov, lriesen@sandia.gov

Mehmet DeveciThe Ohio State Universitymdeveci@bmi.osu.edu

Umit V. CatalyurekThe Ohio State UniversityDepartment of Biomedical Informaticsumit@bmi.osu.edu

MS200

Unstructured Mesh Partitioning to over 500k Parts

Parallel unstructured mesh-based applications running onthe latest petascale systems require partitions with over500k parts. Methods combining the most powerful graphbased and geometric methods with diffusive methods di-rectly operating on the unstructured mesh will be dis-cussed. Initial partitioning results on meshes with over 12billion elements and over 512k parts indicate that thesemethods maintain quality while keeping run times to asmall fraction of application run time.

Cameron SmithScientific Computation Research CenterRensselaer Polytechnic Institutesmithc11@rpi.edu

Dan A. IbanezRensselaer Polytechnic Institute

SCORECdibanez@scorec.rpi.edu

Mark S. ShephardRensselaer Polytechnic InstituteScientific Computation Research Centershephard@rpi.edu

MS200

Zoltan2 for Extreme-Scale Data Partitioning

As the number of cores in modern high performance com-puting architectures has increased, data partitioning algo-rithms have struggled to scale. As part of the DOE Sci-DAC FastMATH Institute, we have been attempting to ad-dress this problem in our load-balancing software Zoltan2.Specifically, we have be focusing on developing partitionersto create high quality partitions for 100k-1M cores. In thistalk, we discuss many of the techniques that we have founduseful in achieving this goal.

Michael WolfSandia National Laboratoriesmmwolf@sandia.gov

MS201

Block-Structured AMR: Applications UsingBoxLib

BoxLib is a publicly available software framework for build-ing parallel block-structured AMR applications using bothMPI and OpenMP. It supports grid-based and particle-mesh operations on adaptive hierarchical meshes with op-tional subcycling in time. This talk focuses on the commoncomponents that form the basis of existing codes in astro-physics, cosmology, combustion and porous media, and al-low construction of new application codes and extension toAMR of existing single-level codes, in a variety of applica-tion areas.

Ann S. AlmgrenLawrence Berkeley National Laboratoryasalmgren@lbl.gov

MS201

Preconditioners for Implicit Atmospheric ClimateSimulations in the Community Atmosphere Model

High resolution, long-term climate simulations are essentialto understanding regional climate variation on the decadescale. To maintain accuracy with time steps commensu-rate with the physical processes of interest, the spectralelement dynamical core of the Community AtmosphereModel (CAM-SE) implements fully implicit schemes uti-lizing FASTMath Trilinos solvers. We discuss the develop-ment of preconditioners to reduce the computational costof ancillary linear system solves within each time step toimprove solver efficiency and scalability.

David J. GardnerLawrence Livermore National Laboratorygardner48@llnl.gov

Katherine J. EvansOak Ridge National Laboratoryevanskj@ornl.gov

Aaron Lott

164 CS15 Abstracts

D-Wave Systems, Inc.palott@gmail.com

Andrew SalingerCSRISandia National Labsagsalin@sandia.gov

Carol S. WoodwardLawrence Livermore Nat’l Labwoodward6@llnl.gov

MS201

Gyrokinetic Poisson Equation Solvers with ExplicitFlux Surface Averaging in XGC1 with PETSc

An accurate representation of the flux surface averagingterm in the gyrokinetic Poisson equation is explored for thefirst time, to our knowledge, in a global extreme-scale Toka-mak code XGC1. We use the FieldSplit preconditioner ca-pability in PETSc, which provides access to a wide varietysolver algorithms, including direct, block near direct, Schurcomplement, Gauss-Seidel, and additive and multiplicativesolver algorithms.

Mark AdamsLawrence Berkeley Laboratorymfadams@lbl.gov

Seung-Hoe KuPrinceton Plasma Physics Laboratorysku@pppl.gov

MS201

Algebraic Multigrid Solvers for Lattice QCD in theHypre Software Library

Algebraic multigrid (AMG) has been instrumental in manysimulation codes for solving the requisite linear systems ina scalable manner. In quantum chromodynamics (QCD),the development of effective AMG methods has been fairlyrecent so their use in QCD simulations has not yet becomecommonplace. In this talk, we discuss work to develop avariant of the bootstrap AMG method in the hypre libraryand efforts to interface it with the USQCD software stack.

Evan BerkowitzLawrence Livermore National Laboratoryberkowitz2@llnl.gov

James BrannickDepartment of MathematicsPennsylvania State Universitybrannick@psu.edu

Robert FalgoutCenter for Applied Scientific ComputingLawrence Livermore National Laboratoryrfalgout@llnl.gov

Chris SchroederLawrence Livermore National Laboratoryschroeder1@llnl.gov

MS202

Optimization Approach for Tomographic Inversion

from Multiple Data Modalities

Fluorescence tomographic reconstruction can be used to re-veal the internal elemental composition of a sample whiletransmission tomography can be used to obtain the spatialdistribution of the absorption coefficient inside the sample.In this work, we integrate both modalities and formulate anoptimization approach to simultaneously reconstruct thecomposition and absorption effect in the sample. By usingmultigrid-based optimization framework (MG/OPT), sig-nificant speedup and improvement of accuracy has shownfor several examples.

Zichao DiArgonne National Labwendydi@mcs.anl.gov

Sven LeyfferArgonne National Laboratoryleyffer@mcs.anl.gov

Stefan WildArgonne National Laboratorywild@mcs.anl.gov

MS202

Multigrid Preconditioning for Space-time Dis-tributed Optimal Control Problems Constrainedby Parabolic Equations

We present some recent results regarding multigrid pre-conditioning of the linear systems arising in the solutionprocess of space-time distributed optimal control problemsconstrained by parabolic equations. While the constructionof the preconditioners is based on ideas extracted from op-timal control problems constrained by elliptic equations, inthe parabolic-constrained case the multigrid precondition-ers exhibit a suboptimal behavior, namely they approxi-mate the operators to be inverted by half an order lessthan optimal.

Andrei DraganescuDepartment of Mathematics and Statistics, UMBCUniversity of Maryland, Baltimore Countydraga@umbc.edu

Mona HajghassemDepartment of Mathematics and StatisticsUniversity of Maryland, Baltimore Countymona4@umbc.edu

MS202

About Some Smoothers for Saddle-point Problems

In this work, we focus on the multigrid solution of saddlepoint problems. A key ingredient in designing an opti-mal multigrid solver is the choice of the smoother. Thesmoothers that we consider are mainly the obtained viaa coupled relaxation approach and they are tuned specifi-cally for the indefinite matrices corresponding to the saddlepoint problems of interest. This is done guided by the lo-cal Fourier analysis (LFA), which allows us to estimate thespectral radius of the k-grid operator in order to obtainquantitative measures for the error reduction and to ac-curately predict the asymptotic convergence factor of themethod. The LFA of such smoothers requires non-standardtechniques, and they are used to adjust the parameters ofthe underlying multigrid method and increase its efficiency.

CS15 Abstracts 165

Carmen Rodrigo, Francisco Jose Gaspar, FranciscoLisbonaUniversity of Zaragozacarmenr@unizar.es, fjgaspar@unizar.es, lisbona@unizar.es

Ludmil ZikatanovPennsylvania State Universityludmil@psu.edu

MS202

Multigrid in Chaos

Dynamics of molecules, fluid flows, the climate, and otherchaotic systems appear in many science and engineeringapplications. The long-time behavior of these dynamicalsystems, and their sensitivity to perturbations, is interest-ing to both scientists and engineers. The multigrid methodmay be the key to finding such sensitivity. Sensitivity ofchaotic dynamical systems can be computed using a newmethod known as Least Squares Shadowing, which requiressolving a space-time system of elliptic nature. Althoughmultigrid shows great promise, this application also bringsnew challenges to multigrid methods.

Qiqi WangMassachusetts Institute of Technologyqiqi@mit.edu

Patrick BloniganMITblonigan@mit.edu

MS203

Fast Solvers for Hierarchical Matrices

Recent years have seen the emergence of novel fast directmethods to solve linear systems with hierarchical matrices.These methods are based on a type of direct elimination ofthe unknowns, in a manner similar to the LU factorization;their accuracy is therefore less sensitive to the conditionnumber and distribution of eigenvalues of the matrix thanwith iterative solvers. We will present a novel class of fastdirect solvers for sparse matrices.

Amirhossein AminfarStanford Universityaminfar@stanford.edu

Sivaram AmbikasaranDepartment of MathematicsCourant Institute of Mathematical Sciencessivaram@cims.nyu.edu

Mohammad Hadi Pour AnsariStanfordhadip@stanford.edu

Eric F. DarveStanford UniversityMechanical Engineering Departmentdarve@stanford.edu

MS203

Rank-Structured Preconditioners for Two andThree-Dimensional Integral and Differential Equa-

tions

The inverses and LR factors of stiffness matrices appearingin the context of partial differential equations and integralequations are frequently rank-structured, i.e., they containsubmatrices that have low numerical rank. This propertycan be exploited to efficiently construct approximations ofthese matrices and thereby find preconditioners for a widerange of problems. This talk presents algorithms for carry-ing out algebraic operations (matrix multiplication, factor-ization, inversion) approximately exploiting and preservingthe low-rank structure. The algorithms rely on sequencesof low-rank updates applied to H2-matrices, a relativelygeneral class of rank-structured matrices that have efficientdata-sparse representations.

Steffen Borm, Knut ReimerUniversitaet Kielsb@informatik.uni-kiel.de, knr@informatik.uni-kiel.de

MS203

A New Integral Formulation and Fast Direct Solverfor Periodic Stokes’ Flow

Many solution techniques have recently been developed toaccurately and efficiently numerically model vesicle flow.The introduction of a periodic confining geometry adds fur-ther complications to such simulations. This talk presentsa new integral formulation which avoids the use of the pe-riodic Green’s function. Additionally, a fast direct solverfor the discretized confining geometry is presented. Thissolver allows for efficient time stepping by decoupling thestatic geometry from the moving vesicles.

Adrianna GillmanDartmouth CollegeDepartment of Mathematicsadrianna.gillman@rice.edu

Alex H. BarnettDepartment of MathematicsDartmouth Collegeahb@math.dartmouth.edu

Shravan Veerapaneni, Gary MarpleDepartment of MathematicsUniversity of Michiganshravan@umich.edu, gmarple@umich.edu

MS203

Practical and Efficient Direct Solvers for BIEs

The discretization of integral equations leads to dense lin-ear systems. For large problems, these systems have tradi-tionally been solved using iterative solvers, often in combi-nation with accelerated techniques for the dense matrix-vector multiplication, such as, e.g., the Fast MultipoleMethod. However, in the last several years a number ofdirect solvers with very high practical efficiency, and fa-vorable (often linear) asymptotic complexity have been de-veloped. This talk will describe techniques aimed at im-proving performance and simplifying coding by using ran-domized methods to accelerate certain structured matrixcomputations. The direct solvers used will be based onthe hierarchical merging of discrete analogs of scatteringmatrices.

Gunnar MartinssonUniv. of Colorado at Boulder

166 CS15 Abstracts

martinss@colorado.edu

MS204

A One-Stage High-Resolution Constrained Trans-port Method for Magnetohydrodynamic Equations

Failure to maintain zero divergence of magnetic field hasbeen known to cause instability of numerical methodsfor solving magnetohydrodynamic equations. In this talkwe will present a high-order conservative finite differenceWENO method that uses constrained transport to enforcea divergence free magnetic field. This method is basedon the Picard Integral Formulation of the PDE, which al-lows us to construct a single-stage single-step scheme. Thismethod is high-resolution, scalable to large clusters, andamenable to Adaptive Mesh Refinement (AMR).

Xiao FengDepartment of MathematicsMichigan State Universityfengxia2@msu.edu

MS204

A Hybrid Weno Reconstruction on UnstructuredMesh

The weighted essentially non-oscillatory (WENO) schemesare a popular class of high order numerical methods for hy-perbolic partial differential equations (PDEs). In this talk,we will first talk about a hybrid approach for WENO recon-structions on the unstructured meshes and then discuss themaximum-principle-preserving/positivity-preserving prop-erties of the schemes. Numerical examples coupled withthird order Runge-Kutta time integrator are reported.

Yuan LiuDepartment of MathematicsMichigan State Universityyliu7@math.msu.edu

MS204

A New RKDG Method with Conservation Con-straint to Improve CFL Condition for Solving Con-servation Laws

Abstract not available at time of publication.

Zhiliang XuUniversity of Notre Damezxu2@nd.edu

MS204

High Order WENO Method for Steady State Prob-lems

High order accurate shock capturing schemes such asWENO schemes often suffer from difficulties in their con-vergence towards steady state solutions. In this talk, I shallpresent our recent results on improving the convergence offifth order WENO scheme for solving steady state hyper-bolic conservation laws by an explicit Gauss-Seidel sweep-ing framework combined with different new techniques.

Liang Wu, Yongtao ZhangUniversity of Notre Damelwu2@nd.edu, yzhang10@nd.edu

Shuhai Zhang

China Aerodynamics Research and Development CenterChinazhang shuhai@tom.com

Chi-Wang ShuBrown UniversityDiv of Applied Mathematicsshu@dam.brown.edu

MS205

Constraint Aggregation Methods for PDE-Constrained Optimization

Many engineering design optimization problems are for-mulated with a bound on a physical quantity over a do-main of interest. Aggregation methods approximate thisinfinite-dimensional constraint in a differentiable manner.However, many classical methods are non-conservative andit is often difficult to assess the error incurred through ag-gregation. To address these issues, we present a new classof aggregation technique for PDE-constrained optimizationand present a post-optimality method to assess the aggre-gation error. We present the results of these new techniqueson large-scale structural optimization problems.

Graeme KennedyGeorgia Institute of TechnologySchool of Aerospace Engineeringgraeme.kennedy@aerospace.gatech.edu

Jason E. HickenRensselaer Polytechnic InstituteAssistant Professorhickej2@rpi.edu

MS205

Large-Scale PDE-Constrained Fluid-Structure Op-timization

A multi-physics fluid-structure optimization problem withmillions of state variables and thousands of design vari-ables is presented. The fluids domain is described by thecompressible Reynolds-Averaged Navier–Stokes equationsand the structural domain is described by the equations oflinear elasticity. Parallel solution techniques for the cou-pled, non-linear multidisciplinary system and the linearizedadjoint system are discussed.

Gaetan KenwayUniversity of MichiganAerospace Engineeringgaetank@gmail.com

Joaquim R. R. A MartinsUniversity of Michiganjrram@umich.edu

MS205

A Krylov-Based Iterative Solver for Equality-Constrained Non-Convex Quadratic Subproblems

Conventional matrix-based constrained-optimization al-gorithms are not well suited to reduced-space PDE-constrained optimization, because, even for modest-sizedprimal and dual spaces, the cost of evaluating the Hessianand Jacobian can be prohibitive. This makes matrix-freeoptimization algorithms attractive for these applications.Some challenges for reduced-space matrix-free algorithms

CS15 Abstracts 167

include Hessians that are nonconvex in the null space ofthe Jacobian, as well as finding effective matrix-free pre-conditioners for the primal-dual system. Several matrix-free algorithms have been proposed to handle nonconvex-ity by adapting existing iterative solvers. In this work,we address nonconvexity within the primal-dual iterativemethod itself by modifying the subspace problem solved byflexible GMRES. The approach is surprisingly simple andeffective. We also present preliminary investigations of amultigrid matrix-free preconditioner.

Jason E. HickenRensselaer Polytechnic InstituteAssistant Professorhickej2@rpi.edu

Pengfei MengRensselaer Polytechnic Universitymengp2@rpi.edu

MS205

Aerodynamic Shape Optimization with Goal-Oriented Error Estimation and Control

We investigate the control of discretization error ingradient-based aerodynamic shape optimization throughuse of adaptive mesh refinement. The approach makesdual use of the adjoint method first in the computation ofthe objective function gradient and second in the estima-tion of discretization error. We focus on progressive opti-mization, where the depth of mesh refinement is system-atically increased as the design improves. The approachis demonstrated on several challenging problems, includingthree-dimensional inverse design for sonic-boom minimiza-tion and the optimization of a flexible wing for transportaircraft. This is an important step in our research towarddynamic error control to improve automation and minimizecost.

Marian NemecScience & Technology Corp.NASA Ames Research Centermarian.nemec@nasa.gov

Michael AftosmisNASA Ames Research Centermichael.aftosmis@nasa.gov

MS206

A Parallel Local Timestepping Runge-Kutta Dis-continuous Galerkin Method with Applications toCoastal Ocean Modeling

Abstract not available at time of publication.

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu

MS206

Development and Validation of DG Wave: a Dis-continuous Galerkin-Based Numerical Wave Pre-diction Model

Abstract not available at time of publication.

Ethan Kubatko

The Ohio State Universityekubatko@gmail.com

MS206

Physically Based Assessment of Hurricane SurgeThreat under Climate Change

Abstract not available at time of publication.

Ning LinPrinceton Universitynlin@princeton.edu

MS206

Understanding Coastal Hydrodynamic Processesand Mitigating Risk Through High Fidelity Com-puter Simulations

Abstract not available at time of publication.

Joannes WesterinkDepartment of Civil Engineering and Geological SciencesUniversity of Notre Damejjw@nd.edu

MS207

FinAT: A Mathematical Structure-Preserving Li-brary of Finite Elements

Currently, automated finite element software generatesfairly traditional algorithms based on black box tabula-tion of basis functions. FInAT is a new project that willexploit the algebraic structure of basis functions to gener-ate more sophisticated algorithms that exploit tensor prod-uct structure. It replaces arrays of tabulated values, withspecialized recipes for performing evaluation and integra-tion. This will create efficient implementations of productelements, vector elements, Bernstein polynomials, and ele-ments such as Morley and Hermite with complicated pull-backs.

David HamImperial College Londondavid.ham@imperial.ac.uk

Rob KirbyBaylor Universityrobert kirby@baylor.edu

MS207

Finite Element Geometric Multigrid Solvers fromHigh-Level Problem Descriptions

We present an implementation of geometric multigridsolvers in the Firedrake finite element framework. Our ap-proach combines composable building blocks – appropriatesmoothers and intergrid transfer operators – with a sym-bolic representation of the PDE to simplify development ofsolvers for users: for many problems they need only pro-vide the fine grid discretisation. Our approach is agnosticto how the operators are applied, allowing simple switchingbetween matrix-free and assembled operators.

Lawrence MitchellDepartment of ComputingImperial College Londonlawrence.mitchell@imperial.ac.uk

168 CS15 Abstracts

Eike H. MuellerUniversity of Bathe.mueller@bath.ac.uk

David HamImperial College Londondavid.ham@imperial.ac.uk

Colin J. CotterImperial College LondonDepartment of Aeronauticscolin.cotter@imperial.ac.uk

MS207

Towards a Unified Framework for Automated aPosteriori Error Estimation and Adaptivity inSpace-Time

Finite element systems that operate at a sufficiently highlevel of abstraction allow for efficient implementation of anumber of automated features. Here, we will discuss how toefficiency extend previous work on automated goal-orientederror control and adaptivity to space-time finite elementmethods. We’ll present a unified framework for automatedderivation of problem-targeted error estimates and indica-tors, and high level interfaces, efficient data structures andalgorithms for arbitrary dimension tensor product finite el-ement methods.

Marie E. RognesSimula Research Laboratorymeg@simula.no

Anders LoggChalmers University of Technologylogg@chalmers.se

Benjamin KehletSimula Research Laboratorybenjamik@simula.no

MS207

Multicore Parallelism for Common Finite ElementOperations

As the number of cores on a chip and in a node increases,the importance of multithreading increases. We identify adesign pattern where an embarrassingly parallel operationon every cell is followed by a reduction. This design patternappears in finite element code through matrix assembly,estimating discretization errors, post-processing, etc. Wealso show a scalable implementation of this design pattern.

Bruno TurcksinTexas A&M Universityturcksin@math.tamu.edu

Martin KronbichlerTechnische Universitat Munchenkronbichler@lnm.mw.tum.de

Wolfgang BangerthTexas A&M University

bangerth@math.tamu.edu

MS208

Thermodynamically Consistent and Meta-StableEquation of State Models for Hydro and Solid Dy-namics

Simulations of real engineering interest require the use ofthermodynamic and constitutive models that go beyondsimple analytic equations of state. In this talk we will dis-cuss the complications that arise from using general equa-tions of states for fluids and solids. Issues that need to beaddressed include equilibrium and non-equilibrium treat-ments for mixed and separated species and robust treat-ments for incompatible mixtures such as metals in tensionand gases.

John W. GroveComputational Physics & Methods, CCS-2Los Alamos National Laboratoryjgrove@lanl.gov

MS208

Modelling of Fabric Surface for Parachute Inflationthrough Front Tracking

We use the front tracking library on a triangulated springsystem to model the dynamic evolution of parachutecanopy surface. The model is numerically convergent un-der the constraints that the summation of point masses isconstant and that both tensile and angular stiffness of thespring conform with the material’s Young modulus andPoisson ratio. This assembly is coupled with the fluidsolver through the impulse method to compute parachuteinflation for comparison with experiments.

Xiaolin LiDepartment of Applied Math and StatSUNY at Stony Brookxiaolin.li@stonybrook.edu

MS208

Overlapping BEM on FEM computations

In this talk I will review some theoretical and computa-tional work on how to deal with time-harmonic wave trans-mission problems by superposing solutions of problems inunbounded domains (discretized with BEM) and boundeddomains with homogeneous properties (discretized withFEM).

Francisco J. J. SayasDepartment of Mathematical SciencesUniversity of Delawarefjsayas@math.udel.edu

Victor DominguezUniversidad Publica de NavarraSpainvictor.dominguez@unavarra.es

Matthew HassellDepartment of Mathematical SciencesUniversity of Delaware

CS15 Abstracts 169

mhassell@math.udel.edu

MS208

Fractional Schrodinger Dynamics

We study the dynamics of the Schrodinger equation witha fractional Laplacian (Δ)α. Analytically, we find equa-tions describing the dynamics of the expected positionand expected momentum in the fractional Schrodingerequation, equations that are the fractional counterpart ofthe Newtonian equations of motion for the non-fractionalSchrodingier equation (α = 1). We also propose a nu-merical method for to study the dynamics of fractionalSchrodinger equation and find that the nonlocal interac-tion from the fractional Laplacian introduces decoherenceinto the wave function.

Yanzhi ZhangMissouri University of Science and Technologyzhangyanz@mst.edu

MS209

Towards Ab-Initio Simulations of NanoelectronicDevices

To accurately simulate always smaller devices and predicttheir ”current vs. voltage” characteristics prior to fabrica-tion, the usage of a quantum transport (QT) solver has be-come a must. Also, empirical models such as tight-bindingcannot be considered as fully reliable when it comes tonanostructures so that in many applications they shouldbe replaced by ab−initio solutions. Here, we will thereforepresent the core algorithms of a DFT-based approach thatcombines the CP2K community code with an existing QTsimulator. As key feature the resulting tool can treat elec-tronic transport in 2-D and 3-D systems with more than10,000 atoms.

Mathieu Luisier, Mauro Calderara, Sascha BrueckIntegrated Systems LaboratoryETH Zurichmluisier@iis.ee.ethz.ch, mcalderara@iis.ee.ethz.ch,bruecks@iis.ee.ethz.ch

Hossein Bani-Hashemian, Joost VandeVondeleNanoscale SimulationsETH Zurichhossein.banihashemian@mat.ethz.ch,joost.vandevondele@mat.ethz.ch

MS209

Truly Scalable O(N) Approach for First-PrinciplesMolecular Dynamics (FPMD) of Non-Metallic Sys-tems

We present a scalable O(N) FPMD algorithm based ona non-orthogonal localized orbitals formulation of DFT. Ascalable strategy is used to approximately compute selectedelements of the inverse of the associated Gram matrix. Thealgorithm exploits sparsity and uses nearest neighor com-munication only for excellent scalability. Accuracy is con-trolled by the mesh spacing of the discretization, the sizeof the localization regions confining the orbitals, and a cut-off radius for the Gram matrix. This work was performedunder the auspices of the U.S. Department of Energy byLawrence Livermore National Laboratory under Contract

DE-AC52-07NA27344.

Jean-Luc FattebertLawrence Livermore National Lab.fattebert1@llnl.gov

Daniel Osei-KuffuorLawrence Livermore National Laboratoryoseikuffuor1@llnl.gov

MS209

Ab Initio Quantum Monte Carlo in ComputationalMaterials Science and Chemistry

Ab initio Quantum Monte Carlo is an electronic structuremethod that is highly accurate, well suited to large scalecomputation, and potentially systematically improvable inaccuracy. The method has recently been applied to transi-tion metal oxides and to the prediction of defect propertiesand thermodynamics of materials, where established elec-tronic structure methods have difficulty reaching the ac-curacies desired to inform experiment and the design andselection of materials. Nevertheless there remain signifi-cant challenges to achieving a methodology that is robustand systematically improvable in practice, e.g., where thestatistical nature of the method precludes the use of algo-rithms developed for density functional theory or quantumchemical techniques. In this talk I will outline the cur-rent state of the art and describe several opportunities foradvances in the mathematical foundation and numericalimplementation of key components of the method.

Paul KentOak Ridge National Laboratorykentpr@ornl.gov

MS209

Using Next-generation Architectures to ModelLarge and Complex Molecular Environments

Modelling large and complex molecular environments re-quires fast, computationally scalable and efficient compu-tational tools utilizing novel algorithmic approaches on thelatest hardware technologies. Results of optimization ef-forts of the high-accuracy coupled cluster triples and thesolid state planewave modules in the NWChem compu-tational chemistry software for Intel Knights Corner andLanding multicore architectures combined with algorith-mic advances will be discussed.

Bert de Jong, Hongzhang ShanLawrence Berkeley National Labwadejong@lbl.gov, hshan@lbl.gov

Leonid OlikerLawrence Berkeley National Laboratoryloliker@lbl.gov

MS210

Segmental Refinement: A Multigrid Technique forData Locality

We investigate a technique, segmental refinement (SR),proposed by Brandt in the 1970s as a low memory multigridmethod. The technique is attractive for modern computerarchitectures because it provides high data locality, mini-mizes network communication, is amenable to loop fusion,and is naturally highly parallel and asynchronous. The

170 CS15 Abstracts

network communication minimization property was rec-ognized by Brandt and Diskin in 1994; we continue thiswork by developing a segmental refinement method for afinite volume discretization of the 3D Laplacian on mas-sively parallel computers. An understanding of the asymp-totic complexities, required to maintain textbook multigridefficiency, are explored experimentally with a simple SRmethod. A two-level memory model is developed to com-pare the asymptotic communication complexity of a pro-posed SR method with traditional parallel multigrid. Per-formance and scalability are evaluated with a Cray XC30with up to 64K cores. We achieve modest improvement inscalability from traditional parallel multigrid with a simpleSR implementation.

Mark AdamsLawrence Berkeley Laboratorymfadams@lbl.gov

MS210

Comparative Performance Analysis of an AlgebraicMultigrid Solver on Leading Multicore Architec-tures

We present a comparative performance analysis of a novelelement-based algebraic multigrid method combined witha robust coarse-grid solution technique based on HSS low-rank sparse factorization. Our test datasets come from theSPE Comparative Solution Project for oil reservoir simu-lations. We contrast the performance of the code on one12-core CPU of a Cray XC30 with that on a 60-core IntelXeon Phi. The steps we required to obtain top performanceare described in detail.

Alex DruinskyComputational Research DivisionLawrence Berkeley National Laboratoryadruinsky@lbl.gov

Brian AustinNERSCLawrence Berkeley National Laboratorybaustin@lbl.gov

Xiaoye Sherry LiComputational Research DivisionLawrence Berkeley National Laboratoryxsli@lbl.gov

Osni A. MarquesLawrence Berkeley National LaboratoryBerkeley, CAoamarques@lbl.gov

Eric Roman, Samuel WilliamsLawrence Berkeley National Laboratoryeroman@lbl.gov, swwilliams@lbl.gov

MS210

Iterative Performance of Monte Carlo LinearSolver Methods

Stochastic linear solvers based on Monte Carlo SyntheticAcceleration are being studied as a potentially resilient al-ternative to standard methods. Our work has shown thatfor certain classes of problems, these methods can alsodemonstrate performance competitive with modern tech-niques. In this talk we will review recent developments in

parallelizing Monte Carlo solvers for linear systems. Ourwork targets large, distributed memory systems by adapt-ing parallel algorithms developed in part by the radiationtransport community.

Massimiliano Lupo PasiniDepartment of Mathematics and Computer ScienceEmory Universitymassimiliano.lupo.pasini@emory.edu

MS210

Parallel Algorithms for the Monte Carlo SyntheticAcceleration Linear Solver Method

Stochastic linear solvers based on Monte Carlo SyntheticAcceleration are being studied as a potentially resilient al-ternative to standard methods. Our work has shown thatfor certain classes of problems, these methods can alsodemonstrate performance competitive with modern tech-niques. In this talk we will review recent developments inparallelizing Monte Carlo solvers for linear systems. Ourwork targets large, distributed memory systems by adapt-ing parallel algorithms developed in part by the radiationtransport community.

Stuart SlatteryComputer Science and Mathematics DivisionOak Ridge National Laboratoryslatterysr@ornl.gov

Tom EvansOak Ridge National Laboratoryevanstm@ornl.gov

Steven HamiltonORNLhamiltonsp@ornl.gov

MS211

Energy-based Inner Products for POD/GalerkinModel Reduction for Compressible Flows

The focus of this talk is the development of energy-basedinner products for POD/Galerkin model reduction for com-pressible flows. An energy stability analysis reveals thatthe inner product employed in the Galerkin projection stepof the model reduction dictates the ROMs stability. Fol-lowing the review of a symmetry inner product that givesrise to a stable formulation for linearized compressible flow,a new energy-based inner product for nonlinear compress-ible flow is derived and evaluated.

Jeffrey Fike, Irina K. Tezaur, Matthew Barone,Srinivasan ArunajatesanSandia National Laboratoriesjafike@sandia.gov, ikalash@sandia.gov,mbarone@sandia.gov, sarunaj@sandia.gov

MS211

Data-driven Optimal Rational Approximation viaNumerical Quadrature

Iterative Rational Krylov Algorithm (IRKA) has provedvery successful in producing optimal rational approxima-tions. The main cost for IRKA is the need to evaluatethe underlying transfer function and its derivatives at newpoints at every step. In this talk, we present a quadrature-based framework for IRKA that will remove this computa-

CS15 Abstracts 171

tional cost. Transfer function will be evaluated only in anoff-line phase at selected quadrature nodes and iterationwill not need new function evaluations.

Christopher A. BeattieVirginia Polytechnic Institute and State Universitybeattie@vt.edu

Zlatko DrmacUniversity of ZagrebDepartment of Mathematicsdrmac@math.hr

Serkan GugercinVirginia Tech.Department of Mathematicsgugercin@math.vt.edu

MS211

Reduced Order Modeling of Geophysical Flows

The reduced order models (ROMs) are frequently used inthe simulation of complex flows to overcome the high com-putational cost of direct numerical simulations. The properorthogonal decomposition (POD), as one of the most com-monly used tools to generate ROMs, has been utilized inmany engineering and scientific applications. For manycomplex flows, however, its original promise of computa-tionally efficient, yet accurate approximation of coherentstructures still remains to be fulfilled. To balance the lowcomputational cost required by ROMs and the complexityof the targeted flows, appropriate closure modeling strate-gies need to be employed. Several closure models for thePOD-ROMs of structurally dominated flows are carefullyderived and numerically investigated in the context of thequasi-geostrophic equations, which model the large scalewind-driven ocean flows.

Traian IliescuDepartment of MathematicsVirginia Techiliescu@vt.edu

MS211

Efficient Reduced Basis Methods for Contact andRelated Problems

We present online-efficient RB methods for contact and re-lated problems. Existing methods are inefficient since theonline cost to compute the error estimates depends on thedimension of the FE problem. Furthermore, the result-ing error bounds are often pessimistic. We present twoalternative, online-efficient approaches. The first approachintroduces an additional problem which enables the com-putation of sharp(er) error bounds. The second approachrecasts the nonlinearity to allow treatment by the Empiri-cal Interpolation Method (EIM).

Karen Veroy-Grepl, Zhenying Zhang, Eduard BaderGraduate School AICESRWTH Aachen Universityveroy@aices.rwth-aachen.de, zhang@aices.rwth-aachen.de,bader@aices.rwth-aachen.de

Mark KaercherRWTH Aachen University

kaercher@aices.rwth-aachen.de

MS212

Optimal Explicit Strong Stability PreservingRungeKutta Methods with High Linear Order andOptimal Nonlinear Order

The search for high order strong stability time-steppingmethods with large allowable strong stability coefficient hasbeen an active area ofresearch over the last two decades.This research has shown that explicit SSP RungeKuttamethods exist only up to fourth order. However, if werestrict ourselves to solving only linear autonomous prob-lems, the order conditions simplify and this order barrieris lifted: explicit SSP RungeKutta methods of any linearorder exist. These methods reduce to second order whenapplied to nonlinear problems. In the current work we aimto find explicit SSP RungeKutta methods with large allow-able time-step, that feature high linear order and simul-taneously have the optimal fourth order nonlinear order.These methods have strong stability coefficients that ap-proach those of the linear methods as the number of stagesand the linear order is increased. This work shows thatwhen a high linear order method is desired, it may be stillbe worthwhile to use methods with higher nonlinear order.

Sigal GottliebDepartment of MathematicsUniversity of Massachusetts Dartmouthsgottlieb@umassd.edu

Zachary J. GrantUniversity of Massachusetts at Dartmouthzgrant@umassd.edu

Daniel L. HiggsUniversity of Massachusetts, DartmouthDanielHiggs@gmail.com

MS212

Strong Stability Preserving General Linear Meth-ods

We describe the construction of strong stability preserving(SSP) general linear methods (GLMs) for ordinary differ-ential equations. This construction is based on the mono-tonicity criterion for SSP methods. This criterion can beformulated as a minimization problem, where the objectivefunction depends on the Courant-Friedrichs-Levy (CFL)coefficient of the method, and the nonlinear constrains de-pend on the unknown remaining parameters of the meth-ods. The solution to this constrained minimization prob-lem leads to new SSP GLMs of high order and stage order.This is a joint work with Giuseppe Izzo from the Universityof Naples.

Zdzislaw JackiewiczArizona State Universityjackiewicz@asu.edu

MS212

Stability-Optimized Time Integrators for WENODiscretizations

We present numerical time integrators designed for usewith WENO and compact-WENO spatial discretizations ofhyperbolic PDEs. These integrators have been optimizedfor, in order of priority

172 CS15 Abstracts

1. Absolute stability with respect to the WENO semi-discretizations (using the convex optimization tech-nique of Ketcheson & Ahmadia)

2. Strong stability preservation

3. Accuracy

We present theoretical and numerical evidence that thesenew methods allow the use of larger time steps withoutsacrificing accuracy.

David I. KetchesonCEMSE DivisionKing Abdullah University of Science & Technologydavid.ketcheson@kaust.edu.sa

Debojyoti GhoshMathematics and Computer Science DivisionArgonne National Laboratoryghosh@mcs.anl.gov

MS212

Implicit-Explicit General Linear Methods

Implicit-explicit (IMEX) time stepping methods can effi-ciently solve differential equations with both stiff and non-stiff components. In this work we study new implicit-explicit methods of general linear type. We develop anorder conditions theory for high stage order partitionedGLMs that share the same abscissae, and show that noadditional coupling order conditions are needed. Conse-quently, GLMs offer an excellent framework for the con-struction of multi-method integration algorithms. Next,we propose a family of IMEX schemes based on diagonally-implicit multi-stage integration methods and constructpractical schemes of order up to five with numerically op-timized stability regions. The new methods have similarstability properties as IMEX Runge-Kutta methods, butthey do not suffer from order reduction, and are superiorin terms of accuracy and efficiency. Numerical experimentswith two and three dimensional test problems illustrate thepotential of the new schemes to speed up complex applica-tions.

Hong ZhangVirginia Techzhang@vt.edu

MS213

Sampling Strategies for L1 Minimization

One of the biggest challenges of uncertainty quantificationis the inability to ‘densely’ sample the model input spacedue to high-dimensionality and/or the immense compu-tational expense of a high-fidelity model. The need to‘densely’ sample can be often be alleviated by buildinga sparse Polynomial Chaos Expansion (PCE) using l1-minimization. In this talk I will present sampling, pre-conditioning and basis adaptive strategies that allow oneto accurately approximate high-dimensional compressiblefunctions from limited data using any orthonormal poly-nomial basis.

John D. JakemanSandia National Labsjdjakem@sandia.gov

Akil NarayanUniversity of Massachusetts Dartmouth

akil.narayan@umassd.edu

MS213

Reweighted Minimization Method for UncertaintyQuantification of Microscopic Modeling

In this talk, reweighted minimization method for uncer-tainty quantification of microscopic modeling will be dis-cussed. Fast and accurate surrogate model is very usefulin mescoscopic modeling. It helps to evaluate the quantityof interest, calibrate the model e?ciently (with Bayesianframework), to study the uncertainty in the system quickly,etc. In this work, reweighted minimization method is em-ployed for microscopic modeling when the system includesi.i.d. uniform random variables. The proposed method en-hances our ability of exploiting information from limitedsource of experiments or simulations. We employ the newmethod to practical problems in mesoscopic modeling inphysical chemistry, electrochemistry, biophysics, biochem-istry, etc., to help to quantify the uncertainty, calibratemodel, design experiments, etc. In conclusion, this workwill provide a ?exible approach of e?ciently utilizing limitedexperimental or simulation results to construct an accuratesurrogate model.

Guang Lin, Xiu Yang, Huan LeiPacific Northwest National Laboratoryguang.lin@pnnl.gov, xiu.yang@pnnl.gov,huan.lei@pnnl.gov

MS213

Least Square Methods for Low-Rank Approxima-tions with Sparsity Inducing Regularization

Approximation of high dimensional stochastic functions us-ing functional approaches is often limited by the so calledcurse of dimensionality. In literature, approximation meth-ods often rely on exploiting particular structures of high di-mensional functions. One such structure which is increas-ingly found to be applicable in these functions is sparsityon suitable basis. Also, these functions exhibit optimal lowrank representation and can be approximated in suitablelow rank tensor subsets. In this work, we exploit sparsitywithin low rank representation to approximate high dimen-sional stochastic functions in a non intrusive setting usingfew sample evaluations. The proposed method can also becombined with clustering and classification approaches toapproximate high dimensional irregular and discontinuousfunctions.

Prashant RaiLUNAM Universite, Ecole Centrale Nantes, CNRS, GeMprashant.rai@ec-nantes.fr

Mathilde ChevreuilLUNAM Universite, Universite de Nantes, CNRS, GeMmathilde.chevreuil@univ-nantes.fr

Loıc GiraldiGeM, Ecole Centrale de Nantesloic.giraldi@ec-nantes.fr

Anthony NouyLUNAM Universite, Ecole Centrale Nantes, CNRS, GeM

CS15 Abstracts 173

anthony.nouy@ec-nantes.fr

MS213

Interpolation Via Weighted L1 Minimization

Functions of interest are often smooth and sparse in somesense. Classical linear interpolation methods are effectiveunder strong regularity assumptions, but cannot incorpo-rate nonlinear sparsity structure. At the same time, non-linear methods such as L1 minimization can reconstructsparse functions from very few samples, but do not neces-sarily encourage smoothness. Here we show that weightedL1 minimization effectively merges the two approaches,promoting both sparsity and smoothness in reconstruction.We consider the implications of these results for spheri-cal harmonic and polynomial interpolation, in the univari-ate and multivariate setting. Along the way, we extendconcepts from compressive sensing such as the restrictedisometry property and null space property to accommodateweighted sparse expansions; these developments should beof independent interest in the study of structured sparseapproximations and continuous-time compressive sensingproblems.

Rachel WardDepartment of MathematicsUniversity of Texas at Austinrward@math.utexas.edu

Holger RauhutAachen Universityrauhut@mathc.rwth-aachen.de

MS214

Nonlinear Image Registration with a Sliding Mo-tion Deformation Model

Common medical image registration approaches are enforc-ing a global continuity of the estimated deformation field.However, for deformations like e.g. the sliding of the lungalong the ribcage a continuous deformation estimation isnot feasible. Therefore we present in this talk a registrationframework that models discontinuities in the deformationfield along organ boundaries described by arbitrary ori-entable submanifolds. The incorporated methods involveconstrained nonlinear registration in the Lagrange frameand a finite element discretization.

Alexander DerksenInstitute of Mathematics and Image ComputingUniversity of Luebeckalexander.derksen@mic.uni-luebeck.de

MS214

Efficient Algorithms for Physically ConstrainedDiffeomorphic Image Registration

We treat image registration as a problem of optimal con-trol. The deformation is represented by its velocity. Thisleads to a constrained variational optimization problem,where the constraints are partial differential equations(PDEs) . We augment standardH1 andH2 smoothing reg-ularization with differential constraints on the velocity thatboth encapsulate prior knowledge and explicitly control thedeterminant of the deformation gradient. The associatedoptimality conditions are a system of space-time non-linearmulti-component PDEs that is challenging to solve in anefficient way. We solve for the first-order optimality con-

ditions using a matrix-free preconditioned Gauss-Newton-Krylov method for the Schur complement of the velocityfield. We use a spectral Galerkin method in time to re-duce the number of unknowns. Also, we use a spectraldiscretization in space, which in turn allows for an efficientpreconditioning of the Hessian.

Andreas MangThe University of Texas at AustinThe Institute for Computational Engineering and Sciencesandreas@ices.utexas.edu

George BirosUniversity of Texas at Austinbiros@ices.utexas.edu

MS214

Efficient Algorithms for High-Resolution Diffusion-Weighted MRI

Diffusion-weighted Magnetic Resonance Imaging (DW-MRI) allows the acquisition of functional information in-vivo and has important clinical applications, for instance,related to Ischemia and Alzheimer’s disease. In this talk, Iwill present computational methods to overcome two lim-itations currently inherent in DW-MRI: Geometrical dis-tortions due to measurement artifacts and low spatial res-olution. The presented 3D correction and super-resolutionmethod is based on a physical prior and employs a slice-wise parallelization to increase computational efficiency.

Lars RuthottoDepartment of Mathematics and Computer ScienceEmory Universitylruthotto@emory.edu

MS214

Constrained Optimal Control Approaches in LargeDeformation Diffeomorphic Metric Mapping

The large deformation diffeomorphic metric mapping (LD-DMM) algorithm, which addresses image or shape regis-tration, can be interpreted as an optimal control prob-lem in some suitable high-dimensional space of shapes. Ithas led to a large number of applications in the domainof computational anatomy, in which the focus is set onthe analysis of anatomical variations in relation with dis-ease. In some cases this algorithm can be invoked withadditional constraints, which leads to interesting new ap-plications and challenging implementation problems. Wewill review some of these examples in this talk, including,in particular, issues related to the combined registrationof multiple shapes, and to the evaluation of deformationswith atrophy constraints.

Laurent YounesCenter for Imaging Science , The Johns HopkinsUniversitylaurent.younes@jhu.edu

MS215

Preconditioned MCMC and Adaptive PosteriorRefinement Leveraging Sparse PCE

The process of performing Bayesian inference is frequentlyhindered by expense and by a lack of reliability in theMCMC sampling used for computing the posterior dis-tribution. We present a recent prototype for adaptive

174 CS15 Abstracts

emulator-based inference that employs �1-regularized re-gression for sparse polynomial chaos emulation, exploitsanalytic derivatives from the emulator to inform the pro-posal density, and then refines the emulator by performingnew model evaluations for points with high posterior den-sity.

Michael S. EldredSandia National LaboratoriesOptimization and Uncertainty Quantification Dept.mseldre@sandia.gov

John D. JakemanSandia National Labsjdjakem@sandia.gov

Laura SwilerSandia National LaboratoriesAlbuquerque, New Mexico 87185lpswile@sandia.gov

MS215

Accelerated Bayesian Inference with TransportMaps

The essential challenge in Bayesian computation for UQ isone of characterizing the posterior distribution, which of-ten is high-dimensional and non-Gaussian. We will showthat the use of transport maps can dramatically accelerateBayesian inference in this setting. First, we use a combi-nation of optimal transport and the Metropolis-Hastingsrule to yield a new adaptive MCMC approach for exact in-ference. Second, we develop new conditioning techniques,with tunable accuracy, that can utilize massively paralleloffline computation.

Matthew Parno, Youssef M. MarzoukMassachusetts Institute of Technologymparno@mit.edu, ymarz@mit.edu

MS215

Sparse, Adaptive Smolyak Quadrature Algorithmsfor Stochastic Inverse Problems

Deterministic, dimension-adaptive quadrature methods forBayesian inverse problems of parametric operator equa-tions with distributed uncertain inputs are proposed. Fordata from a sparsity class, the parametric, deterministicdensity of the Bayesian posterior belongs to the same spar-sity class. Dimension-independent convergence rates fordimension-adaptive Smolyak and QMC integration algo-rithms are shown. In the vanishing observation noise vari-ance limit the posterior concentrates near the MAP es-timate. We give asymptotic expansions of the Bayesianestimate w.r. to observation noise variance. A “variablemetric’ rescaling of the posterior near concentration points“preconditions’ quadrature for vanishing observation noisecovariance. Numerical results in agreement with the the-ory are presented. Supported by SNF and ERC underAdG247277.

Christoph SchwabETH ZuerichSAMchristoph.schwab@sam.math.ethz.ch

Claudia SchillingsETH ZurichSAM

claudia.schillings@sam.math.ethz.ch

MS215

Quasi Optimal Sparse-Grid Approximation of Ran-dom Elliptic PDEs

Solutions of PDEs depending on parameters/random co-efficients can be conveniently approximated by polyno-mial expansions over the parameter space. However, theseapproximations suffer from a performance degradation asthe number of random parameters increases (“curse of di-mensionality’ effect). In this talk we will propose an “a-priori/a-posteriori profit approach’ to minimize such effectfor sparse grids approximations. The efficiency of the pro-posed technique will be supported by theoretical conver-gence results and numerical tests.

Lorenzo TamelliniEPF-Lausanne, Switzerland,lorenzo.tamellini@epfl.ch

Fabio NobileEPFL, Switzerlandfabio.nobile@epfl.ch

Raul F. TemponeMathematics, Computational Sciences & EngineeringKing Abdullah University of Science and Technologyraul.tempone@kaust.edu.sa

MS216

Approaches to Evaluate Interactions in Collabora-tive Groundwater Management

Abstract not available at time of publication.

Joseph AmayaTexas A&M University - Kingsvillejoseph.amaya@tamuk.edu

MS216

Managing Surface Water Resources in Data SparseRegions

Abstract not available at time of publication.

Felipe EstradaTexas Tech Universityfelipe.estrada@ttu.edu

MS216

Climate Change and Water Scarcity

Abstract not available at time of publication.

Donna MitchellTexas Tech Universitydonna.m.mitchell@ttu.edu

MS216

Application of Simulation-Optimization for WaterManagement in Hydraulic Fracturing Operations

Abstract not available at time of publication.

Elma A. UddameriTexas Tech University

CS15 Abstracts 175

annette.hernandez@ttu.edu

MS217

Interface Resolved Numerical Method to StudyElectrokinetic Particle Assembly in Microdevices

A hybrid immersed interface-immersed boundary methodis developed to study electric field driven particle assemblywhere both electric and hydrodynamic forces are calculatedwith interface-resolved approach instead of commonly usedpoint-particle method. In this study, the Maxwell stresstensor is used to calculate the electric force acting on par-ticles by considering the physical effect of particles in thecomputational domain. Thus, this method eliminates theapproximations used in point dipole methods for calculat-ing forces. A comparative study between Maxwell stresstensor and point dipole methods for computing electricforces will be presented to elucidate the shortcoming ofthe latter method. Next, electric field driven particle mo-tions and related fluid flow phenomena will be presentedfor charged, uncharged and bipolar particles. We will par-ticularly demonstrate the particle chaining phenomena forsimilar and dissimilar type particles using applied electricfields.

Prashanta DuttaWashington State Universityprashanta@wsu.edu

MS217

Classical Density Functional Theory of ChargedFluids at Interfaces

Classical density functional theory (DFT) is a statisticalmechanical theory for inhomogeneous fluids, based on theminimization of a free energy functional. Here I will de-scribe the application of DFT to charged systems and inparticular the ionic correlations included by the DFT thatgo beyond the Poisson-Boltzmann treatment. I will presentresults for macroion interactions in electrolyte solutionsand the behavior of charged particles in nanochannels.

Amalie FrischknechtSandia National Laboratoriesalfrisc@sandia.gov

MS217

Efficient Parallel Implementation of ImplicitSPH/MLS using LAMMPS and Trilinos

We present an efficient parallel implementation of 3D im-plicit mesh-free particle methods for incompressible flows.Mesh-free methods are widely used for solving complexproblems that mesh-based methods cannot handle easily.However, implicit time methods are rarely applied to large-scale particle simulations due to the prohibitive computa-tional cost solving linear systems of equations. Our im-plementation is based on LAMMPS and adopts Trilinospackages for implicit time integration. Numerical experi-ments are presented to demonstrate the parallel scalability.

Kyungjoo KimSandia National Laboratorieskyukim@sandia.gov

Mauro PeregoCSRI Sandia National Laboratories

mperego@fsu.edu

Nathaniel TraskBrown UniversityDepartment of applied mathematicsnathaniel trask@brown.edu

Michael L. ParksSandia National Laboratoriesmlparks@sandia.gov

MS217

Meshless Methods for the Mesoscale - High OrderImplicit ALE Schemes using Collocated MLS

Meshless methods are ideal for simulating flows occurringat the mesoscale, since they trivially handle both defor-mation of complex boundaries and interface tracking forflows involving multispecies phenomena. Classical mesh-less methods tend to either be expensive or inconsistentand have mainly gained traction in the past as a low ordertechnique. We present a collocation formulation of mov-ing least squares (MLS) that allows high order discretiza-tion in space, and a fully implicit ALE projection schemethat is demonstrated to provide up to third order accu-racy in time. When the resulting system is solved usingalgebraic multigrid preconditioners, the scheme provides ascalable, flexible framework for simulating multiphysics atthe mesoscale.

Nathaniel TraskBrown UniversityDepartment of applied mathematicsnathaniel trask@brown.edu

Kyungjoo KimSandia National Laboratorieskyukim@sandia.gov

Mauro PeregoCSRI Sandia National Laboratoriesmperego@fsu.edu

MS218

A Sampling Filter for Non-Gaussian Data Assimi-lation

Current operational ensemble-based filters like EnsembleKalman Filter (EnKF), and Maximum Likelihood Ensem-ble Filter (MLEF), usually fail in case of non-linear obser-vations or non-Gaussian distributions. We propose a gen-eral ensemble-based data assimilation method that worksby sampling directly from the posterior distribution fol-lowing a Hybrid Monte Carlo (HMC) ap- proach. Theproposed filter was tested on Lorenz-96 model with severalobservation operators. Results show that this filter is ca-pable of handling non-linear as well as linear observations.

Ahmed AttiaVirginia Techattia@vt.edu

Adrian SanduVirginia Polytechnic Institute andState University

176 CS15 Abstracts

sandu@cs.vt.edu

MS218

Bayesian Nonlinear Smoothing and Adaptive Sam-pling

New schemes are presented for optimal Bayesian nonlinearstate estimation and adaptive sampling of large nonlinearfluid and ocean dynamical systems, both forward and back-ward in time. The Bayesian nonlinear smoothing com-bines reduced-order Dynamically-Orthogonal (DO) equa-tions with Gaussian Mixture Models (GMMs), extendinglinearized backward pass updates to a Bayesian nonlinearsetting. Bayesian nonlinear adaptive sampling schemes arethen derived to predict the observations to be collected thatmaximize information about variables of interest. Whencombined with rigorous time-optimal path planning, weobtain efficient coordinated swarms of autonomous oceansampling systems.

Pierre F.J LermusiauxMassachusetts Institute of Technologypierrel@mit.edu

Tapovan LollaMITltapovan@mit.edu

MS218

An Information Theoretic Approach to Use High-Fidelity Codes to Calibrate Low-Fidelity Codes

In this presentation, we discuss an information theoreticapproach to employ high-fidelity codes to calibrate low-fidelity codes used for design optimization or control im-plementation. The objective is to employ a limited num-ber of high-fidelity code evaluations as data for Bayesiancalibration of the low-fidelity code. We employ the mu-tual information between parameters and designs to deter-mine input values to the high-fidelity code, which maximizethe available information. For computationally expensivecodes, surrogate models are used to approximate the mu-tual information. The framework is illustrated for exam-ples arising in nuclear power plant design.

Allison LewisNorth Carolina State Universityallewis2@ncsu.edu

Ralph C. SmithNorth Carolina State UnivDept of Mathematics, CRSCrsmith@ncsu.edu

Brian WilliamsLos Alamos National Laboratorybrianw@lanl.gov

MS218

Displacement Data Assimilation

We are developing a data assimilation methodology specif-ically geared to problems in which the preservation of fea-tures and topological structures is crucial. The applicationof this methodology is aimed at improving estimates ofsuch things as hurricane tracks and the Lagrangian tracksof tracers in a flow. The basic strategy combines con-ventional nonlinear/non-Gaussian data assimilation on the

state variables as well as on the underlying kinematicsof the flow. In addition to describing the methodologywe show comparisons of displacement data assimilation tomore conventional assimilation in the context of pure ad-vection of a tracer in a flow constrained kinematically byarea preserving maps. This comparison will demonstratethat our methodology minimizes phase errors and thus de-livers better estimates of the topological features of ad-vected tracers.

Juan M. RestrepoDepartments of Mathematics, Atmospheric Physics, andPhysicsUniversity of Arizonarestrepo@math.oregonstate.edu

Steven RosenthalUniversity of Arizonasrosenthal@gmail.com

Shankar C. VenkataramaniUniversity of ArizonaDepartment of Mathematicsshankar@math.arizona.edu

Arthur MarianoRSMAS/MPOUniversity of Miamiamariano@rsmas.miami.edu

MS219

Statistical Metrics for Assessing Quality of Scenar-ios for Unit Commitment and Dispatch

Wind power scenarios for use in stochastic unit commit-ment should accurately represent the stochastic processfor available wind power. We employ statistical evalu-ation metrics to assess whether a scenario set possessesproperties that are expected to minimize expected cost. Anew mass transportation distance rank histogram assessescalibration of unequally likely scenarios according to theirbias, variability and autocorrelation. Energy scores, rankhistograms, and Brier scores are applied to alternative setsof wind power scenarios.

Sarah M. Ryan, Didem SariIowa State Universitysmryan@iastate.edu, dsari@iastate.edu

MS219

Adaptive Robust Optimization with Dynamic Un-certainty Sets for Power System Operations

In this talk, we present an adaptive robust optimizationmodel with a new type of dynamic uncertainty sets forpower system operations under significant renewable gen-eration uncertainty. We introduce a data-driven frame-work that fuses statistical estimation with uncertainty setconstruction to model temporal and spatial correlations ofrenewable generation. Computational results show the ad-vantages of the proposed robust model in terms of opera-tional cost and system reliability over existing deterministicand robust models.

Andy SunGeorgia TechCollege of Engineeringandy.sun@isye.gatech.edu

CS15 Abstracts 177

Alvaro LorcaGeorgia Institute of TechnologyIndustrial and Systems Engineeringalvarolorca@gatech.edu

MS220

Reconstructed Discontinuous Galerkin (RDG)Method for Multi-Material Flows on UnstructuredMeshes

In this work, we discuss extension of the ReconstructedDiscontinuous Galerkin method, developed previously forhigh-order spatio-temporal discretization of single-fluidflows on hybrid unstructured meshes, to fluid flow appli-cations with multi-material interfaces. The focus is placedon challenging issues of hierarchical WENO based limit-ing of discontinuous flow solutions, modal orthogonal basisfunctions, interface tracking using combination of volumetracking and level set methods, sharp treatment of inter-facial jump conditions, and combination with ArbitraryLagrangian-Eulerian (ALE) techniques.

Robert Nourgaliev, Sam SchofieldLLNLnourgaliev1@llnl.gov, schofield5@llnl.gov

MS220

An Eulerian Projection Method for Quasi-StaticElastoplasticity

A well-established numerical approach to solve the Navier–Stokes equations for incompressible fluids is Chorin’s pro-jection method, whereby the fluid velocity is explicitly up-dated, and then an elliptic problem for the pressure issolved, which is used to project the velocity field to main-tain the incompressibility constraint. In this talk, a math-ematical correspondence between Newtonian fluids in theincompressible limit and elastoplastic solids in the slow,quasi-static limit will be presented. Using this correspon-dence, a new fixed-grid, Eulerian numerical method forsimulating quasi-static elastoplastic solids will be devel-oped, whereby the stress is explicitly updated, and thenan elliptic problem for the velocity is solved, which is usedto project the stress to maintain the quasi-staticity con-straint. Numerical tests of the method will be given, anda number of correspondences between incompressible fluidmechanics and quasi-static elastoplasticity will be shown,creating possibilities for translating other numerical meth-ods between the two classes of physical problems.

Chris H. RycroftHarvard SEASchr@seas.harvard.edu

MS220

A Robust and Efficient Solver for Interfacial Multi-phase Flows on Unstructured Grids

We present a robust, accurate and efficient numericalframework for multiphase interfacial fluid dynamics on un-structured grids of arbitrary shapes of elements. The multi-moment finite volume method is used as a reliable andpractical solver for complex flows in presence of complexgeometries, which well balances numerical accuracy andcomputational cost. The free interfaces are computed bythe THINC scheme which is an accurate algebraic VOFmethod well-suited for unstructured grids.

Feng Xiao, Bin Xie, Sun Ziyao

Tokyo Institute of Technologyxiao@es.titech.ac.jp, xie.b.aa@m.titech.ac.jp,sun.z.ab@m.titech.ac.jp

MS220

A New Incompressibility Discretization for a Hy-brid Particle Mac Grid Representation with Sur-face Tension

We take a particle based approach to incompressible freesurface flow motivated by the fact that an explicit represen-tation of the interface geometry and internal deformationsgives precise feedback to an implicit solver for surface ten-sion. Methods that enforce incompressibility directly onthe particles are typically numerically inefficient comparedto those that utilize a background grid. However, back-ground grid discretizations suffer from inaccuracy near thefree surface where they do not properly capture the inter-face geometry. Therefore, our incompressibility discretiza-tion utilizes a particle based projection near the interfaceand a background MAC grid based projection for efficiencyin the vast interior of the liquid domain as well as a novelmethod for coupling these two disparate projections to-gether. We show that the overall coupled elliptic solver issecond order accurate, and remains second order accuratewhen used in conjunction with an appropriate temporaldiscretization for parabolic problems. A similar second or-der accurate discretization is derived when the MAC gridunknowns are located on faces (as opposed to cell centers)so that Navier-Stokes viscosity can be solved for implicitlyas well. Finally, we present a fully implicit approach to sur-face tension that is robust enough to achieve a steady statesolution in a single time step. Beyond stable implicit sur-face tension for our novel hybrid discretization, we demon-strate preliminary results for both standard front trackingand the particle level set method.

Wen Zheng, Bo ZhuStanford Universityzhw@stanford.edu, boolzhu@stanford.edu

Byungmoon KimAdobe Systems Inc.bmkim@adobe.com

Ronald FedkiwStanford Universityfedkiw@cs.stanford.edu

MS221

Applications of Distributed Methods to Non-Traditional Linear Systems

We investigate solutions to multi-dimensional linear sys-tems using single machine parallelization techniques. Thetri-color-channel radioisty method is used as a test casewhere the Jacobi method is applied to solve the radiositylinear equation. The multi-dimensionality of the system isrepresented through a structure of arrays and an array ofstructures, where the latter was found to be optimal. Workdistribution was implemented with CUDA and OpenMPwhere OpenMP threading was found to be optimal.

Julian GilyardDepartment of Computer ScienceWake Forest Universitygilyja12@wfu.edu

Thomas Stitt

178 CS15 Abstracts

Pennsylvania State UniversityDepartment of Electrical Engineeringtms54@psu.edu

Oluwapelumi Adenikinju, Joshua MasseyUniversity of Baltimore Maryland CountyDepartment of Computer Science and ElectricalEngineeringadenik2@umbc.edu, masseyj1@umbc.edu

MS221

Multigrid Solvers on Heterogeneous Architectures

HHG is a multigrid finite element solver that scales to amillion threads and that can solve in excess of a trillion(1012) unknowns in about a minute compute time. This isachieved by a careful co-design of grid structure, discretiza-tion, multigrid components, and the hybrid parallelization,all driven by a meticulous performance engineering process.HHG is now being extended to use GPU kernels and wewill report on the acceleration achieved.

Bjorn GmeinerComputer Science 10 - System SimulationFriedrich-Alexander-University Erlangen-Nuremberg,Germanybjoern.gmeiner@informatik.uni-erlangen.de

Daniel IuhaszFAU Erlangendanieliuhasz@gmail.com

Sebastian KuckukUniversitat Erlangen-Nurnbergkuckuk@i10.informatik.uni-erlangen.de

Markus Stuermer, Harald KoestlerUniversity of Erlangen-Nurembergmarkus.stuermer@informatik.uni-erlangen.de,harald.koestler@informatik.uni-erlangen.de

Ulrich J. RuedeUniversity of Erlangen-NurembergDepartment of Computer Science (Simulation)ulrich.ruede@fau.de

MS221

Speeding Up Sparse Triangular Solution on Multi-cores and GPUs

Multicores have complex memory hierarchy and increasedparallelism; GP-GPUs have tremendous amount of thread-based parallelism. We examine structures to expose theunderlying parallelism present in sparse-matrices to uti-lize multicore NUMA architecture and GPU. Specificallywe have developed CSR-k, a multilevel form of the tradi-tional compressed sparse row format that can be mappedto NUMA hierarchy. We formulate sparse triangular solvein terms of CSR-k with coloring and demonstrate how thisperform with CPU and GPU.

Humayun KabirDepartment of Computer Science and EngineeringThe Pennsylvania State Universityhzk134@psu.edu

Joshua D. BoothThe Pennsylvania State University

jdb5132@cse.psu.edu

Padma RaghavanThe Pennsylvania State Univ.Dept of Computer Science Engr.raghavan@cse.psu.edu

MS221

General SpMV and SpMM for AMG on GPUs

Scientific computations on sparse graphs mainly requiretwo computational patterns: processing of neighbors (gen-eral SpMV) and processing of all neighbors of a set ofnodes, often all neighbors of neighbors (general SpMM).These two patterns have different properties and require-ments for massively parallel implementations. The mainchallenge for the former is the different number of neigh-bors and indirection in access, while the latter has the dom-inating problems of index matching and varying outputsizes. Once these problems are solved in parallel an alge-braic multigrid solver (AMG) can be efficiently assembledon the GPU.

Robert StrzodkaNVIDIAstrzodka@mpi-inf.mpg.de

MS222

Industrial Mathematics Education at WorcesterPolytechnic Institute

Central to the philosophy of learning at Worcester Poly-technic Institute (WPI) is the principle of project-basedlearning. In the Department of Mathematical Sciencesthrough our Center for Industrial Mathematics and Statis-tics (CIMS) we have a strong focus on industry-sponsoredprojects for students. These projects are based on real-world problems that come directly from business or gov-ernment. Students work on these projects under theguidance of a faculty advisor and an industrial liaison.These projects are used in many settings, including se-nior projects for the Bachelor’s degree, Master’s degreeprojects, and summer Research Experience for Undergrad-uates (REU) projects. The focus of this talk will be aboutthe project process and its benefits to our WPI. Exampleswill be provided for illustration.

Marcel BlaisWorcester Polytechnic Institutemyblais@wpi.edu

MS222

PIC Math: Preparation for Industrial Careers inMathematical Sciences

PIC Math is a new program to prepare students in themathematical sciences to succeed in careers in business, in-dustry, and government (BIG). Funded by a 2 million dol-lar NSF grant, this program (a) helps students be aware oftheir choices for non-academic careers and opportunitiesfor internships, (b) helps faculty be more fully aware ofnon-academic career options for their students, make con-nections with people working for local BIG organizations,and develop internship opportunities for their students, (c)offers students the opportunity to have a research expe-rience related to real-world problems from BIG during aspring semester course, and (d) provide training to stu-dents and faculty in how to successfully work on problems

CS15 Abstracts 179

from BIG and develop the needed communications skills.To accomplish these objectives, we are developing a setof educational and informative videos, conducting summertraining workshops for faculty, and preparing materials fora semester-long course in which students learn skills andwork on research problems from BIG.

Michael DorffBrigham Young Universitymdorff@math.byu.edu

MS222

A New Curriculum in Applied and ComputationalMathematics

We present BYU’s new undergraduate curriculum in Ap-plied and Computational Mathematics. We highlight themain features of this program and discuss how we havebeen able to overcome numerous pedagogical, institutional,and cultural challenges, particularly as we’ve launched anapplied math degree in a predominantly pure math de-partment. We also show how we have been able to teacha number of advanced topics to undergraduates, and weshare our approach to recruiting and retaining students.

Jeffrey HumpherysBrigham Young Universityjeffh@math.byu.edu

MS222

A Student Perspective on Industrial Capstones atHarvey Mudd College

This talk will give a student’s perspective on HarveyMudd’s Mathematics Clinic program, in which seniors ma-joring in mathematics work in teams to complete industrialprojects. These projects give ample opportunity not onlyto hone mathematical skills, but also to practice effectivecollaboration, communication, and project management.As a student, the combination of faculty mentorship andstudent-driven work provides an engaging transition intoindustrial careers in mathematics.

Elizabeth SchofieldHarvey Mudd Collegeeschofield@g.hmc.edu

MS223

Multilevel Projection Method for Nonlinear Radia-tive Transfer Problems

This talk presents a deterministic computational methodfor solving coupled radiative transfer and energy balanceequations. It uses a multilevel system of equations con-sisting of the high-order radiative transfer equation, multi-group low-order quasidiffusion (LOQD) and grey LOQDequations defined for moments of the specific intensity. Theenergy balance equation is coupled to the grey LOQD equa-tions. Temperature is evaluated in a projected space ofsmallest dimensionality. We study discretization and lin-earization methods for coupled multiphysics equations.

Dmitriy Y. AnistratovNorth Carolina State Universityanistratov@ncsu.edu

MS223

A Multigrid Method for Two-Dimensional

Discrete-Ordinates Radiation-Transport Cal-culations

We present a multigrid method for discrete-ordinatesradiation-transport calculations, in particular for the Self-Adjoint Angular Flux (SAAF) form of the transport equa-tion in two-dimensional Cartesian geometry. For smooth-ing, we employ multistage cellwise block Jacobi iteration.The use of the SAAF equation allows straightforward de-termination of optimal multistage parameters for smallspatial cells; single-stage cellwise block Jacobi iteration isnot effective in this regime. On coarse grids, we apply aGalerkin discretization based on bilinear interpolation.

Jeffery D. Densmore, Daniel Gill, Justin PoundersBettis Atomic Power Laboratoryjeffery.densmore@unnpp.gov, daniel.gill@unnpp.gov,justin.pounders@unnpp.gov

MS223

A Conservative High-Order / Low-Order MethodBased Upon a Non-Conservative High-Order LeastSquares Sn Formulation

We have developed a high-order/low-order (HO/LO)scheme for neutronics eigenvalue calculations. The HOequation is a second-order least-squares form of the Sn

equations that contains scattering and fission sources fromthe LO equation. The LO equation is an angular momentequation in drift-diffusion form containing closure infor-mation from the HO equation. The HO equation generallyyields a non-conservative solution, while the LO equationalways yields a conservative solution adequate for reactoranalysis.

Jacob PetersonDepartment of Nuclear EngineeringTexas A&Mjrp314@neo.tamu.edu

Jim E. MorelTexas A&Mmorel@tamu.edu

MS223

Multilevel Monte Carlo Methods for Kinetic Equa-tions

The adaptation of the Multilevel Monte Carlo (MLMC)method - introduced by Giles for SDEs in finance - to ki-netic equations will be presented. MLMC introduces multi-ple time-steps and uses correlations between them for vari-ance reduction, thereby reducing the complexity of achiev-ing RMS error ε from O(ε−3) to O(ε−2). Application tothe spatially homogeneous Landau-Fokker-Planck model ofCoulomb collisions will be presented, as well as progress to-ward an MLMC-type scheme for the inhomogeneous Vlasovequation.

Lee F. RicketsonUCLAlfr224@cims.nyu.edu

MS224

Greedy Algorithms for Parametric EigenvalueProblems

Some greedy algorithms will be presented to compute thesolution of parametric eigenvalue problems. This work is

180 CS15 Abstracts

a continuation of the results presented in [1] where the au-thors presented algorithms for non-parametric eigenvalueproblems. The principle of the method is to compute areduced-order model for the solution of a parametric eigen-value problem as a sum of pure tensor-product functions,each term being computed in an iterative way which willbe precised in the talk. Some theoretical results on theconvergence of these algorithms will be presented and theirnumerical behaviour will be illustrated on some simple testcases. [1] E. Cancs, V. Ehrlacher and T. Lelivre. ”Greedyalgorithms for high-dimensional eigenvalue problems”, ac-cepted for publication in Constructive Approximation.

Virginie Ehrlacher

CERMICS - Ecole des Ponts Paristech / INRIAehrlachv@cermics.enpc.fr

MS224

Semi-Supervised Robust Matrix Completion forDynamic Subspace Estimation and Tracking

Recent SVD-free matrix factorization formulations haveenabled rank minimization for systems with millions ofrows and columns, paving the way for matrix completionfor extremely high dimensional data. In this talk, we dis-cuss a robust matrix completion and subspace tracking al-gorithm that uses factorized matrix decomposition witha pre-specified rank to detect and track a low rank sub-space from incomplete measurements and in the presenceof sparse noise. We demonstrate the performance of ouralgorithm for video background subtraction.

Hassan MansourMitsubishi Electric Research Laboratoriesmansour.hassan@gmail.com

MS224

Low-rank Approximation of Matrices and Tensorsfor Dynamical and Optimization Problems

In this talk we will consider several topics that are con-nected through the ideas of low-rank approximation. First,we propose a new method for the approximate solution ofthe Lyapunov equation. Second, we will discuss how thelow-rank methods help to solve reaction-diffusion equationswith time-dependent potential. Third, we will describe theideas of efficient multidimensional sampling via cross ap-proximation methods apply them to the problems of globaloptimization.

Ivan OseledetsInstitute of Numerical MathematicsRussian Academy of Sciences, Moscowivan.oseledets@gmail.com

Denis Kolesnikov, Mikhail LitsarevSkolkovo Institute of Science and Technologydenis.kolesnikov@skolkovotech.ru,m.litsarev@skolkovotech.ru

MS224

Preconditioned Riemannian Optimization for Low-Rank Tensor Equations

The solution of very large linear systems is a challengingtask often encountered as a core ingredient when solvingpartial differential equations on high-dimensional domains.In these cases, the degrees of freedom in the linear system

grow exponentially with the number of dimensions, makingclassic approaches unfeasible. Approximation of the solu-tion by low-rank tensor formats often allows us to avoidthis curse of dimensionality by exploiting the underlyingstructure of the linear operator. We propose a new algo-rithm that performs a preconditioned gradient method onthe manifold of tensors of fixed rank. In particular, wefocus on tensors represented in the Tensor Train (TT) /Matrix Product States (MPS) format. We demonstrate theflexibility of our algorithm by comparing different approx-imations of the Riemannian Hessian as preconditioners forthe gradient directions. Finally, we compare the efficiencyof our algorithm with other tensor-based approaches suchas the Alternating Linear Scheme (ALS). This is joint workwith Michael Steinlechner and Daniel Kressner (EPF Lau-sanne).

Bart VandereyckenDepartment of MathematicsPrinceton Universitybartv@math.princeton.edu

MS225

Accurate Adaptive Loops for Finite DeformationPlasticity in Albany

The Parallel Albany Adaptive Loop with Scorec software(PAALS) provides an automated framework for adap-tive finite element simulations on massively parallel ma-chines. Within the context of finite deformation plasticityin PAALS, remapping the material state during adapta-tion, maintaining high quality element shapes, and updat-ing the reference configuration are necessary to produce ac-curate solution results. Methods to handle these situationswill be discussed and results will be shown that emphasizethe interaction of these components.

Brian GranzowRensselaer Polytechnic Institutegranzb@rpi.edu

Glen HansenSandia National Laboratoriesgahanse@sandia.gov

Dan A. IbanezRensselaer Polytechnic InstituteSCORECdibanez@scorec.rpi.edu

Mark S. ShephardRensselaer Polytechnic InstituteScientific Computation Research Centershephard@rpi.edu

MS225

Massively Parallel Flow Simulation using PETSc

Implicit computational fluid dynamics solvers have recentlybeen shown to scale to the full machine at several of thelargest computer facilities using linear equation solvers thatwere coded to match the data structures of the equationdiscretization. In this work, we describe efforts to applyPETSCs broad class of preconditioners to flow simulationsat large core count to understand the tradeoff between im-proved preconditioners and the cost of the required addi-tional data structure translation.

Michel Rasquin, Benjamin Matthews

CS15 Abstracts 181

University of Colorado Bouldermichel.rasquin@colorado.edu,benjamin.a.matthews@colorado.edu

Cameron SmithScientific Computation Research CenterRensselaer Polytechnic Institutesmithc11@rpi.edu

Kenneth JansenUniversity of Colorado at Boulderkenneth.jansen@colorado.edu

MS225

Variational Multiscale Analysis of Stochastic Par-tial Differential Equations in Albany

We present the variational multiscale (VMS) method forstochastic PDEs to compute an accurate solution in acoarse physical and stochastic space while accounting forthe missing scales through a model term. The model termis based on an algebraic approximation of the fine-scalestochastic Green’s function and is rational in the randomvariables. We consider computationally efficient approxi-mations of this term and demonstrate their efficacy usingthe Albany code.

Onkar SahniRensselaer Polytechnic Institutesahni@rpi.edu

Jason Li, Jayanth Jagalur-MohanDepartment of Mechanical, Aerospace and NuclearEngineeringRPIlij14@rpi.edu, jagalj@rpi.edu

Assad OberaiDepartment of Mechanical, Aerospace and NuclearEngineeringRensselaer Polytechnic Instituteoberaa@rpi.edu

MS225

Albany: A Trilinos-based code for Ice Sheet Simu-lations and other Applications

Albany is a finite element application code that incorpo-rates capabilities through interoperable software compo-nents. By leveraging independently developed mathemat-ical libraries, Albany-based applications have ready accessto advanced technologies, spanning: discretizations, auto-matic differentiation, linear and nonlinear solvers, adjoint-based optimization and UQ, performance-portable kernels,mesh adaptivity, and dynamic load balancing. This strat-egy enables rapid development of sophisticated new codes,including the Albany/FELIX Ice Sheet application. Al-bany incorporates libraries from Trilinos, Dakota, andPUMI, some with FASTMath support.

Andrew SalingerCSRISandia National Labsagsalin@sandia.gov

Glen Hansen, Irina K. TezaurSandia National Laboratoriesgahanse@sandia.gov, ikalash@sandia.gov

Mauro PeregoCSRI Sandia National Laboratoriesmperego@fsu.edu

Ray S. TuminaroSandia National LaboratoriesComputational Mathematics and Algorithmsrstumin@sandia.gov

MS226

Fast Algorithms for Shape Analysis of Planar Ob-jects

Effective computational tools for shape analysis are neededin many areas of science and engineering. We address thisproblem and propose a fast iterative algorithm to com-pute the elastic geodesic distance between boundaries ofplanar objects. This algorithm is the most important com-ponent for data mining of shapes, and a fast algorithm isessential for large-scale shape analyses.The key to our algo-rithm is the decoupling of the optimization for the startingpoint and rotation and the optimization for the reparame-terization function in the distance formulation. Moreover,we develop a fast dynamic programming algorithm and anonlinear constrained optimization algorithm that work intandem to compute optimal reparameterizations fast.

Gunay DoganTheiss Research, NISTgunay.dogan@nist.gov

MS226

Deflation-based Domain Decomposition Methods

Domain decomposition methods are widely used in ap-plied mathematics and regarded as highly scalable algo-rithms that can be seen as specific cases of multigrid meth-ods. Projection operators are one of the essential tools forachieving scalability: they are used for building deflationpreconditioners. A C++ framework will be presented ac-companied by theoretical results to show how effective itcan be to solve problems arising from Darcy’s law, elastic-ity, or Helmholtz equation.

Pierre JolivetLaboratoire Jacques-Louis Lionsjolivet@ann.jussieu.fr

Frederic NatafLaboratoire J.L. Lionsnataf@ann.jussieu.fr

Christophe Prud’hommeUniversity of StrasbourgFranceprudhomme@unistra.fr

MS226

Multiscale Methods for Networks

Networks are a widely used type of abstraction for com-plex data. Optimization of different quantitative objectiveson networks often plays a crucial role in network science,not only when a practical solution is needed, but also fora general understanding of structural and statistical fea-tures of networks. We present multiscale approaches fortwo problems: optimal response to epidemics, and networkgeneration. Both approaches are inspired by AMG scheme

182 CS15 Abstracts

reinforced by the algebraic distance connectivity strength.

Ilya SafroSchool of ComputingClemson Universityisafro@g.clemson.edu

MS226

The Auxiliary Space Solvers and Its Applications

We talk about the mathematically optimal multigridsolvers for general unstructured grids which are robustand easy to use in practice based on the methodologyof Fast Auxiliary Space Preconditioning. a new parallelunsmoothed aggregation algebraic multigrid (UA-AMG)method has also been developed based the idea of FASP.It provides (nearly) optimal load balance and predictablecommunication patterns factors that make our new algo-rithm suitable for parallel computing.

Lu WangPenn State Universitywang l@math.psu.edu

MS227

Robust Algorithms for Periodic Problems andEvaluation of Layer Potentials

I overview methods developed recently by our group forsolving time-harmonic acoustics and Maxwell scatteringfrom media with 103 layers, doubly-periodic obstacles in3D (with efficiency for axisymmetric obstacles), and Stokesflow in periodic pipes and doubly-periodic porous media.In each case we use only the free-space Greens function,an auxiliary field, and a small linear system, to circumventthe traditional but problematic periodic Greens function.We also develop quadrature components such as 3D QBXand close evaluation for Stokes.

Alex H. BarnettDepartment of MathematicsDartmouth Collegeahb@math.dartmouth.edu

Shravan VeerapaneniDepartment of MathematicsUniversity of Michiganshravan@umich.edu

Adrianna GillmanDartmouth CollegeDepartment of Mathematicsadrianna.gillman@rice.edu

Min Hyung ChoDepartment of MathematicsDartmouth Collegemin.h.cho@dartmouth.edu

Lin Zhao, Yuxiang LiuDartmouth Collegelin.zhao.gr@dartmouth.edu,yuxiang.liu.gr@dartmouth.edu

Bowei WuUniversity of Michiganbobbielf2@gmail.com

Gary MarpleDepartment of MathematicsUniversity of Michigangmarple@umich.edu

Leslie GreengardCourant InstituteNew York Universitygreengar@cims.nyu.edu

MS227

Adaptive Boundary Element Methods

One particular strength of the boundary element method isthat it allows for a high-order pointwise approximation ofthe solution of the related partial differential equation viathe representation formula. We propose an adaptive mesh-refining algorithm and discuss recent results on its quasi-optimal convergence behavior with respect to the point er-ror in the representation formula. Numerical examples forthe weakly-singular integral equations for the Laplacianunderline our theoretical findings.

Michael Feischl, Thomas Fuhrer, Gregor Ganter,Alexander Haberl, Dirk PraetoriusVienna University of Technologymichael.feischl@tuwien.ac.at,thomas.fuehrer@tuwien.ac.at,gregor.gantner@tuwien.ac.at,e0925297@student.tuwien.ac.at,dirk.praetorius@tuwien.ac.at

MS227

Fast Algorithms for the Evaluation of Layer Poten-tials using ‘Quadrature by Expansion’

Quadrature by Expansion, or ‘QBX’, is a systematic, high-order approach to singular quadrature that applies to layerpotential integrals with general kernels on curves and sur-faces. Being based on a scheme for close evaluation due toBarnett, the scheme provides a unified evaluation capabil-ity for layer potentials. This talk discusses algorithmic op-tions for using QBX within a variant of the Fast MultipoleMethod. A method is presented that preserves accuracy,generality and close evaluation capability while only re-quiring a relatively modest increase in computational costin comparison to a point-to-point FMM. In addition, anoptionally GPU-accelerated set of open-source software li-braries is discussed that implements the proposed method.

Andreas KloecknerDepartment of Computer ScienceUniversity of Illinois at Urbana-Champaignandreask@illinois.edu

MS227

Title Not Available at Time of Publication

Abstract not available at time of publication.

Denis ZorinComputer Science DepartmentCourant Institute, New York University

CS15 Abstracts 183

dzorin@cs.nyu.edu

MS228

Compact-Reconstruction WENO on Non-uniformMeshes

Compact-Reconstruction WENO (CRWENO) schemes usesolution-dependent combinations of compact schemes toproduce a higher-order scheme that is non-oscillatory andhas the superior spectral resolution of compact schemes.Previous work on these schemes has used uniform gridsexclusively. In this talk we present a generalization of thefifth-order CRWENO scheme to non-uniform meshes in onespace dimension, with some results concerning the effectsof unequal spacing on the scheme’s accuracy and spectralresolution.

Kilian CooleyUniversity of Marylandkcooley2@math.umd.edu

James BaederDepartment of Aerospace EngineeringUniversity of Marylandbaeder@umd.edu

MS228

Superconvergence Properties of DiscontinuousGalerkin Methods Based on Upwind-Biased Fluxesfor Linear Hyperbolic Equations

Superconvergence properties of discontinuous Galerkin(DG) methods using purely upwind fluxes under the as-sumptions of periodic boundary conditions and a uniformmesh for solving linear hyperbolic equations with smoothsolutions have been studied through various approaches:pointwise a posteriori spacial discretization error estimates;spectral analyses based on the Fourier approach; and thesmoothness increasing accuracy conserving (SIAC) filteredsolution. We analyze via these approaches DG methodsusing upwind-biased fluxes, illustrating the discussion withnumerical experiments.

Daniel FreanUniversity of East Angliad.frean@uea.ac.uk

MS228

A Compact-Reconstruction WENO Scheme withSemi-Implicit Time Integration

Weighted, nonlinear compact finite difference schemes arewell suited for flows with a large range of length scales suchas atmospheric flows. Semi-implicit time integration meth-ods allow for efficient solutions by treating the stiff compo-nents of the hyperbolic flux implicitly. We propose a high-order finite-difference algorithm for atmospheric simula-tions based on the CRWENO scheme and implicit-explicittime stepping. The performance and scalability of the al-gorithm are evaluated for benchmark flow problems.

Debojyoti GhoshMathematics and Computer Science DivisionArgonne National Laboratoryghosh@mcs.anl.gov

Emil M. ConstantinescuArgonne National Laboratory

Mathematics and Computer Science Divisionemconsta@mcs.anl.gov

MS229

Parallel Preconditioning for Time-DependentPDE-Constrained Optimization

All-at-once schemes aim to solve all time-steps of time-dependent PDE-constrained optimization problems in onecoupled computation, leading to exceedingly large linearsystems requiring efficient iterative methods. We presenta new block diagonal preconditioner which is both opti-mal with respect to the mesh parameter and parallelizableover time, thus can provide significant speed-up. We willpresent numerical results to demonstrate the effectivenessof this preconditioner.

Eleanor McDonaldUniversity of Oxfordeleanor.mcdonald@new.ox.ac.uk

Andy WathenOxford University, UKwathen@maths.ox.ac.uk

MS229

Preconditioning of Active-Set Newton Methods forPDE-Constrained Optimal Control Problems

We address the problem of preconditioning saddle point lin-ear systems arising in the solution of PDE-constrained opti-mal control problems via active-set Newton methods, withcontrol and (regularized) state constraints. We present twopreconditioners based on a full block matrix factorizationof the Schur complement of the Jacobians matrices wherethe active-set blocks are merged into the constraint blocks.The robustness of the new preconditioners is discussed andexhaustive numerical experiments are presented.

Margherita PorcelliDipartimento di MatematicaUniversita di Bolognamargherita.porcelli@unibo.it

Valeria Simoncini, Mattia TaniUniversita’ di Bolognavaleria.simoncini@unibo.it, mattia.tani2@unibo.it

MS229

HPC Methods for Structured Inverse Modeling inDiffusive Processes

In this talk we present a method which combines high per-formance computing and large scale applications with anoptimized, inverse shape identification procedure. We in-troduce a limited memory BFGS approach for optimizingthe shape of the distribution of a jumping permeability indiffusive flow processes. These techniques are utilized tofit a model of the human skin to data measurements andnot only estimate the permeability coefficients but also theshape of the cells.

Martin SiebenbornUniversity of Triersiebenborn@uni-trier.de

Volker H. SchulzUniversity of Trier

184 CS15 Abstracts

Department of MathematicsVolker.Schulz@uni-trier.de

MS229

Nonstandard Sobolev Spaces for PreconditioningMixed Methods

In mixed methods for elliptic boundary value problemsauxiliary variables are used to reformulate the involveddifferential equation as a system of differential equationsof lower order. These methods can often be written asPDE-constrained optimization problems, whose analysismotivates the introduction of nonstandard Sobolev spacesfor the auxiliary variables and leads to efficient solutiontechniques. The approach is exemplified for the Hellan-Herrmann-Johnson method applied to biharmonic bound-ary value problems.

Walter ZulehnerUniversity of Linz, Austriazulehner@numa.uni-linz.ac.at

Wolfgang KrendlJohannes Kepler University Linz, Austriawolfgang.krendl@dk-compmath.jku.at

MS230

Strengthening the Hurricane Wave and Surge Fore-cast Guidance provided to Coastal Communities inNorth Carolina

North Carolina is sensitive to hurricane waves, storm surgeand flooding. A computational modeling system is uti-lized operationally to provide daily forecast guidance forcoastal waves and inundation (http://nc-cera.renci.org/).This guidance has been expanded beyond Web-based de-livery to include additional formats that are targeted tothe needs of users within the state, are representative ofthe guidance at high levels of resolution, and are portableto widely-used geographic information systems.

Rosemary CyriacNorth Carolina State UniversityDept. of Civil, Construction and EnvironmentalEngineeringrcyriac@ncsu.edu

J. Casey DietrichUniversity of Texas at Austinjcdietrich@ncsu.edu

Jason FlemingSeahorse Coastal ConsultingMorehead City, NCjason.fleming@seahorsecoastal.com

Brian BlantonUniversity of North Carolina at Chapel HillRenaissance Computing Institutebblanton@renci.org

Rick LuettichUniversity of North Carolina - Moorehead Cityrick luettich@unc.edu

MS230

Three-Dimensional Coupled Wind-Wave and Co-

hesive Sediment Transport Modeling in South SanFrancisco Bay

Abstract not available at time of publication.

Oliver FringerEnvironmental Fluid Mechanics LaboratoryStanford Universityfringer@stanford.edu

MS230

Discontinuous Galerkin Methods for SpectralWave/Circulation Modeling

On large geographic scales, waves are represented in a spec-tral sense via the action balance equation. We present acomputational spectral wave model developed using dis-continuous Galerkin (DG) methods. DG methods allowfor the use of unstructured meshes and adaptive, higher-order approximations, which we show leads to increasedaccuracy and efficiency. We loosely couple the new DGspectral wave model to the DG-Shallow Water EquationModel (DG-SWEM), an existing circulation model.

Jessica MeixnerUniversity of Notre Damejdmeixner@gmail.com

MS230

Computational Modeling of Storm Surge in Galve-ston Bay

Abstract not available at time of publication.

Jennifer ProftUniversity of Texas at Austinjennifer@ices.utexas.edu

MS231

Simulating Coupled Pressure-Temperature Equa-tions for Trace Gas Sensors Using FEniCS andPETSc

Trace gas sensors are currently used in many applicationsfrom leak detection to national security and may some dayhelp with disease diagnosis. These sensors are modelledby a coupled system of complex elliptic partial differen-tial equations for pressure and temperature. Solutions areapproximated using the finite element method which re-quires the development of custom block preconditioners.Finite element solutions are approximated using FEniCSand PETSc4py.

Brian W. BrennanBaylor Universityb brennan@baylor.edu

MS231

Mesh-Independent Convergence for PDE-Constrained Optimisation Solvers in Dolfin-Adjoint

A key feature of dolfin-adjoint is its high-level frameworkfor solving PDE-constrained optimisation problems usingthe finite element environment FEniCS. In this talk we dis-cuss the mesh-independent convergence of the optimisationframework. This is achieved by formulating standard opti-misation algorithms in a Hilbert space setting. We discuss

CS15 Abstracts 185

the implementation, show its effectiveness and compare itto preconditioning approaches. Thanks to the high-levelproblem formulation in FEniCS the resulting frameworkrequires minimal user input, is fully parallel and scales tolarge problems.

Simon W. Funke, Magne NordaasCenter for Biomedical ComputingSimula Research Laboratorysimon@simula.no, magneano@simula.no

MS231

Spectral/HP Element Modelling in Nektar++

In this talk we will highlight the high-level aspects ofthe Nektar++ high order finite element framework, whichenables rapid development of high-performance parallelsolvers. Using a straightforward linear PDE as an illus-trative example, we will demonstrate how the library canbe utilised at a variety of levels to fit the requirementsof the end-user, and how simulation parameters such asthe time-stepping scheme can be changed without detailedtechnical knowledge of the underlying methods.

David Moxey, Chris Cantwell, Spencer SherwinImperial College Londond.moxey@imperial.ac.uk, c.cantwell@imperial.ac.uk,s.sherwin@imperial.ac.uk

Mike KirbyUniversity of UtahSchool of Computingkirby@cs.utah.edu

MS231

Supporting Modern HPC Hardware in the DUNEFramework

Upcoming exa-scale computers will exhibit multiple lev-els of concurrency. Specialized implementations, exploit-ing all levels of parallelism, can gain a significant part ofthe peak performance. For high flexibility the C++ frame-work DUNE [Bastian et.al., 2008] defines generic interface,which allow various different implementations. The EXA-DUNE project follows this approach to enable all levels ofconcurrency for general DUNE applications. We presentrecent results and discuss implications on the interface de-sign.

Christian Engwer, Fahlke JorritINAM, University of Munsterchristian.engwer@uni-muenster.de,jorrit.fahlke@uni-muenster.de

Steffen MuthingHeidelberg Universitysteffen.muething@iwr.uni-heidelberg.de

MS232

Transitioning from Game Design to Simulation Us-ing Agent-Based Modeling

The objective of the Scalable Game Design project is tocreate a pipeline of people to work in computer-relatedfields by introducing them to game design. Hopefully, theywill then transfer their interests and skills from game de-sign to science simulation. Over the past five years severalthousand students have participated in the project, with

encouraging results. AgentSheets and AgentCubes are vi-sual programming agent-based modeling applications thatare ideally suited to this projects goals.

Fred GluckAgentSheets, Inc.fred.gluck@comcast.net

MS232

Applying Run-Modify-Build Templates for Agent-Based Models

Students can grow in competence and confidence in mod-eling and simulation through well-scaffolded templates ofworking models. Instead of typing code or building struc-tures, students can learn any given syntax in the contextof real models, focusing on learning the science and im-proving the model. This is especially true for agent modelsthat require more detailed descriptions of behavior. Exam-ples of complex model templates across the computationalsciences and for different tools will be shown.

Robert M. PanoffPresident and Executive DirectorShodorrpanoff@shodor.org

MS232

Teaching Freshman Science Using Agent-BasedComputational Laboratories

With improved computational abilities and explosion ofamounts of data, scientists routinely implement computa-tion to test hypotheses and guide their research. We havedeveloped a course that employs computational approachesto investigate scientific questions. Students explore scienceconcepts, and using computational tools and algorithmicthinking, implement the scientific method to understandthe natural world. Satisfying a science requirement, thecourse is designed so faculty from any science or computerscience department can teach it.

George W. ShifletWofford Collegeshifletgw@wofford.edu

Angela B. ShifletMcCalla Professor of Math. & CS, Dir. of ComputationalSci.Wofford Collegeshifletab@wofford.edu

MS232

NetLogo in the Secondary Life Science Classroom

In response to the adoption of new middle school sciencetextbooks which incorporated NetLogo models as well asother visualization software, NetLogo models were modi-fied or created for use in middle school life science and en-vironmental lessons as well as in high school biology class-rooms. Large group professional development, individualinstructional coaching and classroom co-teaching were usedto help teachers and students interact with the simulationssuccessfully.

Charlotte M. TroutWCPS-Retired

186 CS15 Abstracts

scitrout@icloud.com

MS233

Microstructure for Free Surface Flows

Numerical simulations of turbulent mixing in the LargeEddy Simulation regime are nonunique, with the selectionof solution microstructure regulated by subgrid turbulencemodels. Validation, ie comparison to experiments, is thenessential. We give examples of successfully validated FrontTrecking simulations with extrapolation to flows outsideof the experimental range. Appllcation to the selection ofatomic vs. chunk mix for an inertial confinement fusioncontext will be given.

James G. GlimmStony Brook UniversityBrookhaven National Laboratoryglimm@ams.sunysb.edu or glimm@bnl.gov

MS233

Volume-Preserving Adaptive Moment-of-FluidMethod for Interface Tracking

We have developed a method to preserve the volume of acell when the vertices of the cell move freely in a divergence-free velocity field. An optimization procedure is proposedto minimize the total variation of the node positions ofthe vertices after they are advanced according to the ve-locity field. A matrix-free Newton Krylov method is usedto solve the nonlinear system generated by the optimiza-tion. The method has been applied to the multi-materialmoment-of-mluid interface tracking method with adaptivemesh refinement. Examples are provided to demonstratethe effectiveness of our numerical algorithm.

Shengtai LiLos Alamos National Laboratorysli@lanl.gov

Hyung T. AhnUniversity of Ulsanhtahn@ulsan.ac.kr

Mikhail ShashkovLos Alamos National Laboratoryshashkov@lanl.gov

MS233

A Fictitious Domain Method with a Hybrid CellModel for Simulating Motion of Cells in Fluid Flow

In this work, we develop a hybrid model to representmembranes of biological cells and use the distributed-Lagrange multiplier/fictitious-domain (DLM/FD) formu-lation for simulating the fluid/cell interactions. The hybridmodel representing the cellular structure consists of a con-tinuum representation of the lipid bilayer, from which thebending force is calculated through energetic variationalapproach, a discrete cytoskeleton model utilizing the worm-like chain to represent network filament, and area/volumeconstraints. For our computational scheme, a formallysecond-order accurate fractional step scheme is employedto decouple the entire system into three sub-systems: afluid problem, a solid problem and a Lagrange multiplierproblem. Numerical results compare favorably with pre-viously reported numerical and experimental results, andshow that our method is suited to the simulation of the

cell motion in flow. This work is in collaboration with W.Hao, C. Liu and G. Lin.

Zhiliang XuUniversity of Notre Damezhiliangxu@nd.edu

MS233

Dissipation and Dispersion Errors of DiscontinuousGalerkin Method and Its Application to Level SetEquations

The discontinuous Galerkin (DG) method is known to pro-vide high resolution properties, especially when applyingafter long time run. In this talk, we consider analysing theerror behaviour of the DG method for linear hyperbolicequations. Through Fourier analysis we observe, with P2quadratic polynomial approximations, the dissipation er-ror is on the order of 5 and the dispersion error is on theorder of 6. The part of the error that grows linearly in timeis on the order of 6. When solving interface problems ina complex incompressible flow, the DG method is shownto dramatically improve the mass conservation propertyof the level set method. Numerical examples demonstratethe high order accuracy of the scheme and the high resolu-tion property especially when the interface undergoes largetopological changes.

Jue YanDept. of Math.Iowa State Universityjyan@iastate.edu

MS234

Massively Parallel GW Calculations for Currentand Next-generation HPC

The traditional GW-Bethe-Salpeter (BSE) approach has,in practice, been prohibitively expensive on systems withlarge numbers of atoms. We show that through a com-bination of methodological and algorithmic improvements,the standard GW-BSE approach can be applied to sys-tems with thousands of atoms. We will discuss the mas-sively parallel GW-BSE implementation in the Berke-leyGW package (on-top of common DFT packages) includ-ing the importance of hybrid MPI-OpenMP parallelism,parallel IO and library performance. We will discuss opti-mization strategies for and performance on many-core ar-chitectures.

Jack DeslippeNational Energy Research Scientific Computing Centerjrdeslippe@lbl.gov

MS234

Recent Progress on Quantum Mechanics Embed-ding Theory

Abstract not available at time of publication.

Chen HuangTheoretical Division, T-1Los Alamos National Laboratorychuang3@fsu.edu

MS234

Towards Predictive Modeling of Correlation Effects

CS15 Abstracts 187

in Many-electron Systems

In this presentation we will discuss the development of scal-able and unique computational capabilities for modelingquasi-degenerate systems using implementations of multi-reference coupled-cluster (MRCC) methods in NWChem.We will discuss novel parallel algorithms for several MRCCmethodologies, which are capable of taking advantage ofexisting peta-scale architectures. In this context, the emer-gence of the heterogeneous computer architectures offers aunique chance to advance accurate yet expensive MRCCformalisms. We will also outline the recent development ofcoupled-cluster Green function formalism geared towardsefficient inclusion of higher-order correlation effects.

Karol KowalskiPacific Northwest National Laboratorykarol.kowalski@pnnl.gov

MS234

A Parallel Orbital-Updating Approach for Elec-tronic Structure Calculations Based on SingularityDecompositions

In this presentation, we will introduce an orbital-basedparallelization algorithm for electronic structure calcula-tions and demonstrate the efficiency of our algorithm bynumerical experiments. This algorithm is based on ourunderstanding of the single-particle approximation equa-tions of independent particles that move in an effectivepotential and a singularity decomposition of the effectivepotential. With this algorithm, the solution to the single-particle equation can be reduced to some solutions of sev-eral independent linear algebraic systems and a small scalealgebraic eigenvalue problem. This presentation is basedon some joint works with Xiaoying Dai, Xingao Gong, andXin Zhang.

Aihui ZhouChinese Academy of Sciencesazhou@lsec.cc.ac.cn

MS235

Algorithmic Adaptations for Scalable CommunityDetection on the Tilera Many-Core Architecture

As power constraints and data movement costs become sig-nificant barriers for high-end computing, the Tilera many-core architecture offers a low-power platform exhibitingkey characteristics of future systems: a large number ofsimple cores, a sophisticated network-on-chip, and fine-grained control over memory locality. We implementeda graph community detection application using platform-aware memory layouts and scheduling techniques resultingin speedups of up to 46x on the TileGX36 and comparableresult quality and performance to x86 platforms.

Daniel Chavarria, Howard Lu, Mahantesh HalappanavarPacific Northwest National Laboratorydaniel.chavarria@pnl.gov, luhowardmark@hotmail.com,hala@pnnl.gov

Ananth KalyanaramanAssociate ProfessorSchool of EECS, Washington State University

ananth@eecs.wsu.edu

MS235

Using Performance Tools to Assist Porting to NewPlatforms

Performance tool play a critical role in porting applicationsto new platforms. They not only enable identifying hotspots; the first targets for acceleration, but can also showthe context of these hot spots. Tracing and profilingtools can be used in combination to provide differentresolution of detail and amounts of runtime perturba-tion. Tools like Score-P can capture all parallel activity(MPI/OpenMP/pthreads/CUDA/OpenCL/OpenACC)and display it to the user using analysis engines likeVampir.

Guido JuckelandTU-Dresdenguido.juckeland@tu-dresden.de

MS235

Algorithmic Selection, Autotuning, and Schedulingfor Accelerator-Based Codes for Numerical LinearAlgebra

Often, a rewrite of the scientific software is unsustainablein the long run as the complexity increases to respond tothe more parallel and heterogeneous hardware. In this talk,I will give practical perspective on how algorithmic selec-tion, software autotuning at installation time, and variousforms of dynamic runtime scheduling for multicore systemswith accelerators can alleviate the aforementioned prob-lems in the context of widely used numerical linear algebralibraries.

Piotr LuszczekDepartment of Electrical Engineering and ComputerScienceUniversity of Tennessee, Knoxvilleluszczek@eecs.utk.edu

MS235

Toward Heterogeneous Memory Systems for HPC

Compute nodes equipped with a variety of memory tech-nologies such as scratchpad memory, on-chip 3D-stackedmemory, or NVRAM-based memory, apart from traditionalDRAM, are already a reality. Careful use of the differentmemory subsystems is mandatory in order to exploit thepotential of such supercomputers. I will present our viewon upcoming heterogeneous memory systems, which com-prises exposing the different memory subsystems as first-class citizens to efficiently exploit their capabilities.

Antonio J. PenaArgonne National Labapenya@mcs.anl.gov

MS236

Reduced Order Models for Patient-SpecificHaemodynamics of Coronary Artery BypassGrafts

In this talk we present a POD-Galerkin reduced ordermodel to simulate the haemodynamics of coronary arterybypass grafts. Clinically relevant physical (inlet flow rates)and geometrical (stenoses severity, anastomoses geometry)

188 CS15 Abstracts

quantities are considered in a parametrized setting for un-steady incompressible Navier-Stokes equations. The pro-posed ROM is applied to some patient-specific cases. Apresentation of a comparison, with respect to such param-eters, and a clinical discussion of the resulting flow patternsfollows.

Francesco BallarinPolitecnico di Milano, Italyfrancesco.ballarin@polimi.it

Elena FaggianoPolitecnico di MilanoItalyelena.faggiano@polimi.it

Sonia IppolitoLuigi Sacco HospitalMilan, Italyippolito.sonia@hsacco.it

Andrea ManzoniEPFL, MATHICSE-CMCSSwitzerlandandrea.manzoni@epfl.ch

Alfio QuarteroniEcole Pol. Fed. de LausanneAlfio.Quarteroni@epfl.ch

Gianluigi RozzaSISSA, International School for Advanced StudiesTrieste, Italygianluigi.rozza@sissa.it

Roberto ScrofaniLuigi Sacco HospitalMilan, Italyscrofani.roberto@hsacco.it

MS236

pyMOR - A New Model Order Reduction SoftwareFramework

Over the past years, projection-based model order re-duction (MOR) techniques, such as the reduced basismethod (RB) ([1] and references therein), have becomewell-established tools for efficient numerical solution ofpartial differential equations. However despite the factthat RB-methods are very generic in nature, most soft-ware solutions still provide only ad-hoc implementationswhich are tailor-made for specific application problems andare tied to a given software ecosystem. In this talk wepresent pyMOR [2], a new open source library for build-ing MOR-applications with the Python programming lan-guage. pyMOR’s main focus lies on the easy application ofRB-methods to parameterized partial differential equationssolved by external high-dimensional discretization pack-ages. We give a brief overview of pyMOR’s main com-ponents and highlight the design philosophy and choicesthat allow us to arrive at a set of completely generic re-duction algorithms which can be readily incorporated withany external solver connected to pyMOR via its lightweightoperator and vector interfaces. As a result of this abstrac-tion, well-proven MOR-algorithms can be easily appliedto new real-world problems. At the same time, differentreduction algorithms can be compared for a given prob-lem without modification of the high-dimensional solver.We conclude our presentation by illustrating these benefits

by the example of our current work on the reduction ofmicroscale lithium-ion battery models. [1] B. Haasdonk,M. Ohlberger, Reduced basis method for finite volume ap-proximations of parametrized linear evolution equations,M2AN Math. Model. Numer. Anal., 42 (2008), 277–302.[2] R. Milk, S. Rave, F. Schindler, pyMOR - Model OrderReduction with Python, http://pymor.org.

Rene MilkUniversity of Muensterrene.milk@uni-muenster.de

Mario OhlbergerUniversitat MunsterInstitut fur Numerische und Angewandte Mathematikmario.ohlberger@uni-muenster.de

Stephan RaveUniversity of Muensterstephan.rave@wwu.de

Felix SchindlerWWUfelix.schindler@wwu.de

MS236

Reduced Basis Methods for Option Pricing

We present a reduced basis method for pricing Europeanand American options based on the Black-Scholes and He-ston model. To tackle each model numerically, we formu-late the problem in terms of a time dependent variationalequality or inequality and propose a method that combinesPOD-Greedy and Angle-Greedy procedures for the con-struction of the reduced spaces. In addition, we obtain aposteriori error estimators. Numerical examples illustratethe efficiency of our approach.

Julien SalomonCEREMADE, Universite Paris-Dauphinejulien.salomon@dauphine.fr

Olena BurkovskaTechnical University of Munichburkovsk@ma.tum.de

Bernard HaasdonkUniversity of Stuttgarthaasdonk@mathematik.uni-stuttgart.de

Barbara WohlmuthTechnical University of Munichbarbara.wohlmuth@ma.tum.de

MS236

Adaptivity and Reduced Basis Methods

Usually, the computations in a Reduced Basis Method(RBM) are split into an offline and an online phase. In theoffline phase, expensive computations are used to constructa Reduced Basis in terms of snapshots of a detailed model.This has a number of consequences that are also possiblecriticisms on the RBM itself: (1) The snapshots need tobased upon the same discretization (at least for parts ofthe parameter range); (2) If the problem itself is challeng-ing, offline costs may be significant; (3) The separationinto offline and online phase hides the overall complexityof the problem. At an extreme, one could pre-compute

CS15 Abstracts 189

‘everything’ offline and just pick the right data online. Onthe other hand, several adaptive methods are known andproven to be asymptotically optimal for a wide class of op-erator equations. Asymptotically optimal means that therate of convergence is comparable to a best-possible bench-mark and the computational cost is linear in the requirednumber of degrees of freedom. This is the motivation toconsider the combination of adaptive numerical methodsand the RBM. We show some consequences of using adap-tive computations both for the snapshot generation as wellas the evaluation of standard RB error estimates. The talkis based upon joint work with Kristina Steih (Ulm).

Karsten UrbanInstitute of Numerical Mathematics, University of Ulmkarsten.urban@uni-ulm.de

MS237

An Accelerated Domain Decomposition Methodfor Time Dependent Problems

We consider the time integration of the system of ODEswhich results from the semi-discretization of PDEs. Thesolution components are assumed to evolve on differenttime scales and hence some sort of multi-rate time integra-tion method which allows different time steps for differentcomponents may be suitable. Here we consider two algo-rithms for such problems: a multi-rate Schwarz Waveformrelaxation hybrid algorithm and a multi-rate acceleratedSchwarz Waveform relaxation method.

Ronald HaynesMemorial University of NewfoundlandSt. John’s, NL, Canadarhaynes74@gmail.com

MS237

Developing a Custom Time Integrator for the Non-linear Schrodinger Equation for An Application inParaxial Laser Propagation

I will report on the construction of a temporal inte-gration scheme designed to be used with a higher-orderfinite-difference spatial approximation to the nonlinearSchrodinger equation with perfectly matched layer bound-ary conditions. The temporal method is based on a semi-implicit spectral deferred corrections approach coupledwith an alternating direction implicit (ADI) approximationto the (linear) implicit terms. The accuracy and efficiencyof methods up to tenth-order in both time and space will bepresented as well as some preliminary results on space-timeparallelization of the method.

Michael MinionStanford Universitymlminion@lbl.gov

MS237

Spatially Partitioned Embedded Runge-KuttaMethods

We study spatially partitioned embedded Runge-Kuttaschemes for partial differential equations (PDEs), in whicheach of the component schemes is applied over a differentpart of the spatial domain. Such methods may be conve-nient for problems in which the smoothness of the solutionor the magnitudes of the PDE coefficients vary strongly inspace. We focus on embedded partitioned methods as theyoffer greater efficiency and avoid the order reduction that

may occur in non-embedded schemes. We demonstratethat the lack of conservation in partitioned schemes canlead to non physical effects and propose conservative addi-tive schemes based on partitioning the fluxes rather thanthe ordinary differential equations. A variety of schemesare presented, including an embedded pair suitable forthe time evolution of fifth-order weighted non-oscillatory(WENO) spatial discretizations. Numerical experimentsare provided.

Steven RuuthMathematicsSimon Fraser Universitysruuth@sfu.ca

David I. KetchesonCEMSE DivisionKing Abdullah University of Science & Technologydavid.ketcheson@kaust.edu.sa

Colin B. MacdonaldOxford Universitymacdonald@maths.ox.ac.uk

MS237

A Massively Parallel Solver for the IncompressibleNavier–Stokes Equations

In 2011, Guermond and Minev proposed a massively par-allelizable directional splitting method for the time dis-cretization of the incompressible Navier–Stokes equations.It was shown to scale well in a distributed memory environ-ment of up to 1024 CPUs. We modified this method to takeadvantage of the high computational throughput affordedby (multiple) GPUs as well as the efficiency of variable timesteps. We demonstrate that the modified method exhibitssubstantial performance gains over the original.

Raymond J. SpiteriUniversity of Saskatchewan, CanadaDepartment of Computer Sciencespiteri@cs.usask.ca

MS238

Coherence Motivated Sampling of PolynomialChaos Expansions

We investigate solution recovery, particularly regardingmethods for sampling basis functions associated with Her-mite and Legendre Polynomial Chaos Expansions. Recentresults have identified interesting quantities related to thebasis functions and their sampling which are computable,and analytically fruitful. Through these parameters we an-alyze asymptotically motivated samplings, and constructsampling methods with statistical optimality. We demon-strate these methods on examples motivated from Uncer-tainty Quantification.

Jerrad HamptonUniversity of Colorado, Boulderjerrad.hampton@colorado.edu

Alireza DoostanDepartment of Aerospace Engineering SciencesUniversity of Colorado, Boulder

190 CS15 Abstracts

Alireza.Doostan@Colorado.EDU

MS238

Sparse Solutions to Large-Scale Nonlinear Subsur-face Flow Inverse Problems

We present sparse inversion formulations for nonlinear sub-surface flow model calibration problems. By promotingsparsity, the inversion is transformed into a feature selec-tion problem that is flexible and robust against prior uncer-tainty. Specifically, in addition to effective low-rank repre-sentation, the formulation allows for discriminating againstalternative plausible prior geologic scenarios based on non-linear multiphase flow data from scattered well locations.Using several case studies, we demonstrate the advantagesof sparse nonlinear inversion for geoscience application.

Benham JafarpourViterbi School of EngineeringUniversity of Southern Californiabehnam.jafarpour@usc.edu

Reza KhaninezhadElectrical EngineeringUniversity of Southern Californiam.khaninezhad@usc.edu

MS238

An Efficient Method for the Computation of theStochastic Galerkin Projections by Means of Ten-sor Format Representations

The stationary diffusion problem with an uncertain per-meability coefficient is solvedin a low-rank tensor repre-sentation without changes of the available deterministiccode. The presented uncertainty is modeled by a randomfield, which is discretized by KLE as well as by PCE. Itwas shown in previous works [Espig et al 2012, 2013] un-der which conditions the stochastic Galerkin operator canbe approximated/represented in a low-rank tensor format.The obtained symmetrical and positive defined linear sys-tem is solved by the new iterative method. The iterationmatrix as well as the whole computations are done alsoin that low-rank tensor format. The choice of the tensorformat is not crucial here. The computational cost andstorage (independent on the tested tensor formats) are lin-ear in the stochastic dimension.

Alexander LitvinenkoSRI-UQ Center, King Abdullah University of Science andTechnalexander.litvinenko@kaust.edu.sa

Mike EspigMax Planck Institute for Mathematics in the Sciencesmike.espig@alopax.de

Matthies HERMANN G.Instiute of Scientific ComputingTU Braunschweigh.matthies@tu-bs.de

MS238

Tensor Approximation Methods for StochasticProblems

Spectral stochastic methods have gained wide acceptanceas a tool for efficient modelling of uncertain stochastic sys-

tems. The advantage of those methods is that they pro-vide not only statistics, but give a direct representation ofthe measure of the solution as a so-called surrogate model,which can be used for very fast sampling. Especially at-tractive for elliptic stochastic partial differential equationsis the stochastic Galerkin method, since it preserves essen-tial properties of the differential operator. One drawbackof the method is, however, that it requires huge amounts ofmemory, as the solution is represented in a tensor productspace of spatial and stochastic basis functions. Differentapproaches have been investigated to reduce the memoryrequirements, for example, model reduction techniques us-ing subspace iterations to reduce the approximation spaceor methods of approximating the solution from successiverank-1 updates. See more in my dissertation [1]. [1] ElmarK. Zander, Tensor Approximation Methods for StochasticProblems, Dissertation, TU Braunschweig, 2013.

Elmar ZanderTU BraunschweigInst. of Scientific Computinge.zander@tu-bs.de

MS239

Novel Priors and Algorithms for 4d Tracking andClassification of Cells

In biomedical imaging efficient reconstruction and trackingmethods play a fundamental role. Particularly in cell bi-ology and medical tomography innovative spatio-temporalimaging models are of strongly growing interest. The aimof this talk is to highlight novel priors and related convexoptimization for reconstruction and flow quantification in4D image sequences. Motivated by the success of L1 andhigher-order (e.g. TGV) regularization for static imag-ing we will focus on spatio-temporal priors for the optimaltransportation of cells.

Christoph BruneDepartment of Applied MathematicsUniversity of Twentec.brune@utwente.nl

MS239

Parameter Estimation for Malignant Brain Tumors

Determining patient specific tumor parameters is impor-tant in choosing optimal treatment plans. We present aninverse problem formulation to approximate the parame-ters of interest using PDE-constrained optimization algo-rithms. The choice of the optimization method is impor-tant as solving this problem has a high computational cost.We will present a reduced space formulation, novel precon-ditioners to speed up the solution process, and numericalexperiments on a synthetic dataset for preliminary evalua-tion of the method.

Amir GholaminejadPhD Student, Institute for Computational Engineeringand Sciences, University of Texas at Austini.amirgh@gmail.com

George BirosUniversity of Texas at Austinbiros@ices.utexas.edu

MS239

Incorporating Uncertainty in MR Images of

CS15 Abstracts 191

Glioblastoma when Leveraging Models to InterpretTherapeutic Efficacy

There is a lack of response metrics that can quickly and ac-curately predict the therapeutic efficacy for glioblastoma.Recently, a mathematical model of glioma growth has beenused to define a response metric based on patient-specificparameters of proliferation and invasion calibrated frompre-treatment imaging which was shown to be prognosticfor overall survival. This talk will focus on how data un-certainty affects the calibrated parameters, the responsemetric, and the implications for clinical translation.

Andrea Hawkins-DaarudDepartment of Neurological SurgeryNorthwestern Universityandrea.hawkins-daarud@northwestern.edu

Kristin R. SwansonNorthwestern Universitykristin.swanson@northwestern.edu

MS239

Platform-independent Description of Image Regis-tration Algorithms

In the last years real-time imaging and more complex mod-els for the various imaging applications like image registra-tion became feasible mostly because of the progress madein parallel computer architectures like found in GPUs andmodern multi-core CPUs. However, the implementationeffort increases, if one wants to achieve good performance.A solution to this problem is to formulate the image regis-tration algorithms in an abstract way in a domain-specificlanguage (DSL) and then automatically generate efficientC++ or CUDA code. A multi-layered approach is sketchedthat allows users to describe applications in a natural wayfrom the mathematical model down to the program speci-fication.

Harald KoestlerUniversity of Erlangen-Nurembergharald.koestler@informatik.uni-erlangen.de

MS240

Computational Complexity of Stochastic Galerkinand Collocation Methods for PDEs with RandomCoefficients

We will present a rigorous cost metric, used to comparethe computational complexity of a general class of stochas-tic Galerkin methods and stochastic collocation methods,when solving high-dimensional stochastic PDEs. Our ap-proach allows us to calculate the cost of preconditioningboth the Galerkin and collocation systems, as well as ac-count for the sparsity of the Galerkin projection. The-oretical complexity estimates will also be presented andvalidated with use of several computational examples.

Nick DexterUniversity of Tennesseendexter@utk.edu

Clayton G. Webster, Guannan ZhangOak Ridge National Laboratory

webstercg@ornl.gov, zhangg@ornl.gov

MS240

QoI Basis Adaptation

We demonstrate the efficiency and scope of the basis adap-tation methodology developed for Gaussian polynomialchaos. The approach is based on adapting the basis inL2 by applying an isometry to its Gaussian base. We dis-cuss error estimates associated with this approach, and thethe concept of an optimal isometry. We also present imple-mentation details and applications to large scale problemsfrom across science and engineering. We also explore theimportance of specific quantities of interest to the adapta-tion process, and extend the approach to situations definedby multiple quantities of interest.

Roger GhanemUniversity of Southern CaliforniaAerospace and Mechanical Engineering and CivilEngineeringghanem@usc.edu

Kenny ChowdharySandia National Laboratorieskennychowdhary@gmail.com

Habib N. NajmSandia National LaboratoriesLivermore, CA, USAhnnajm@sandia.gov

MS240

Numerical Methods for SPDEs with Levy JumpProcesses SPDES: Stochastic and DeterministicApproaches

We present numerical results on SPDEs with multiple Levyjump processes of various depen- dence structures by gPC(stochastic approach) and by joint PDF from the general-ized Fokker- Planck equations for spatial modes to decom-pose the SPDEs into SODEs (deterministic ap- proach).As examples, we solve SPDEs with TaS jump processes,with tempered fractional PDEs as joint density functions.We will demonstrate that we largely improve the accuracyand efficiency of the traditional MC method!

Mengdi Zhengapplied math, brown universitymengdi zheng@brown.edu

George E. KarniadakisBrown UniversityDivision of Applied Mathematicsgeorge karniadakis@brown.edu

MS240

Optimal Least-Squares Projection: Applications toUq

In this talk, we discuss the problem of approximating amultivariate function by discrete least-squares projectiononto a general polynomial space, using a random chosensub-grid of the tensor grid of Gaussian points. The inde-pendent variables of the function are assumed to be randomvariables, and thus, the framework provides a non-intrusiveway to construct the generalized polynomial chaos expan-sions, stemming from the motivating application of Un-

192 CS15 Abstracts

certainty Quantification (UQ). We prove the stability andan optimal convergence estimate, provided the number ofpoints scales linearly (up to a logarithmic factor) with thedimension of the polynomial space. The framework in-cludes both the bounded measures such as the uniformand the Chebyshev measure, and the unbounded measureswhich include the Gaussian measure. Several numericalexamples are given to confirm the theoretical results.

Tao ZhouInstitute of Computational Mathematics, AMSSChinese Academy of Sciencestzhou@lsec.cc.ac.cn

Akil NarayanUniversity of Massachusetts Dartmouthakil.narayan@umassd.edu

Dongbin XiuUniversity of Utahdongbin.xiu@utah.edu

MS241

N-Body Algorithms for Matrices with Decay: Mul-tiplication, Projection, Inverse Factorization &Fock-Exchange

We report on several fast algorithms for operations ondense matrices with decay. Based on the SpAMM algo-rithm [arXiv:1203.1692 and 1403.7458] for matrix-matrixmultiplication, we develop methods for spectral projectionand inverse factorization with reduced, O(N) complexityas well as error control in accordance with estimates. Wefurther demonstrate the generalization of these methodsto the higher dimensional problem of Fock-exchange, in-volving multi-level multipole approximation with nestedSpAMM contraction.

Matt ChallacombeLos Alamos National LaboratoryTheoretical DivisionMChalla@lanl.gov

Nicolas BockLos Alamos National Laboratorynicolasbock@freeon.org

Terry HautUniversity of Colorado, Boulderterry.haut@colorado.edu

MS241

Linear-Cost Storage and Computation with KernelMatrices

Kernel matrices embrace a rich structure that enables moreefficient storage and computation than does a usual densematrix. The FMM and tree code methods are prominentexamples exploiting such a structure: far-field low-rankinteraction. In this talk, we lay the fundamental O(n)data structure in the context of linear algebra and presentO(n) algorithms for performing matrix operations, includ-ing matrix-vector multiplication, matrix inversion, and de-terminant calculation. We demonstrate numerical stability,linear scaling, and applications in statistical data analysis.

Jie ChenArgonne National Laboratory

jiechen@mcs.anl.gov

MS241

Parallel Randomized Structured MultifrontalMethod for Sparse Direct Solutions

We present a fast parallel direct solver for general sparsematrices based on a fully structured randomized multi-frontal method. Distributed memory is used. A sequenceof innovative parallel strategies are designed for random-ized compression, hierarchical structures, and structuredmultifrontal solution. Multilevel parallelism is built upontwo hierarchical tree layers. This gives a significant newdirection for designing fast scalable sparse direct solvers.

Zixing Xin, Jianlin XiaDepartment of MathematicsPurdue Universityzxin@purdue.edu, xiaj@math.purdue.edu

MS242

Fluctuating Hydrodynamics Methods for Elec-trokinetics and Capillary Electrophoresis ofCharged Colloids

Motivated by problems in the design and operation of re-cent microfluidic and nanofluidic devices, we present fluctu-ating hydrodynamic methods for confined electrokinetics.We investigate the capillary electrophoresis of charged col-loids. We show that the colloid counter-ion layers exhibitdeviations from Poisson-Boltzmann theory and interestingphenomena arising from discrete ion effects, hydrodynamicinteractions, and overlap with ion layers near the channelwalls.

Paul J. AtzbergerUniversity of California-Santa Barbaraatzberg@math.ucsb.edu

MS242

Mesoscale Models for Molecular Solvation: FunnyBusiness at the Solute-Solvent Interface

Electrostatic interactions between biomolecules (proteins)and the surrounding aqueous environment are crucial forcorrect function. Continuum electrostatic models are sig-nificantly faster than atomistic molecular-dynamics sim-ulations, but trade off realism: e.g., at protein surfaces,solvent is not a bulk material. Although multiscale mod-els resembling gradient-elasticity theories improve accuracysomewhat, non-standard boundary conditions capture rele-vant interfacial-solvent effects much better. These findingsmotivate the development of rigorous methods for obtain-ing boundary conditions between multiscale materials.

Jaydeep BardhanNortheastern Universityj.bardhan@neu.edu

Matthew G. KnepleyUniversity of Chicagoknepley@ci.uchicago.edu

MS242

Mesoscopic Modeling of Temperature-dependentProperties in Non-isothermal Fluid Systems

We develop an energy conserved dissipative particle

CS15 Abstracts 193

dynamics model to capture the correct temperature-dependent properties of fluids. We demonstrate that theproposed model can predict correctly the temperature de-pendence of the diffusivity, viscosity and thermal conduc-tivity of liquid water, which is consistent with available ex-perimental data of water at various temperatures. Subse-quently, this mesoscopic model is applied to investigationsof the nonisothermal hydrodynamic flows and the phasetransition of thermoresponsive polymers.

Zhen LiBrown UniversityBrown UniversityZhen Li@brown.edu

Yu-Hang Tang, Bruce CaswellBrown Universityyuhang tang@brown.edu, bruce caswell@brown.edu

George E. KarniadakisDivision of Applied MathematicsBrown Universitygeorge karniadakis@brown.edu

MS243

Ensemble Kalman Filters Without Tuning forLarge Applications

Ensemble Kalman filters are widely used for large geophys-ical data assimilation problems but generally require signif-icant tuning of inflation and localization to produce goodresults in the presence of sampling error from small ensem-bles. Methods to reduce the tuning required by estimatingand correcting for errors in ensemble sample covariancesare presented. The feasibility of treating ensemble filtersas a black box for general applications is discussed.

Jeffrey AndersonNational Center for Atmospheric ResearchInstitute for Math Applied to Geophysicsjla@ucar.edu

MS243

Orthogonal Transformations for the EnsembleKalman Filter

Data assimilation of complex physical systems is common-place in many areas of science in order to predict phenom-ena of interest. In this talk we use orthogonal transforma-tions in the ensemble Kalman filter to capture the domi-nant correlations within a model and reduce noise. A seriesof assimilation experiments are presented for a ionosphere-thermosphere model using real observational data. Theresults show a reduction in forecast error using orthogonaltransformation compared with assimilation without trans-formation.

Humberto C. GodinezLos Alamos National LaboratoryApplied Mathematics and Plasma Physicshgodinez@lanl.gov

Earl LawrenceLos Alamos National Laboratoryearl@lanl.gov

Dave HigdonLos Alamos National LaboratoryStatistical Sciences

dhigdon@lanl.gov

MS243

Multi-Scale Data Assimilation for Fine-ResolutionModels

The commonly used data assimilation algorithms are basedon optimal estimation theory, in which error covariance isof fundamental importance. It is shown that the stan-dard optimal estimation algorithm is inherently ineffectivewhen it is applied to fine resolution models, and the inef-fectiveness arises from its filtering nature. We propose amulti-scale data assimilation algorithm, in which the costfunction is decomposed for a set of distinct spatial scales.Data assimilation is implemented sequentially from largeto fine scales. Results are presented to demonstrate thealgorithm.

Zhijin LiJet Propulsion LaboratoryCalifornia Institute of Technologyzhijin@jpl.nasa.gov

MS243

Unified Ensemble-Variational Data AssimilationSystem

In this presentation we present a development of a unifiedensemble-variational data assimilation system that com-bines best properties of ensemble and variational DA meth-ods, as well as filter and smoother methodologies. Themain idea is to create a practical, yet theoretically ad-vanced system for general data assimilation applications.The new system has a complete feedback in terms of un-certainties and optimal states. Recent progress and resultswill be presented.

Milija ZupanskiCooperative Institute for Research in the AtmosphereColorado State UniversityMilija.Zupanski@colostate.edu

MS244

An Adaptive Augmented Lagrangian Method forLarge-Scale Constrained Optimization

We present augmented Lagrangian (AL) methods for solv-ing nonlinear optimization problems. AL methods are ad-vantageous as they can be implemented matrix-free, andso are scalable for solving large scale problems. However,they often suffer from poor initial choices of the penaltyparameter and Lagrange multipliers. Our methods over-come this disadvantage by incorporating dynamic updatesfor the penalty parameter while minimizing the AL func-tion. Numerical experiments with LANCELOT softwareillustrate the benefits of our proposed methods.

Frank E. CurtisIndustrial and Systems EngineeringLehigh Universityfrank.e.curtis@gmail.com

Nicholas I.M. GouldRutherford Appleton LaboratoryUKnick.gould@stfc.ac.uk

Hao Jiang

194 CS15 Abstracts

Department of Applied Mathematics and StatisticsJohns Hopkins Universityhjiang13@jhu.edu

Daniel RobinsonNorthwestern Universitydaniel.p.robinson@gmail.com

MS244

A Data-Driven Approach to PDE-Constrained Op-timization Under Uncertainty

I present an approach for incorporating data in PDE-constrained optimization. First, I develop a data-drivendiscretization for probability measures of uncertain PDEparameters and prove rigorous error bounds. I then for-mulate a robust optimization problem that accounts forthe uncertainty in the estimated probability measures. Fi-nally, I propose an algorithm to solve the resulting semidis-cretized minimax problem. This algorithm employs trustregions and permits inexact derivative computations. Iconclude with preliminary numerical results.

Drew P. KouriOptimization and Uncertainty QuantificationSandia National Laboratoriesdpkouri@sandia.gov

MS244

PDE-Constrained Optimization Under Uncer-tainty for Convection-Diffusion-Reaction Systems

We present an overview of algorithms for large-scale opti-mization of partial differential equations (PDEs) with un-certain coefficients. Our algorithms minimize risk-basedobjective functions using sparse-grid discretizations. Wedemonstrate our approach on large scale source inversionfor multi-spieces convection-diffusion-reaction dynamics.

Bart G. Van Bloemen WaandersSandia National Laboratoriesbartv@sandia.gov

Harriet LiMITkameeko@mit.edu

Drew P. KouriOptimization and Uncertainty QuantificationSandia National Laboratoriesdpkouri@sandia.gov

Denis RidzalSandia National Laboratoriesdridzal@sandia.gov

MS244

Inexact Primal-Dual Interior Point Filter Method

Abstract not available at time of publication.

Victor ZavalaArgonne National Laboratoryvzavala@mcs.anl.gov

MS245

A Finite-Volume Based Formulation for Viscoelas-

tic Two-Phase Flows

We present computational schemes for the study of vis-coelastic two-phase flows. A new formulation that trans-forms the constitutive equation for viscoelastic stress into aconservative form is developed and combined with a finite-volume discretization of the Navier-Stokes equations. Thenumerical method is based on a volume of fluid algorithmfor tracking the interface. Numerical examples are pre-sented to demonstrate the higher order accuracy of devel-oped schemes.

Shahriar AfkhamiDepartment of Mathematical SciencesNew Jersey Institute of Technologyshahriar.afkhami@njit.edu

MS245

A Moment-of-Fluid Method for Computing Solu-tions to Multi-Phase Flows

The Moment-of-Fluid (MOF) reconstruction algorithm isvolume preserving, generalizable to arbitrary number ofmaterials, and uses only information local to the compu-tational cell. These properties enable one to develop amultiphase flow algorithm that accurately computes com-pressible or incompressible multiphase flows consisting ofany number of materials without the aid of Riemann solversand no acoustic time step constraint required. An outlineof the MOF multiphase flow algorithm will be explained,and example multiphase flow simulations with applicationsin energy and medicine will be shown.

Mark SussmanDepartment of MathematicsFlorida State Universitysussman@math.fsu.edu

MS245

A Time Splitting Projection Scheme for Compress-ible Two-Phase Flows : Application to the Inter-action of Bubbles and Droplets with UltrasoundWaves

We will present a time-splitting scheme for pressure andvelocity in order to account with surface tension effects inthe framework of projection method for compressible two-phase flows. Several benchmarks, based on the Rayleigh-Plesset theory (volume oscillation of a bubble), will be pre-sented in order to demonstrate the efficiency of this newtime-splitting scheme in comparisons with others existingmethods (HLLC solver, Turkel preconditionning) in situa-tions involving a low Mach number.

Sebastien TanguyUniversite de Toulousesebastien.tanguy@imft.fr

MS245

Fourth-Order Interface Tracking and CurvatureEstimation for An Arbitrary Number of Materialsin Two Dimensions

We present the iPAM method as the first fourth-order in-terface tracking method in two dimensions, prove its con-vergence rates by mapping and adjusting regular semi-algebraic sets, and propose fourth-order algorithms for es-timating the unit normal and the curvature. Exploiting al-gorithms and theories in computational geometry, general

CS15 Abstracts 195

topology, and algebraic geometry, iPAM directly applies toboth structured and unstructured grids, both incompress-ible and compressible flows, and an arbitrary number ofphases without any algorithmic modifications.

Qinghai Zhang, Aaron L. FogelsonUniversity of Utahqinghai@math.utah.edu, fogelson@math.utah.edu

MS246

Large-Scale 3D Electromagnetic Imaging Using Ju-lia

In this talk we discuss the implementation of large scaleelectromagnetic inverse problems with multiple sources andfrequency using Julia. We discuss how asynchronous opti-mization and regularization techniques can be implementedin an efficient way and propose a paradigm for general datarich inverse problems that invoke with nontrivial simula-tions.

Eldad HaberDepartment of MathematicsThe University of British Columbiahaber@math.ubc.ca

MS246

JuMP: Algebraic Modeling of Optimization Prob-lems in Julia

We present JuMP, an open-source algebraic modeling lan-guage for mathematical optimization (cf. AMPL, GAMS,CVX, YALMIP). We describe how JuMP takes advantageof Julia’s advanced technical features like just-in-time com-pilation and metaprogramming to achieve competitive per-formance with commercial tools, including a reimaginedimplementation of Automatic Differentiation (AD) tech-niques for computing exact Hessian matrices for nonlinearoptimization. JuMP supports a number of commercial andopen-source solvers for linear, mixed-integer, quadratic,conic, and nonlinear optimization.

Miles LubinOperations Research CenterMassachusetts Institute of Technologymlubin@mit.edu

Iain DunningOperations Research CenterMassachusetts Insitute of Technologyidunning@mit.edu

Joey HuchetteOperations Research CenterMassachusetts Institute of Technologyhuchette@mit.edu

MS246

Distributed and Parallel Computing for Pde Con-strained Optimization in Julia

This talk presents a Julia framework for the solution oflarge-scale PDE constrained optimization problems. Itis based on a discretize-then-optimize approach, uses a(projected) Gauss-Newton method, and provides interfacesstate-of-the-art linear solvers (both explicit and iterative).The framework uses Julia’s potential for parallel and dis-tributed computation. Being written in a dynamic lan-

guage, it is easily extendable and yet fast as will be outlinedfor a large electromagnetic test problem.

Lars RuthottoDepartment of Mathematics and Computer ScienceEmory Universitylruthotto@emory.edu

MS246

An Extensible Test Matrix Collection for Julia

Matrix Depot is an open source project aiming to provide arich collection of test matrices. This software can be easilyextended and therefore facilitate exchange of matrices be-tween researchers in numerical linear algebra community.We will describe the design and implementation of thissoftware. Matrix Depot supports a variety of languages,including Fortran and Python, but in this talk, we willfocus on how to use Matrix Depot in Julia.

Weijian Zhang, Nicholas HighamSchool of MathematicsThe University of Manchesterweijian.zhang@postgrad.manchester.ac.uk,nick.higham@manchester.ac.uk

MS247

Meet Informally with the CSE15 Co-Chairs andSeveral Invited Speakers

Meet Informally with the CSE15 Co-Chairs and SeveralInvited Speakers.

Hans De SterckUniversity of WaterlooApplied Mathematicshdesterck@uwaterloo.ca

Christopher JohnsonUniversity of UtahDepartment of Computer Sciencecrj@sci.utah.edu

Lois Curfman McInnesMathematics and Computer Science DivisionArgonne National Laboratorycurfman@mcs.anl.gov

MS248

Approximation of the Boltzmann Equation withthe Method of Moments for Low Speed Gas Flow

Gas flows in micro-electro-mechanical systems (MEMS) areusually at a low speed and in the transition regime. TheNavier-Stokes-Fourier equations are no longer adequate tocapture the non-equilibrium phenomena in MEMS and theBoltzmann equation is necessary to describe the flow fieldcorrectly. However, the full solution of the Boltzmannequation is complicated and expensive. Approximation ofthe Boltzmann equation with the moment method is intro-duced and the accuracy and validity range of the methodwill be discussed.

Xiaojun GuScientific Computing DepartmentSTFC Daresbury Laboratoryxiaojun.gu@stfc.ac.uk

196 CS15 Abstracts

David Emerson, Jianping MengScientific Computing Department STFC DaresburyLaboratorydavid.emerson@stfc.ac.uk, jianping.meng@stfc.ac.uk

MS248

A Framework on Moment Model Reduction for Ki-netic Equation

Model reduction of kinetic equation turns a high dimen-sional problem to a low dimensional quasi-linear system,which not only provides further understanding of the prob-lem, but also essentially improves the efficiency of the nu-merical simulation. As a quasi-linear system with Cauchydata, the well-posedness of the model deduced is requiredto be hyperbolic. In the existed models, some of themare hyperbolic, and some of them may be regularized tobe hyperbolic, while there are seldom progress on the elsemodels. Studies indicate that the hyperbolicity is possiblyrelated with H-theorem, preserving of certain physics, etc.In this talk, I will reveal the underlying reason why someexisted models are hyperbolic and the others are not, andhow the hyperbolic regularization works. It is pointed outthat the hyperbolicity is not related to H-theorem, con-servation, etc, at all. The even fascinating point is, withonly routine calculation, symmetric hyperbolic models canalways be deduced with any ansatz for generic kinetic equa-tion by the framework we proposed. By this framework,existing models are re-presented and brand new models arediscovered. Even if the study is restricted in the scope ofthe classical Grad’s 13-moment system, a new model withglobal hyperbolicity can be deduced.

Ruo LiSchool of Mathematical SciencePeking Universityrli@math.pku.edu.cn

MS248

Numerical Solution of a Fourteen-Moment Closurefor Non-equilibrium Gases

Recently, a hyperbolic fourteen-moment closure for theBoltzmann equation from gaskinetic theory has been pro-posed that is based on an interpolation technique betweenlocal equilibrium and realizability boundaries using en-tropy maximization as a guide. This closure has provento be very accurate for moderately non-equilibrium flows,however a singularity in the closing flux presents challengesto numerical solution. This talk discusses the handling ofthese challenges and presents solutions to canonical flowproblems.

James McDonald, Amir BaradaranDepartment of Mechanical EngineeringUniversity of Ottawajames.mcdonald@uottawa.ca, abara061@uottawa.ca

Boone TensudaUniversity of TorontoInstitute for Aerospace Studiesboone.tensuda@mail.utoronto.ca

Clinton P. GrothUniversity of Toronto Institute for Aerospace StudiesCanada

groth@utias.utoronto.ca

MS248

Theoretical and Computational Investigations ofthe Non-linear Coupled Constitutive Relations(NCCR)

In a classical framework, the Navier-Stokes-Fourier (NSF)equations can be obtained via linear uncoupled thermo-dynamic flux-force relations which guarantee the non-negativity of the entropy production. It is commonly ac-cepted that the conventional thermodynamic descriptionis only valid when the Knudsen number is sufficientlysmall. Here, we will show that the range of validity ofthe NSF equations may be extended further by consider-ing the nonlinear coupling between thermodynamic fluxesand forces. The resulted Nonlinear Coupled ConstitutiveRelations (NCCR) can capture many interesting rarefac-tion effects, such as Knudsen paradox, transpiration flows,thermal stress, heat flux without temperature gradients,etc. We will also derive a set of phenomenological bound-ary conditions for NCCR which respect the second law ofthermodynamics. We will explore some boundary valueproblems by comparing the NCCR and the DSMC simula-tions.

Anirudh Singh RanaGNU Building 404 Room 305Dept: ACML, GNU, South Koreaanirudh@uvic.ca

Rho Shin MyongSchool of Mechanical and Aerospace EngineeringGyeongsang National University, South Koreamyong@gnu.ac.kr

MS249

Exploiting Active Subspaces for Nonlinear Pro-gramming

The active subspace of function f : Rm → R is the spanof n < m vectors constructed so that input perturba-tions along the active subspace change f more on aver-age than input perturbations orthogonal to the active sub-space. Such directions may help optimize complex nonlin-ear functions of several variables.

Paul ConstantineColorado School of MinesApplied Mathematics and Statisticspconstan@mines.edu

David F. GleichPurdue Universitydgleich@purdue.edu

MS249

Using Stochastic Optimization Methods for thePolyadic Decomposition of Large-Scale Tensors

Large-scale higher-order datasets pose many challenges interms of computational and storage costs. As these tensorsmay not fit into the computer’s memory, most canonicalpolyadic decomposition algorithms cannot be used. In thistalk, we propose to use stochastic optimization methods,as these kind of algorithms require only a small amount ofentries in memory in every iteration. The power of thesemethods will be illustrated on both synthetic and real life

CS15 Abstracts 197

data.

Nico VervlietDepartment of Electrical Engineering (ESAT)KU Leuvennico.vervliet@esat.kuleuven.be

Lieven De LathauwerKatholieke Universiteit Leuvenlieven.delathauwer@kuleuven-kulak.be

MS249

Non-Convex Low-Rank Matrix and Tensor Recov-ery

In this talk, I will present algorithms for solving non-convex low-rank matrix and also tensor recovery models.Global convergence to stationary point or in terms of first-order optimality condition is given. Although we cannotguarantee global optimal solutions, numerical experimentsdemonstrate that our algorithms can give more faithful so-lutions than those for solving convex models on both syn-thetic and real-world data.

Yangyang XuRice Universityyangyang.xu@rice.edu

MS249

Towards an Optimal Scalability in Computing Ex-treme Eigenpairs of Large Matrices

SVD and/or eigen-decomposition are fundamental prob-lems in scientific and engineering computing. For large-scale data and on modern computers, classic algorithmshave encountered scalability bottlenecks. In this work,we study two block methods that are based on, respec-tively, the Gauss-Newton and the power methods. Wepresent theoretical and numerical results to demonstratetheir promises. In particular, we show that the proposedmulti-power method can frequently achieve an optimalscalability.

Yin ZhangRice UniversityComputational and Applied Mathematicsyzhang@rice.edu

Zaiwen WenPeking UniversityBeijing International Center For Mathematical Researchwendouble@gmail.com

Xin LiuAcademy of Mathematics and Systems ScienceChinese Academy of Sciencesliuxin@lsec.cc.ac.cn

MS250

Towards a Recursive Graph Bipartitioning Algo-rithm for Well Balanced Domain Decomposition

In the context of hybrid sparse linear parallel solvers basedon Schur complement approaches, getting a domain decom-position tool leading to a good balancing of both internaland interface nodes for all the domains is a critical pointfor parallel efficiency. In this presentation, we introduceseveral variations of the existing algorithms in the multi-

level Scotch partitioner that take into account these mul-tiple criteria. We illustrate the results on graphs used fornumerical scientific applications.

Astrid CasadeiINRIA Bordeaux Sud-Ouest & CNRS (LaBRI UMR5800)Bordeaux Universityastrid.casadei@gmail.com

Pierre RametLaBRI, Univ Bordeaux, France701868

Jean RomanINRIAJean.Roman@inria.fr

MS250

Handling Multiple Communication Metrics for Hy-pergraph Partitioning

We investigate connectivity-based partitioning methods,specifically hypergraph partitioning-based methods, fortask mapping problem in order to efficiently parallelize thecommunicating tasks. A good partitioning method shoulddivide the load among the processors as evenly as possibleand minimize the inter-processor communication overhead.The total communication volume is the most popular com-munication overhead metric which is reduced by the ex-isting state-of-the-art hypergraph partitioners. However,other metrics such as the total number of messages, themaximum amount of data transferred by a processor, ora combination of them are equally, if not more, impor-tant. We propose a directed hypergraph model to capturemultiple communication metrics and a one-phase approachwhere all the communication cost metrics can be effectivelyminimized in a multi-objective setting. We wrapped theproposed model and methods in a multi-objective, multi-level hypergraph partitioner called UMPa. The partitionertakes various prioritized communication metrics into ac-count, and optimizes all of them together. Compared tothe state-of-the-art methods which only minimize the to-tal communication volume, we show on a large number ofproblem instances that UMPa produces better partitionsin terms of several communication metrics.

Mehmet DeveciThe Ohio State Universitymdeveci@bmi.osu.edu

Kamer KayaThe Ohio State UniversityDepartment of Biomedical Informaticskamer@bmi.osu.edu

Bora UcarLIP, ENS-Lyon, France.Bora.Ucar@ens-lyon.fr

Umit V. CatalyurekThe Ohio State UniversityDepartment of Biomedical Informaticsumit@bmi.osu.edu

MS250

Complex Objective Partitioning of Small-World

198 CS15 Abstracts

Networks Using Label Propagation

We present PULP, a parallel and memory-efficient graphpartitioning method specifically designed to partition low-diameter networks with skewed degree distributions. Par-titioning determines the in-memory layout of a graph,which affects locality, inter-task load balance, communi-cation time, and overall memory utilization of graph ana-lytics. A novel feature of our method PULP (Partitioningusing Label Propagation) is that it optimizes for multipleobjective metrics simultaneously, while satisfying multiplegraph constraints. Using our method, we are able to parti-tion a web crawl with billions of edges on a single computeserver in under a minute. For a collection of test graphs,we show that PULP uses 8-39x less memory than state-of-the-art partitioners, and is up to 14.5x faster, on average,than alternate approaches (with 16-way parallelism). Wealso achieve better partitioning quality results for both themulti-constraint as well as multi-objective scenarios.

George Slota, Kamesh MadduriPennsylvania State Universitygslota@psu.edu, madduri@cse.psu.edu

Siva RajamanickamSandia National Laboratoriessrajama@sandia.gov

MS250

Load Balancing Multiscale Simulations

Adaptive procedures and associated load-balancing opera-tions are requirements for a high-performance parallel sim-ulations to take full advantage of computational resources.Multiscale simulations introduce additional sensitivitiesand costs into adaptive processes which are not present inthe standard single-program multiple-data (SIMD) parallelmodel used by the overwhelming majority of single-scalecodes. The Adaptive Multiscale Simulation Infrastruc-ture (AMSI) supports the implementation and executionof general multiscale simulations, and provides methods forglobal and local scale-sensitive load balancing and adaptiveoperations. An implementation of a multiscale simulationof soft-tissue mechanics using AMSI is discussed along withits usage of the scale-sensitive adaptive and load-balancingprocedures provided by AMSI.

William R. Tobin, Daniel FovargueRensselaer Polytechnic Institutetobinw2@rpi.edu, dfovargue@gmail.com

Mark S. ShephardRensselaer Polytechnic InstituteScientific Computation Research Centershephard@rpi.edu

MS251

High-Order Accurate Numerical Methods for El-liptic and Parabolic Interface Models

Designing numerical methods with high-order accuracy forproblems with interfaces (for example, models for compos-ite materials or fluids, etc), as well as models in irregulardomains is crucial to many physical and biological appli-cations. In this talk we will discuss recently developedefficient numerical schemes based on the idea of the Dif-ference Potentials for elliptic and parabolic composite do-main/interface problems. Numerical experiments to illus-trate high-order accuracy and the robustness of the devel-

oped methods will be presented as well.

Yekaterina EpshteynDepartment of mathematicsUniversity of Utahepshteyn@math.utah.edu

MS251

A High-Order Adaptive Finite Volume Solver forSteady Euler Equations

In this talk, we will present our work on high-order adap-tive finite volume methods for steady Euler equations.There are two main components in our solver. The firstone is a high-order finite volume solver for steady Eulerequations. To reach the high-order accuracy, the k-exactreconstruction is used. The Newton iteration is appliedto linearize the equations, then the linear system is solvedby a geometrical multigrid method. In the second compo-nent, we use the framework of the goal oriented a posteriorierror estimation, and develop some new and efficient tech-niques to generate the error indicator. Then a h-adaptivemethod will be introduced to optimize the distribution ofthe mesh grids, and the improvement of the efficiency onthe algorithm implementation can be expected. The nu-merical results verify our theoretical results, and the high-order behavior of our method will be demonstrated by thebenchmark examples.

Guanghui HuUniversity of Macaugaryhu@umac.mo

MS251

A Seventh Order Hybrid Weighted CompactScheme Based on WENO Stencil for HyperbolicConservation Laws

In this paper, we propose a hybrid seventh order weightedcompact scheme for shock capturing. In smooth region,present scheme recovers a seventh linear compact scheme.Near discontinuities, fifth order weighted compact schemeis used. To guarantee convergence condition, the sev-enth order scheme and fifth order scheme are coupled bya new smooth indicator based on WENO weights. Presentscheme only uses five points which is the same as fifth orderWENO scheme.

Jun Peng, Yiqing ShenState Key Laboratory of High Temperature GasDynamicsInstitute of Mechanics, Chinese Academy of Sciencepengjun@imech.ac.cn, yqshen@imech.ac.cn

MS251

Maximum Principle and Positivity Preserving FluxLimiters for High Order Schemes

Abstract not available at time of publication.

Zhengfu XuMichigan Technological UniversityDept. of Mathematical Scienceszhengfux@mtu.edu

MS252

PDE-constrained Optimization with Local Control

CS15 Abstracts 199

and Boundary Observations: Robust Precondition-ers

We consider PDE-constrained optimization problems withcontrol functions defined on a subregion of the domain ofthe state equation. The main purpose of this paper is todefine and analyze robust preconditioners for KKT systemsassociated with such optimization tasks. That is, precon-ditioners that lead to iteration bounds, for the MINRESscheme, that are independent of the regularization param-eter α and the mesh size h. Our analysis addresses ellipticcontrol problems, subject to Tikhonov regularization, andcovers cases with boundary observations only and locallydefined control functions. A number of numerical experi-ments are presented

Ole Løseth ElvetunDepartment of Mathematical Sciences and TechnologyNorwegian University of Life Sciencesole.elvetun@nmbu.no

Bjørn F. NielsenSimula Research Laboratorybjorn.f.nielsen@nmbu.no

MS252

Robust Preconditioners for PDE-Constrained Op-timization with Limited Observation Data

Regularization robust preconditioners have been success-fully developed for some PDE-constrained optimizationproblems. These methods, however, typically assume thatobservation data is available throughout the entire domainof the state equation. For many inverse problems, this is anunrealistic assumption. We propose and analyze precondi-tioners for PDE-constrained optimization problems withlimited observation data, e.g. observations are only avail-able at the boundary of the computational domain. Ourmethods are robust with respect to both the regularizationparameter and the mesh size.

Magne NordaasCenter for Biomedical ComputingSimula Research Laboratorymagneano@simula.no

Kent-Andre MardalSimula Research Laboratory and Department ofInformaticsUniversity of Oslokent-and@simula.no

Bjørn F. NielsenSimula Research Laboratorybjorn.f.nielsen@nmbu.no

MS252

All-at-once Approach to Optimal Control ProblemsConstrained by PDEs with Uncertain Inputs

We present an efficient approach to simulate optimizationproblems governed by partial differential equations involv-ing random coefficients. This class of problems leads toprohibitively high dimensional saddle point systems withKronecker product structure, especially when discretizedwith the stochastic Galerkin finite element method. Here,we derive robust Schur complement-based block diago-nal preconditioners for solving the resulting stochasticGalerkin systems with all-at-once low-rank solvers. Finally,

we illustrate the effectiveness of our solvers with numericalexperiments.

Akwum Onwunta, Peter BennerMax Planck Institute, Magdeburg, Germanyonwuntajunior@gmail.com,benner@mpi-magdeburg.mpg.de

Martin StollMax Planck Institute, Magdeburgstollm@mpi-magdeburg.mpg.de

MS252

Accelerated Source-Encoding Full-Waveform Seis-mic Inversion with Additional Constraints

We present a semismooth Newton-PCG method for full-waveform inversion governed by the elastic wave equationthat can handle additional constraints on the material.Source-encoding substantially reduces the computationalcosts compared to conventional approaches that considerevery source individually. In particular, we accelerate theminimization of a sample average approximation model byusing inexact Hessian information based on mini-batchesof the samples. Furthermore, we compare the performancewith preconditioned stochastic descent schemes.

Michael UlbrichTechnische Universitaet MuenchenChair of Mathematical Optimizationmulbrich@ma.tum.de

Christian BoehmTechnische Universitat Munchenboehm@ma.tum.de

MS253

Improved Understanding of Atmospheric StabilityEffects on Wind Farm Performance Using Large-Eddy Simulation

Recent evidence from operational wind farms has shownthat atmospheric stability, especially heat fluxes at thesurface, can have a profound effect on turbine-atmosphereinteractions. We use two LES codes to study atmo-spheric stability effects in wind farms: the Simulator forOffshore/Onshore Wind Farm Applications (SOWFA), apublicly-available, finite-volume code developed in C++by the National Renewable Energy Laboratory, and theWind Turbine and Turbulence Simulator (WiTTS), a new,finite-difference, Fortran code developed in-house. Com-prehensive results will be presented for both single- andmultiple-turbine cases under a variety of initial conditions.

Cristina L. ArcherUniversity of Delewarecarcher@udel.edu

Shengbai Xie, Niranjan GhaisasUniversity of Delawaresxie@udel.edu, nghaisas@udel.edu

MS253

Characterizing Turbulence in Wind Turbine Wake:

200 CS15 Abstracts

Role of Stratification

Abstract not available at time of publication.

Kiran BhaganagarUniversity of TExas, San Antoniokiran.bhaganagar@utsa.edu

MS253

Les Study of a Large Wind Farm Within a DiurnalAtmospheric Boundary Layer

Abstract not available at time of publication.

Marc CalafUniversity of Utahmarc.calaf@utah.edu

MS254

Bootstrap and Adaptive Methods

In this talk, I will highlight several recent advances in thedevelopment and analysis of AMG coarsening algorithms.I will discuss various strategies for selecting the coarse vari-ables and defining interpolation, in both the adaptive AMGand Bootstrap AMG settings. Numerical experiments ofthe proposed techniques applied to various applications willalso be provided.

James BrannickDepartment of MathematicsPennsylvania State Universitybrannick@psu.edu

MS254

Algebraic Multigrid for H-hermitian Matrices

We develop an algebraic multigrid method for solving linearsystems of equation Ax = b with non-Hermitian matrices Athat possess a simple symmetrizing operator, e.g., Saddle-point problems, Hamiltonian matrices. That is there ex-ists a simple matrix H such that HA is hermitian. Weobserve that by carefully constructing the intergrid trans-fer operators it is possible not only to transfer this non-standard symmetry to coarse scales, but also to reduce ageneral Petrov-Galerkin to a Galerkin coarse grid construc-tion, namely for HA. We show that by using this con-struction and a Kaczmarz smoother we obtain a methodthat yields the same iterates when applied to Ax = b orHAx = Hb. To demonstrate the applicability of this ap-proach we develop a method for the Wilson discretizationof the 2-dimensional Dirac equation. The proposed ap-proach uses a bootstrap setup algorithm based on a multi-grid eigensolver. It computes test vectors which define theleast squares interpolation operators by working mainlyon coarse grids, leading to an efficient and integrated selflearning process for defining algebraic multigrid interpola-tion. The algorithm is motivated by the γ5-symmetry ofthe Dirac equation, which carries over to the Wilson dis-cretization. This discrete γ5-symmetry is used to reducea general Petrov Galerkin bootstrap setup algorithm to aGalerkin method for the Hermitian and indefinite formu-lation of the Wilson matrix. Kaczmarz relaxation is usedas the multigrid smoothing scheme in both the setup andsolve phases of the resulting Galerkin algorithm. Extensivenumerical results are presented to motivate the design anddemonstrate the effectiveness of the proposed approach.

Karsten Kahl

Bergische Universitat WuppertalDepartment of Mathematicskkahl@math.uni-wuppertal.de

MS254

Root-Node Based Algebraic Multigrid

Recent approaches to improving multigrid convergencethrough modified coarsening and enhanced interpolationhave shown to be effective in a general setting (e.g. com-plex, non-Hermitian, and indefinite). Yet, the the resultingmultigrid hierarchies may exhibit higher complexities thannecessary. In this talk we outline a root-node based ap-proach to multigrid, which can be viewed as a hybrid ofclassical and aggregation based multigrid methods. Thisallows both point-wise decisions in the setup while retain-ing the framework of aggregation. We give an overviewof root-node multigrid using interpolation based on energyminimization and show how the complexity of the multi-grid cycle is controlled through selective filtering by utiliz-ing a root-node. The method yields improved interpolation(and convergence), while limiting the total work of the cy-cle with minimal tuning of parameters. We present somenumerical results in support and discuss directions for fur-ther theoretical and numerical development.

Luke OlsonDepartment of Computer ScienceUniversity of Illinois at Urbana-Champaignlukeo@illinois.edu

Jacob B. SchroderLawrence Livermore National Laboratoryschroder2@llnl.gov

MS254

Algebraic Multigrid Method for Implicit SmoothedParticle Hydrodynamics

Recently, a Lagrangian particle model based on smoothedparticle hydrodynamics (SPH) is proposed to numericallysolve the coupled system that describes the electrokineticphenomena. We generalize the aggregation based Alege-braic multigrid (AMG) method to solve the large-scalelinear system of equations discretized from implicit SPH.Auxiliary grid approach is used to improve the efficiencyand reduce the computational complexity. Numerical ex-periments for modeling electroosmotic flow in microchan-nels and flow throgh charged membranes are presentedto demonstrate the effectiveness of the proposed AMGmethod.

Xiaozhe HuThe Pennsylvania State Universityxiaozhe.hu@tufts.edu

Wenxiao PanPacific Northwest National Laboratorywenxiao.pan@pnnl.gov

Jinchao XuPennsylvania State Universityxu@math.psu.edu

Hongxuan ZhangPenn State University

CS15 Abstracts 201

zhxsxuan@gmail.com

MS255

Designing Visualizations for Biological Research

Advances in measurement devices in the last decade havegiven rise to an explosion of scientific data. In biology,access to massive amounts of quantitative data has fun-damentally changed how discoveries are made, and nowan important component of the scientific process is mak-ing sense of this data using visualization methods. Formost biologists, however, their toolbox is made up of onlybroadly-available tools that were designed for over-archingproblems, often leaving them without answers to their spe-cific questions. A growing trend in the visualization com-munity is to develop tools that focus on specific, real-worldproblems. Called a design study, the process of developingthese tools relies on a close collaboration with end-usersas well as the use of methods from design. In this talkI’ll present several design studies that target complex, bio-logical data analysis, from discovering trends in molecularnetworks to understanding the results of comparative ge-nomics algorithms.

Miriah MeyerUniversity of Utahmiriah@cs.utah.edu

MS255

Block-Based Analysis of Scientific Data

Block-based analysis is the division of an analysis probleminto blocks (not processes) that communicate. By allow-ing blocks to be configurable size and number, flexibly as-signing blocks to processes, and migrating blocks amongdifferent levels of memory/storage hierarchy, an analysisinfrastructure can scale and adapt to current and futurescience applications and HPC platforms. We will discussthese fundamental concepts and their implementation in areusable data movement library designed for block-basedscientific data analysis.

Tom PeterkaArgonne National Laboratorytpeterka@mcs.anl.gov

MS255

Exascale Scientific Data Analytics and Visualiza-tion

Among many existing feature descriptors, statistical infor-mation derived from data samples is a promising approachto taming the big data avalanche because data distribu-tions computed from a population can compactly describethe presence and characteristics of salient data featureswith minimal data movement. The ability to computa-tionally summarize and process data using distributionsalso provides an efficient and representative capture of in-formation that can adjust to size and resource constraints,with the added benefit that uncertainty associated with re-sults can be quantified and communicated. In this talk, Iwill discuss applying distribution-based approaches for vi-sualization and data analytics, including multivariate anal-ysis, vector/scalar field analysis, and histogram compres-sion and query.

Han-Wei ShenThe Ohio State University

hwshen@cse.ohio-state.edu

MS255

Exploring Big Urban Data

For the first time in history, more than half of the world’spopulation lives in urban areas. Given the growing volumeof data that is being captured by cities, the explorationof urban data will be essential to inform both policy andadministration, and enable cities to deliver services effec-tively, efficiently, and sustainably while keeping their cit-izens safe, healthy, prosperous, and well-informed. Urbandata analysis is a growing research field that will not onlypush computer science research in new directions, but willalso enable many others, including urban planners, socialscientists, transportation experts. We have been workingon methods and systems that support urban data analy-sis, with a focus on spatio-temporal aspects. We will de-scribe these efforts, in particular our work on analyzing theNYC taxi dataset, which contains information about over850 million yellow cab trips. Supported by NSF, Google,Moore-Sloan Data Science Environment, IBM, and CUSP.

Claudio T. SilvaNYUcsilva@nyu.edu

MS256

Probability Density Methods for the Analysis ofPower Grids Under Uncertainty

We present the probability density function (PDF) methodfor the analysis of power grids under uncertainty due torandom renewable energy inputs. We derive determinis-tic equations for the evolution of the PDF of the powersystems using various closures. The resulting PDEs aresolved numerically, and results are compared against refer-ence Monte Carlo simulations to assess the accuracy of theproposed closures.

David A. Barajas-SolanoPacific Northwest National Labdavid.barajas-solano@pnnl.gov

Alexander TartakovskyPacific Northwest National Laboratoryalexandre.tartakovsky@pnnl.gov

Debojyoti GhoshMathematics and Computer Science DivisionArgonne National Laboratoryghosh@mcs.anl.gov

Emil M. ConstantinescuArgonne National LaboratoryMathematics and Computer Science Divisionemconsta@mcs.anl.gov

Shrirang AbhyankarArgonne National Laboratoryabhyshr@mcs.anl.gov

Zhenyu HuangPacific Northwest National Laboratory

202 CS15 Abstracts

zhenyu.huang@pnnl.gov

MS256

Distributed Optimization Algorithms for Wide-Area Oscillation Monitoring in Power Systems

In this talk we will present three distributed optimiza-tion algorithms based on Alternating Directions MultiplierMethod (ADMM) for estimating the electro-mechanical os-cillation modes of large power system networks using Syn-chrophasors. Both synchronous and asynchronous commu-nications will be considered. Each architecture integrates acentralized Prony-based algorithm with several variants ofADMM. We will discuss convergence and resiliency prop-erties of each architecture using analytical results as wellas simulations of IEEE prototype power system models.

Aranya ChakraborttyNorth Carolina State Universityachakra2@ncsu.edu

Seyedbehzad NabaviNC State Universitysnabavi@ncsu.edu

MS256

Exploiting Network Laplacian Structure in PowerGrid Dynamics

The electromechanical dynamics of the power grid possessa structure that is ”nearly” Hamiltonian, with the gradientan underlying scalar function capturing much of the infor-mation needed to reconstruct the vector field. This workwill go further to exploit added structure in this scalarpotential function, demonstrating that its network relatedportion can be written as a Hermitian form in the com-plex variables of the voltage phasors (i.e., the fundamentalcomponent for a windowed Fourier transform of the nearlysinusoidal bus voltages of the power grid). Moreover, thedefining matrix of this Hermitian from is a weighted Lapla-cian, defined by the topology and electrical characteristicsof the transmission grid. We show how this structure canbe exploited to build tractable dynamic models of cascad-ing failure phenomena, in which overload and protectivedisconnection of one transmission line may induce subse-quent overloads and disconnects of further links, with therisk of cascade into system-wide failure.

Christopher DeMarco, Honghao ZhengUniversity of Wisconsin-Madisondemarco@engr.wisc.edu, hustfreedom.zheng@gmail.com

MS256

Fast Algorithms for Synchrophasor Computations

There is an urgent need to develop fast real-time algorithmsthat can extract operator friendly information out of large-scale high speed synchronized measurement devices beingimplemented in power systems all over the world. Thistalk will highlight the stability monitoring algorithms de-veloped recently in this context while emphasizing the com-putational challenges in realizing the theoretical methods.Distributed algorithms as well as centralized formulationswill be compared.

Vaithianathan Venkatasubramanian, Tianying Wu, SeyedArash Sarmadi, Ebrahim RezaeiWashington State University

mani@eecs.wsu.edu, lilyrosejam@hotmail.com,arash.sarmadi@gmail.com, rezaee.ebrahim@gmail.com

MS257

A multi-physics Domain Decomposition Methodfor Navier-Stokes-Darcy Model

This presentation discusses a multi-physics domain de-composition method for solving the coupled steady-stateNavier-Stokes-Darcy system with the Beavers-Joseph in-terface condition. The wellposedness is first showed byusing a branch of singular solutions. Robin boundary con-ditions on the interface are constructed based on the phys-ical interface conditions to decouple the Navier-Stokes andDarcy parts. Then a domain decomposition method is de-veloped and analyzed. Numerical examples are presentedto validate this method.

Xiaoming HeDepartment of Mathematics and StatisticsMissouri University of Science and Technologyhex@mst.edu

MS257

Improvements in the Level Set Method with a Fo-cus on Curvature-Dependent Forcing

One particular subset of moving interface problems is whenthe interface exerts a curvature-dependent force on the sur-rounding material. Such a force can arise, for example,when the interface is resistant to bending or has surfacetension. Stable numerical computation of the interface cur-vature can be difficult as it is often expressed as high-orderderivatives of either marker particle positions or of a levelset function. Focusing on the latter, the level set methodis modified to track not only the interface position, but thecurvature as well. The definition of the signed-distancefunction that is used in this approach is also used to de-velop an interpolation-free, closest-point method for solv-ing surface PDEs.

Chris VoglUniversity of Washingtoncvogl@u.washington.edu

MS257

Optimal Energy Conserving DiscontinuousGalerkin Methods for the Wave PropagationProblems in Heterogeneous Media

Solving wave propagation problems within heterogeneousmedia has been of great interest and has a wide range ofapplications in physics and engineering. The design of nu-merical methods for such general wave propagation prob-lems is challenging because the energy conserving propertyhas to be incorporated in the numerical algorithms in or-der to minimize the phase or shape errors after long timeintegration. In this talk, we will discuss multi-dimensionalwave problems and consider linear second-order wave equa-tion in heterogeneous media. We will present an LDGmethod, in which numerical fluxes are carefully designedto maintain the energy preserving property and accuracy.We propose compatible high order energy conserving timeintegrators and prove the optimal error estimates and theenergy conserving property for the semi-discrete methods.Our numerical experiments demonstrate optimal rates ofconvergence, and show that the errors of the numerical so-lution do not grow significantly in time due to the energy

CS15 Abstracts 203

conserving property.

Yulong XingDepartment of MathematicsUniveristy of Tennessee / Oak Ridge National Labxingy@math.utk.edu

MS257

Surface Phase Separation Mediated by NonlocalInteractions

Motivated by the lipid phase separation on membrane me-diated by electrostatic interactions, we propose here a gen-eral Cahn-Hilliard equation with nonlocal electrostatic in-teractions. A C-0 interior penalty discontinuous Galerkinmethod is adapted to solve the coupled system of PDEs onarbitrary surfaces. Phase separation of smaller scales arefound compared to scenario without nonlocal interaction,indicating that the nonlocal interaction may generate lipidrafts.

Yongcheng ZhouDepartment of MathematicsColorado State Universityyzhou@math.colostate.edu

MS258

The Role of Autotuning Compiler Technology

Autotuning empirically evaluates a search space of possibleimplementations of a computation to identify the imple-mentation that best meets its optimization criteria (e.g.,performance, power, or both). Autotuning compilers gen-erate this search space of different implementations eitherautomatically or with programmer guidance. This talk willexplore the role of compiler technology in achieving veryhigh levels of performance, comparable to what is obtainedmanually by experts. It will focus on the optimizations re-quired for specific domains: geometric multigrid, stencils,and tensor contraction computations.

Mary HallSchool of ComputingUniversity of Utahmhall@cs.utah.edu

MS258

Active Harmony: Making Autotuning Easy

Active Harmony is an auto-tuning framework for paral-lel programs. In this talk, I will describe how the systemmakes it easy (sometime even automatic) to create pro-grams that can be auto-tuned. I will present example froma few applications and programming languages.

Jeffery HollingsworthComputer Science DepartmentUniversity of Marylandhollings@cs.umd.edu

MS258

Towards Auto-tuning in the Era of 200+ ThreadParallelisms — FIBER Framework and MinimizingSoftware Stack —

Currently, parallelism of 200+ threads is pervasive bymany-core processors, such as the Xeon Phi. In the pro-cessors, we need careful optimizations with respect to ex-

ecution conditions at run-time, such as problem sizes andhybrid MPI/OpenMP. In this talk, we introduce FIBERframework of Auto-tuning (AT) to optimize codes for themany-core processors. We also show effect of the AT withmulti nodes of the Xeon Phi with an application of FiniteDifference Method.

Takahiro KatagiriInformation Technology Center, The University of Tokyokatagiri@cc.u-tokyo.ac.jp

Satoshi OhshimaThe University of TokyoInformation Technology Centerohshima@cc.u-tokyo.ac.jp

Masaharu MatsumotoInformation Technology CenterThe University of Tokyomatsumoto@cc.u-tokyo.ac.jp

MS258

A Framework for Separation of Concerns BetweenApplication Requirements and System Require-ments

An HPC application is usually optimized for a particu-lar platform and unable to run efficiently on other plat-forms. The Xevolver framework is designed to sepa-rate such platform-specific optimizations from applicationcodes. In Xevolver, a code portion that needs to be modi-fied for system-specific code optimization is just annotatedfor user-defined code transformations to prevent messingup the original code. The usefulness and practicality ofXevolver are discussed on the basis of some case studies.

Hiroyuki Takizawa, Shoichi Hirasawa

Tohoku University/JST CRESTtacky@isc.tohoku.ac.jp, hirasawa@sc.isc.tohoku.ac.jp

Hiroaki KobayashiTohoku University, Japankoba@isc.tohoku.ac.jp

MS259

Microstructural Modeling of Fracture in Uraniumdioxide Using a Phase-Field Based Approach

A phase-field model is implemented in MOOSE to inves-tigate the effect of porosity and grain size on the inter-granular brittle fracture in UO2. The grain boundary frac-ture parameters are obtained from the results of molecu-lar dynamics simulations. A numerical sensitivity studyis then performed to obtain a microstructurally informedstress-based fracture model usable at the engineering scale.

Pritam Chakraborty, Michael TonksIdaho National Laboratorypritam.chakraborty@inl.gov, michael.tonks@inl.gov

MS259

Computational Microstructure Science Using theMoose Framework

Mesoscale modeling and simulation provide a bridge be-tween atomistic data and engineering scale computation.However, mesoscale modeling can be complicated due to

204 CS15 Abstracts

the multiphysics nature of the problems, and the typicallyhigh computation costs. The open source MultiphysicsObject-Oriented Simulation Environment (MOOSE) pro-vides a number of physics modules that are aimed specif-ically at mesoscale simulation. These tools model thecoevolution of microstructure and properties due to ap-plied load, temperature, and radiation damage. The PhaseField Module provides all the necessary tools to predict mi-crostructure evolution using the phase field method and theTensor Mechanics Module provides the tools for finite de-formation mechanics simulations at the level of microstruc-ture. Also, effective mechanical and thermal properties canbe calculated as the microstructure evolves. Since thesetools are based on MOOSE, they are massively parallel,work in 1D, 2D, and 3D and can use mesh and time stepadaptivity. We have also developed the capability to re-construct experimental microstructures directly into thesimulations, to set the initial condition for simulations, tosimplify validation and to facilitate virtual property mea-surement.

Bradley Fromm, Daniel Schwen, Michael TonksIdaho National Laboratorybradley.fromm@inl.gov, daniel.schwen@inl.gov,michael.tonks@inl.gov

MS259

Fission Bubble Modeling in Uranium Carbide

Fission gas bubble behavior is a complex microscopic effectthat leads to macroscopic changes in nuclear fuel. The in-terplay between thermal diffusion causing bubble growth,pitted against physical knock-outs from fission fragmentscausing bubble shrinkage, creates a non-linear problemthat is not easily solved. MOOSE allows for character-ization of this behavior within the code BISON by usinglower-length scale effects to estimate the large bubble struc-ture and swelling of irradiated uranium carbide.

Christopher Matthews, Andrew KleinOregon State Universitymatthchr@engr.orst.edu, andrew.klein@oregonstate.edu

MS259

Grizzly: A Simulation Tool for Nuclear PowerPlant Component Aging

To determine the risk associated with extending the life ofnuclear power plants, the effects of age-related degradationof critical components in those plants must be understood.Grizzly is a MOOSE-based tool being developed to simu-late aging processes and understand the effects that age-related degradation will have on those components. Aninitial application of Grizzly is for coupled physics simula-tions to assess the susceptibility of aged reactor pressurevessels to fracture under accident conditions.

Benjamin SpencerIdaho National Laboratorybenjamin.spencer@inl.gov

MS260

Iterative Solution Techniques in Reduced-orderModeling

Reduced-order models (ROMs) efficiently solve related lin-ear systems arising in many-query applications. The fulllinear system is projected onto a smaller dimensional sub-space resulting in a ROM whose solution approximates the

solution of the original system. The reduced model sizeis problem dependent and could be smaller than the fullproblem, but large enough to make direct solution costly.In this scenario, the iterative solution of the ROM can bemore effecient.

Virginia ForstallUniversity of Maryland at College Parkvhfors@gmail.com

Howard C. ElmanUniversity of Maryland, College Parkelman@cs.umd.edu

MS260

Model Reduction in Physics-Based Sound Synthe-sis

Synthesizing physics-based sounds by time-stepping com-putational models of coupled solid and fluid systems is ex-tremely time consuming due to long-time integration andthe desire for real-time auditory feedback. This talk willhighlight some of our recent work on reduced-order mod-eling of vibration and acoustic radiation: (1) basis com-pression to reduce the memory footprint of modal soundmodels, and (2) reduced-order modeling of bubble-basedliquid sounds.

Doug L. James, Timothy LangloisCornell Universitydjames@cs.cornell.edu, langlois@cs.cornell.edu

MS260

Online Adaptive Model Reduction

Model reduction approximates the nonlinear manifold in-duced by full-order solutions with a (linear) reduced space.We present a nonlinear approximation of the manifoldbased on adapting the reduced space online. The adap-tation relies on low-rank basis updates derived from sparsedata of the full-order model. In particular in the presenceof nonlinearities, our nonlinear approximation achieves ahigher accuracy than the classical linear approximation.The sparsity of the data ensures computational efficiency.

Benjamin PeherstorferACDL, Department of Aeronautics & AstronauticsMassachusetts Institute of Technologypehersto@mit.edu

Karen E. WillcoxMassachusetts Institute of Technologykwillcox@MIT.EDU

MS260

Reduced-order Models using Dynamic Mode De-composition

Dynamic mode decomposition (DMD) is a technique thatuses data to express “black-box” dynamics in terms of theeigenvalues, eigenfunctions, and modes of the correspond-ing Koopman operator. For a linear system, these modesare the eigenvectors, and they have a similar role in non-linear settings. We describe Extended DMD, an exten-sion that uses a richer set of functions to approximate theKoopman eigenfunctions, and demonstrate the method on

CS15 Abstracts 205

several examples, including flow past a cylinder.

Clarence RowleyPrinceton UniversityDepartment of Mechanical and Aerospace Engineeringcwrowley@princeton.edu

Matthew O. WilliamsApplied MathematicsUniversity of Washingtonmow2@Princeton.edu

Maziar S. Hemati, Scott DawsonPrinceton Universitymhemati@princeton.edu, stdawson@princeton.edu

MS261

A Posteriori Analysis of the Parareal Algorithm:Efficient Resource Allocation and Convergence Cri-teria

We carry out a posteriori analysis of the parareal algorithmusing adjoint based methods. The analysis is carried outrelatively cheaply and allows for quantification of error ina quantity of interest. Furthermore, the analysis providesguidance in choosing discretization parameters so as to en-hance load balancing in the parallel stage of the algorithmand by quantifying different sources of error, suggests ap-propriate strategies to accelerate convergence.

Jehanzeb H. ChaudhryFlorida State Universityjehanzeb.hameed@gmail.com

Don Estep, Simon TavenerColorado State Universityestep@stat.colostate.edu, tavener@math.colostate.edu

MS261

An Overview of the Multigrid Reduction in Time(MGRIT) Method

The multigrid-reduction-in-time (MGRIT) method is ascalable, truly multilevel approach to parallel time integra-tion, derived based on multigrid reduction principles. Inthis talk, we present the algorithm and demonstrate thatMGRIT offers excellent strong and weak parallel scaling upto thousands of processors. Complementary convergenceanalysis methodologies such as a semi-algebraic approachto mode analysis, which provides a predictive analysis toolfor MGRIT and related algorithms on space-time grids,will also be discussed.

Stephanie FriedhoffKU Luevenstephanie.friedhoff@cs.kuleuven.be

MS261

Parareal Library for Time-Dependent PDEs inMedical Applications

The parallel-in-time integration method Parareal providesan additional direction for concurrency when solving time-dependent PDEs numerically. Thus, it can extend thestrong scaling limit of a purely space-parallel approach. Inthis talk, we present a new C++ ‘Library for the PararealMethod’ (Lib4PrM). To illustrate its performance, a cou-pling with the ug4 package is used to solve a PDE modeling

permeation through human skin.

Andreas KreienbuehlUniversity of Luganoandreas.kreienbuehl@usi.ch

Arne NaegelGoethe University Frankfurtarne.naegel@gcsc.uni-frankfurt.de

Daniel RuprechtInstitute of Computational ScienceUniversita della Svizzera italianadaniel.ruprecht@usi.ch

Robert SpeckJuelich Supercomputing CentreForschungszentrum Juelichr.speck@fz-juelich.de

Gabriel WittumGoethe Center for Scientific ComputingGoethe University Frankfurtwittum@gcsc.uni-frankfurt.de

Rolf KrauseInstitute of Computational ScienceUniversity of Luganorolf.krause@usi.ch

MS261

Multigrid Reduction in Time (MGRIT): A Flexibleand Non-Intrusive Method

This talk highlights practical aspects of the parallel-in-time method, multigrid-reduction-in-time (MGRIT). Thealgorithm is non-intrusive and wraps existing time step-ping codes. MGRIT is versatile by allowing for varioustime discretizations (e.g., Runge-Kutta and multistep) andfor adaptive refinement and coarsening in time and space.Non-linear problems are handled through full approxima-tion scheme (FAS) multigrid. Details of the software phi-losophy and practical experience and results (e.g., from anonlinear compressible Navier-Stokes code), will also begiven.

Jacob B. SchroderLawrence Livermore National Laboratoryschroder2@llnl.gov

Robert FalgoutCenter for Applied Scientific ComputingLawrence Livermore National Laboratoryrfalgout@llnl.gov

Ulrike Meier YangLawrence Livermore National Laboratoryyang11@llnl.gov

Tzanio V. KolevCenter for Applied Scientific ComputingLawrence Livermore National Laboratorytzanio@llnl.gov

Veselin DobrevLawrence Livermore National Laboratorydobrev1@llnl.gov

206 CS15 Abstracts

Stephanie FriedhoffKU Luevenstephanie.friedhoff@cs.kuleuven.be

Scott MaclachlanDepartment of MathematicsTufts Universityscott.maclachlan@tufts.edu

MS262

Demonstrating Improved Application PerformanceUsing Dynamic Monitoring and Task Mapping

We present a framework enabling dynamic applicationmapping based on run-time analysis of system-wide net-work data, architecture-specific routing algorithms, andapplication communication patterns. We demonstrate dy-namic remapping of MPI tasks based on route-length,bandwidth, and credit-stalls metrics for a parallel sparsematrix-vector multiplication kernel. Remapping based ondynamic network information in a congested environmentin a shared network topology recovers up to 50% of thetime lost to congestion, reducing matrix-vector multiplica-tion time by 8%.

Ann Gentile, James Brandt, Karen D. Devine, KevinPedrettiSandia National Laboratoriesgentile@sandia.gov, brandt@sandia.gov, kd-devin@sandia.gov, ktpedre@sandia.gov

MS262

Topology Aware Process Placement and Data Man-agement

Programming multicore or manycore architectures effi-ciently is a challenge because numerous hardware char-acteristics have to be taken into account, especially thememory hierarchy. In this talk we will show how we canefficiently manage data and reduce communication cost bytaking into account the topology of the machine and theaffinity of the application processes in different contexts:process placement, load-balancing, resource allocation.

Emmanuel JeannotINRIAemmanuel.jeannot@inria.fr

MS262

Local Search to Improve Geometric Task Mapping

We present a local search strategy to improve the mappingof a parallel job’s tasks to the MPI ranks of its parallel allo-cation in order to reduce network congestion and the job’scommunication time. The goal is to reduce the numberof network hops between communicating pairs of ranks.Using the miniGhost mini-app, which models the shockphysics application CTH, we demonstrate that our strat-egy reduces application running time while also reducingthe runtime variability.

Vitus LeungSandia National Laboratoriesvjleung@sandia.gov

David BundeKnox College

dbunde@knox.edu

MS262

Process Mapping onto Complex Architectures andPartitions Thereof

The Scotch software computes process-processor mappingsby assigning recursively parts of the process graphs to partsof the target graphs. To date, while regular target archi-tectures can be described using pre-coded routines, irreg-ular architectures or parts of regular ones require P 2 datastructures, which makes them unpractical for very big ma-chines. We will present a new, multilevel description oftarget architectures that alleviates this problem, trading-off memory for run time.

Francois PellegriniUniversity of Bordeauxfrancois.pellegrini@labri.fr

MS263

Fluctuating Hydrodynamics of Reactive Multi-species Mixtures

This paper describes the extension of the fluctuatingNavier-Stokes (FNS) equations to multispecies, reactivemixtures. In FNS, hydrodynamic effects of thermal fluc-tuations are represented by adding stochastic flux terms,whose magnitude are set by fluctuation dissipation bal-ance, to the Navier Stokes equations. Incorporating re-actions into the system introduces a number of additionalcomplexities. We discuss approaches to addressing these is-sues and present numerical results illustrating the impactof fluctuations in reacting systems.

John B. BellCCSELawrence Berkeley Laboratoryjbbell@lbl.gov

MS263

Modeling Multi-Phase Flow Using Fluctuating Hy-drodynamics

Incorporating thermal fluctuations in continuum Navier-Stokes equations requires the development of numericalmethods that solve the complex stochastic partial differen-tial equations of fluctuating hydrodynamics. The situationbecomes more complex when more than one fluid phaseis involved as in a liquid-vapor system. These stochas-tic PDE’s require a special spatio-temporal discretizationso that the correct Gibbs-Boltzmann equilibrium distribu-tion is achieved at long times and the correct fluctuation-dissipation balance is preserved at each time step. We de-scribe a stochastic method of lines discretization of thefully compressible Landau-Lifshitz-Navier-Stokes (fluctu-ating hydrodynamics) equations with the van der Waalsequation of state. The diffuse interface method is used tomodel the order parameter (density) as a smooth variationacross the interface. The surface tension effects give rise toKorteweg type stresses that show up as additional termsin the momentum and energy equations. The numericalscheme is validated by comparison of measured structurefactors and capillary wave spectra with equilibrium theory.We also present several non-equilibrium examples to illus-trate the capability of the algorithm to model multi-phasefluid phenomena in a neighborhood of the critical point.These examples include a study of the impact of fluctu-

CS15 Abstracts 207

ations on the spinodal decomposition following a rapidquench, as well as the piston effect in a cavity with super-cooled walls. The conclusion in both cases is that thermalfluctuations affect the size and growth of the domains inoff-critical quenches.

Anuj Chaudhri, John B. BellCCSELawrence Berkeley Laboratoryachaudhri@lbl.gov, jbbell@lbl.gov

Alejandro GarciaSan Jose State Universityalgarcia@algarcia.org

Aleksandar DonevCourant Institute of Mathematical SciencesNew York Universityaleks.donev@nyu.edu

MS263

The Long-time Tail of the Velocity AutocorrelationFunction of a Particle in a Molecular Fluid

Through large-sized-ensemble runs of molecular dynamicssimulation for a tracer particle suspended in a molecularfluid, its velocity autocorrelation function and diffusion co-efficient are very accurately determined. The finite-system-size effects of molecular dynamics simulation and the effectsof molecular character of the surrounding fluid are investi-gated. In addition, our results are compared with theoret-ical results obtained from the fluctuating hydrodynamicsand computational results obtained from the smoothed-particle hydrodynamics.

Changho Kim, George E. KarniadakisBrown UniversityDivision of Applied Mathematicschangho kim@brown.edu, george karniadakis@brown.edu

MS264

A Low-Rank Approximation Method for High-Dimensional Uncertainty Quantification

This work introduces a model reduction technique that ex-ploits the low-rank structure of the solution of interest,when exists, for fast propagation of high-dimensional un-certainties. To construct this low-rank approximation, theproposed method utilizes a hierarchy of models with lowerfidelities, than the intended model, which can be simulatedcheaply. Several numerical experiments will be provided todemonstrate the efficiency of the proposed approach.

Alireza DoostanDepartment of Aerospace Engineering SciencesUniversity of Colorado, BoulderAlireza.Doostan@Colorado.EDU

Dongbin XiuUniversity of Utahdongbin.xu@utah.edu

Akil NarayanUniversity of Massachusetts Dartmouthakil.narayan@umassd.edu

Hillary FairbanksDepartment of Applied Mathematics

University of Colorado, Boulderhillary.fairbanks@colorado.edu

MS264

Bayesian Compressive Sensing Framework forHigh-Dimensional Surrogate Construction

Surrogate construction for high-dimensional models is chal-lenged in two major ways: obtaining sufficient train-ing model simulations becomes prohibitively expensive,and non-adaptive basis selection rules lead to excessivelylarge basis sets. We enhanced select state-of-the-art toolsfrom statistical learning to build efficient sparse surro-gate representations, with quantified uncertainty, for high-dimensional complex models. Specifically, Bayesian com-pressive sensing techniques are supplemented by iterativebasis growth and weighted regularization. Application toa 70-dimensional climate land model shows promising re-sults.

Khachik Sargsyan, Cosmin SaftaSandia National Laboratoriesksargsy@sandia.gov, csafta@sandia.gov

Bert J. DebusschereEnergy Transportation CenterSandia National Laboratories, Livermore CAbjdebus@sandia.gov

Habib N. NajmSandia National LaboratoriesLivermore, CA, USAhnnajm@sandia.gov

MS264

Inverse Subspace Iteration for Spectral StochasticFinite Element Methods

We study random eigenvalue problems in the context ofspectral stochastic finite elements. We assume that thematrix operator is given in the form of a polynomial chaosexpansion, and we search for the coefficients of the polyno-mial chaos expansions of the eigenvectors and eigenvalues.We formulate a version of stochastic inverse subspace iter-ation, which is based on stochastic Galerkin finite elementmethod, and we compare its accuracy with that of MonteCarlo and stochastic collocation methods.

Bedrich SousedikUniversity of Marylandsousedik@umbc.edu

Howard C. ElmanUniversity of Maryland, College Parkelman@cs.umd.edu

MS264

Preconditioner for Parameter-dependent LinearSystems Based on an Empirical Interpolation of theMatrix Inverse

We consider parameter-dependent linear systems of equa-tions, e.g. arising from the discretization of a parameter-dependent or stochastic PDE. We propose a parameter de-pendent preconditioner defined as an interpolation of thematrix inverse based on a Frobenius norm projection. Wethen show how such preconditioner can be used for projec-tion based model reduction methods such as the reduced

208 CS15 Abstracts

basis method. We propose constructions of interpolationpoints that are dedicated either to the improvement ofGalerkin projections or to the estimation of projection er-rors.

Loıc GiraldiGeM, Ecole Centrale de Nantesloic.giraldi@ec-nantes.fr

Anthony Nouy, Olivier ZahmLUNAM Universite, Ecole Centrale Nantes, CNRS, GeManthony.nouy@ec-nantes.fr, olivier.zahm@ec-nantes.fr

MS265

Numerical Applications of Weak Galerkin FiniteElement Methods

Weak Galerkin finite element methods are new numericalmethods for solving partial differential equations that werefirst introduced by Wang and Ye for solving general secondorder elliptic partial differential equations (PDEs). Thedifferential operators in PDEs are replaced by their weakforms through the integration by parts, which endows highflexibility for handling complex geometries, interface dis-continuities, and solution singularities. This new methodis a discontinuous finite element algorithm, which is param-eter free, symmetric, and absolutely stable. Furthermore,through the Schur-complement technique, an effective im-plementation of the weak Galerkin is developed a linearsystem involving unknowns only associated with elementboundaries. In this talk, several numerical applications ofweak Galerkin methods will be discussed.

Lin MuMichigan State State Universitynmu@math.msu.edu

MS265

BPX Preconditioner for Nonstandard Finite Ele-ment Methods for Diffusion Problems

We propose and analyze an optimal preconditioner fora general linear symmetric positive definite (SPD) sys-tem by following the basic idea of the well-known BPXframework. The SPD system arises from a large num-ber of nonstandard finite element methods for diffusionproblems, including the well-known hybridized Raviart-Thomas and Brezzi-Douglas-Marini mixed element meth-ods, the hybridized discontinuous Galerkin method, theWeak Galerkin method, and the nonconforming Crouzeix-Raviart element method. We prove that the presentedpreconditioner is optimal, in the sense that the conditionnumber of the preconditioned system is independent of themesh size. Numerical experiments provided confirm thetheoretical result.

Xiaoping XieSichuan University, Chinaxpxie@scu.edu.cn

MS265

Recent Development of Weak Galerkin Methods

Newly developed weak Galerkin finite element methodswill be introduced for solving partial differential equations.Weak Galerkin methods have the flexibility of employingdiscontinuous elements and share the simple formulationsof continuous finite element methods at the same time.

The Weak Galerkin method is an extension of the standardGalerkin finite element method where classical derivativeswere substituted by weakly defined derivatives on functionswith discontinuity. Recent development of weak Galerkinmethods will be discussed in the presentation.

Xiu YeUniversity of Arkansas, Little Rockxxye@ualr.edu

MS265

A Divergence-free Weak Galerkin Finite Element

A weak Galerkin finite element is designed so that the com-puted velocity is divergence-free. The significance of sucha method is shown by solving a low-viscosity Stokes prob-lem. The traditional finite elements, weak Galerkin finiteelements and discontinous Galerkin finite flements fail toproduce a meaningful solution in solving such a test prob-lem.

Shangyou ZhangUniversity of Delawareszhang@udel.edu

MS266

Implementation of a Fast Multifrontal Solver UsingRandomized HSS Compression

We present an efficient code for solving large sparse linearsystems using the multifrontal method with hierarchicallysemi-separable (HSS) matrices. The low rank compressionin HSS limits fill-in and reduces complexity of the solver.The HSS matrices are constructed using randomized sam-pling and rank-revealing QR. ULV decomposition replacesthe traditional dense LU. The factorization acts as solveror preconditioner. Shared and distributed memory parallelresults are presented for a range of applications.

Pieter GhyselsLawrence Berkeley National LaboratoryComputational Research Divisionpghysels@lbl.gov

Francois-Henry RouetLawrence Berkeley National Laboratoryfhrouet@lbl.gov

Xiaoye Sherry LiComputational Research DivisionLawrence Berkeley National Laboratoryxsli@lbl.gov

MS266

Deterministic and Randomized CUR and NystromApproximations

The goal is to improve the accuracy and efficiency of CURand Nystrom approximations, by exploiting traditional ma-trix decompositions. To this end we establish connectionsbetween CUR approximations and LU decompositions, andderive conditions for the optimality of CUR decomposi-tions. Furthermore, we express the standard Nystro ap-proximation as an incomplete Cholesky decomposition, themodified Nystrom approximation as a CUR approxima-tion, and derive residual bounds for deterministic approxi-mations based on rank revealing QR decompositions. Theresults for the deterministic approximations are used to

CS15 Abstracts 209

guide and calibrate the randomized algorithms, and we de-rive new bounds for uniform and leverage score sampling.

Ilse IpsenNorth Carolina State UniversityDepartment of Mathematicsipsen@ncsu.edu

MS266

Fast Generation of Random Orthogonal Matrices

Random orthogonal matrices have a wide variety of appli-cations. They are used in the generation of various kindsof random matrices and random matrix polynomials. Therandom orthogonal matrix (ROM) simulation method usesrandom orthogonal matrices to generate multivariate ran-dom samples with the same mean and covariance as anobserved sample. The natural distribution over the spaceof orthogonal matrices is the Haar distribution. One wayto generate a random orthogonal matrix from the Haardistribution is to generate a random matrix A with ele-ments from the standard normal distribution and computeits QR factorization A = QR, where R is chosen to havenonnegative diagonal elements; the orthogonal factor Q isthen the required matrix. Stewart develops a more effi-cient algorithm that directly generates an n×n orthogonalmatrix from the Haar distribution as a product of House-holder transformations built from Householder vectors ofdimensions 1, 2, . . . , n − 1 chosen from the standard nor-mal distribution. The goal of this work is to design analgorithm that reduces the computational cost of Stew-art’s algorithm by giving up the property that Q is exactlyHaar distributed. We generate orthogonal random Q usingk Householder transformations. We will argue that for thepurpose of test matrix generation we can take k much lessthan the matrix dimension and still obtain an acceptablematrix. We will give performance results on a variety ofarchitectures to show the benefits of the new algorithm.

Amal KhabouNRIA Saclay, 4 Rue Jacques Monod 91893amal.khabou@manchester.ac.uk

Francoise TisseurUniversity of ManchesterDepartment of Mathematicsftisseur@maths.manchester.ac.uk

Nicholas J. HighamUniversity of ManchesterSchool of MathematicsNicholas.J.Higham@manchester.ac.uk

MS266

Performance of Computing Low-Rank Approxima-tion on Hybrid CPU/GPU Architectures

Low-rank matrix approximations play important roles inmany statistical, scientific, and engineering applications.In this talk, we study the performance of various algo-rithms (including random projection/sampling) to com-pute such approximation of large sparse matrices on a hy-brid CPU/GPU architecture. Ultimately, we would like todevelop robust, efficient, and flexible software that com-putes such approximation for a wide range of applications.One objective for this talk is to seek inputs from such ap-

plication experts.

Ichitaro YamazakiUTKic.yamazaki@gmail.com

Theo MaryUniversite de Toulouse, INPT ENSEEIHTtheo.mary@etu.enseeiht.fr

Jakub Kurzak, Stanimire TomovUniversity of Tennessee, Knoxvillekurzak@icl.utk.edu, tomov@icl.utk.edu

Jack J. DongarraDepartment of Computer ScienceThe University of Tennesseedongarra@cs.utk.edu

MS267

Optimized Reduced Order Modeling and Data As-similation for Hydrodynamics with Large TimeStep Observations

This presentation focuses on the theoretical developmentof numerical methods for problems originating from me-teorology and application of two complementary methodsof decomposing the flow field from experimental measure-ments into coherent structures namely: the Proper Or-thogonal Decomposition (POD) and the Dynamic ModeDecomposition (DMD). Additionally, we aim to apply thefour-dimensional variational approach of data assimilation(4D-Var) to seek for the model coefficients such that thederived ROM will inherit good dynamical properties.

Diana BistrianDept. of Electrical Engineering and IndustrialInformationUniversity ”Politehnica” of Timisoaradiana.bistrian@fih.upt.ro

Ionel M. NavonFlorida State UniversityDepartment of Scientific Computinginavon@fsu.edu

MS267

Model Reduction and Sensor Placement in a Feed-back Flow Control Problem

We consider the flow control problem of stabilizing thewake behind a circular cylinder through the cylinder’s rota-tion. Model reduction methods are applied for computingthe optimal linear feedback control as well as for choosingthe location of a number of velocity measurements that canbe used to practically implement the control law. Numer-ical results demonstrate the effectiveness of the controllerreduction when compared to the full-state linear feedbackcontrol.

Jeff BorggaardVirginia TechDepartment of Mathematicsjborggaard@vt.edu

Serkan GugercinVirginia Tech.Department of Mathematics

210 CS15 Abstracts

gugercin@math.vt.edu

Lizette ZietsmanVirginia TechInterdisciplinary Center for Applied Mathematicslzietsma@vt.edu

MS267

Goal-Based Rom Adjoint for Optimal Sensor Loca-tions and Data Assimilation

An goal-based reduced order modelling (ROM) adjoint ap-proach is developed for optimising sensor locations. Anadjoint (or sensitivity) based error measure is formulatedwhich measures the error contribution of each solution vari-able to an overall goal (defined as a measure of what isdeemed important in a problem). It provides importancemaps for determining where best to place the monitoringdevices. The expensive data resources will be efficientlyused for data assimilation.

Fangxin FangDepartment of Earth Science and EngineeringImperial College London, U.K.f.fang@imperial.ac.uk

Christopher PainImperial Collegec.pain@imperial.ac.uk

Ionel M. NavonFlorida State UniversityDepartment of Scientific Computinginavon@fsu.edu

Zhizhao CheChemical Engineering, Imperial College Londonz.che@imperial.ac.uk

Andrew G. Buchan, Pavlidis DimitriosDepartment of Earth Science & EngineeringImperial Collegeandrew.buchan@imperial.ac.uk,dimitrios.pavlidis@imperial.ac.uk

Dunhui XiaoDepartment of Earth Science and EngineeringImperial Colleg Londondh.xiao@imperial.ac.uk

MS267

Reduced Order Modelling (rom) of the Navier-Stokes Equations for 3D Free Surface Flows

This article presents a reduced order modelling method forNavier-Stokes Equations for 3D free surface flows. Thiswork is the first to introduce ROM into 3D free surfaceflows. This newly ROM reduced CPU time for solving 3Dfree surface problems by orders of magnitude while keepinga high accuracy. This ROM has significant potential ad-vantages in : interactive use, emergency response, controland uncertainty analysis.

Dunhui XiaoDepartment of Earth Science and EngineeringImperial Colleg Londondh.xiao@imperial.ac.uk

Fangxin FangDepartment of Earth Science and EngineeringImperial College London, U.K.f.fang@imperial.ac.uk

Christopher PainImperial Collegec.pain@imperial.ac.uk

Andrew G. BuchanDepartment of Earth Science & EngineeringImperial Collegeandrew.buchan@imperial.ac.uk

Ionel M. NavonFlorida State UniversityDepartment of Scientific Computinginavon@fsu.edu

MS268

Higher Order Finite Volume Approximations of theInviscid Primitive Equations in a Complex Domain

We construct the cell-centered finite volume discretizationof the two-dimensional inviscid primitive equations in a do-main with topography. To compute the numerical fluxes,the so-called (first order) upwind scheme and the (secondorder) central-upwind scheme are introduced. Numericalsimulations verify that the upwind and central-upwind arerobust schemes regardless of the shape or size of the topog-raphy.

Gung-Min GieIndiana UniversityUSAgungmin.gie@louisville.edu

Arthur Bousquet, YoungJoon HongIndiana Universityarthbous@indiana.edu, hongy@umail.iu.edu

Roger M. TemamInst. for Scientific Comput. and Appl. Math.Indiana Universitytemam@indiana.edu

MS268

A New Atmospheric Dynamic Core using 4th Or-der Flux Reconstruction Method with WENO Lim-iting

In this talk, we present a dynamic core for compress-ible non-hydrostatic atmosphere by using a newly devisedhigh-resolution scheme, so-called FR4-CD-WENO (4th or-der Flux-Reconstruction with Constrained Derivative us-ing WENO limiting). Compared to the existing WENO-DG paradigm, the FR4-CD-WENO method shows supe-riorities in at least three aspects. 1) It makes use of thesub-cell information of the local reconstruction instead ofthe cell-averaged values, which results in a compact stencilfor reconstruction, 2) It is more accurate than the WENO-DG scheme using the same degrees of freedom, and 3) Itis algorithmically simpler and more computationally effi-cient. We have developed the FR4-CD-WENO dynamiccore for atmospheric flows and shown it as a very promis-ing framework for high-performance atmospheric models.

CS15 Abstracts 211

Xingliang LiCenter of Numerical Weather Predication,China Meteorological Administrationlixl@ou.edu

Ziyao SunDepartment of Energy SciencesTokyo Institute of Technologysun.z.ab@m.titech.ac.jp

Feng XiaoTokyo Institute of Technologyxiao@es.titech.ac.jp

Chungang ChenXi’an Jiaotong Unversitycgchen@mail.xjtu.edu.cn

Xueshun ShenCenter of Numerical Weather Predication,China Meteorological Administrationshenxs@cams.cma.gov.cn

Ming XueCenter for Analysis and Prediction of StormsUniversity of Oklahomamxue@ou.edu

MS268

Numerical Weather Prediction in Two Dimensionswith Topography, using a Finite Volume Method

We aim to study a finite volume scheme to solve the twodimensional inviscid primitive equations of the atmospherewith humidity and saturation, in presence of topographyand subject to physically plausible boundary conditions tothe system of equations. The equations are a nonlinearsystem of equations close to the Euler equations (the in-viscid Primitive Equations), which are coupled with theequation for the content of water vapor. These equationsform a nonlinear system of partial differential equations,with discontinuities due to the change of phase. A versionof the projection method is introduced to enforce the com-patibility condition on the horizontal velocity field, whichcomes from the boundary conditions. The resulting schemeallows for a significant reduction of the errors near the to-pography when compared to more standard finite volumeschemes. In the numerical simulations, we first present theconvergence results that are satisfied by the solutions simu-lated by our scheme when compared to particular analyticsolutions. We then report on numerical experiments usingrealistic parameters. Finally, the effects of a random small-scale forcing on the velocity equation is numerically inves-tigated. The numerical results show that such a forcing isresponsible for recurrent large-scale patterns to emerge inthe temperature and velocity fields.

Roger M. TemamInst. for Scientific Comput. and Appl. Math.Indiana Universitytemam@indiana.edu

Arthur BousquetIndiana Universityarthbous@indiana.edu

Mickael Chekroun

University of California, Los AngelesDepartment of Atmospheric and Oceanic Sciencesmchekroun@atmos.ucla.edu

YoungJoon HongIndiana Universityhongy@umail.iu.edu

Joseph J. TribbiaNat’l Center for AtmosphericResearchtribbia@ncar.ucar.edu

MS268

Title Not Available at Time of Publication

Abstract not available at time of publication.

Yau Shu WongUniversity of Albertayauwong@ualberta.ca

MS269

Towards Efficient N-x Contingency Selection UsingGroup Betweenness Centrality

The goal of N - x contingency selection is to pick a sub-set of critical cases to assess their potential to initiate asevere crippling of an electric power grid. Even for a mod-erate sized system there can be an overwhelmingly largenumber of contingency cases that need to be studied. Thenumber grows exponentially with x. This combinatorialexplosion renders any exhaustive search strategy computa-tionally infeasible, even for small to medium sized systems.We propose a novel method for N - x contingency selectionfor x ¿ 1 using group betweenness centrality and show thatcomputation can be relatively decoupled from the prob-lem size. Thus, making contingency analysis feasible forlarge systems with x ¿ 1. Consequently, it may be that N- x (for x ¿ 1) contingency selection can be effectively de-ployed despite the combinatorial explosion of the numberof potential N - x contingencies.

Mahantesh HalappanavarPacific Northwest National Laboratoryhala@pnnl.gov

Yousu ChenPacific Northwest National Labyousu.chen@pnnl.gov

Zhenyu HuangPacific Northwest National Laboratoryzhenyu.huang@pnnl.gov

MS269

Computational Study of Security-Constrained Eco-nomic Dispatch with Multi-Stage Rescheduling

Security-constrained economic dispatch with multiplestages of rescheduling gives rise to a linear program thatis not solvable by traditional LP methods due to its largesize. We devise a series of algorithmic enhancements basedon the Benders’ decomposition method to ameliorate thecomputational difficulty. We also propose a set of onlinemeasures to correct infeasibility encountered in the solu-tion process. The approach, coded in GAMS, is able to

212 CS15 Abstracts

process large network cases.

Yanchao LiuUniversity of Wisconsinyliu67@wisc.edu

Michael C. FerrisUniversity of WisconsinDepartment of Computer Scienceferris@cs.wisc.edu

Feng ZhaoISO New Englandfzhao@iso-ne.com

MS269

Moment-Based Relaxations of the Optimal PowerFlow Problem

The optimal power flow (OPF) problem seeks an optimaloperating point for an electric power system subject to con-straints from both the network physics and engineering lim-its. We present a hierarchy of moment-based convex relax-ations that globally solve many non-convex OPF problemsfor which existing relaxations fail. This talk demonstratesthe capabilities of the moment relaxations using illustra-tions of the feasible spaces of small example OPF problems.We also describe recent work on computational improve-ments for the moment relaxations, including the exploita-tion of sparsity, which enable global solution of larger OPFproblems.

Daniel Molzahn, Ian HiskensUniversity of Michigandan.molzahn@gmail.com, hiskens@umich.edu

MS269

Decomposition Algorithms for Transmission andGeneration Investment Planning

Stochastic transmission and generation expansion plan-ning models are receiving increasing attention among re-searchers today. They are being used to explicitly modeluncertainties that result from the increasing penetrationof renewable energy technologies, as well as from long-term market and regulatory conditions. However, existingcommercial planning tools still lack stochastic capabilities.We propose a two-stage investment-planning model thattakes into account the aforementioned uncertainties, andwe describe a scalable decomposition algorithm to solvereal-sized problems. An application of our algorithm isillustrated using a 240-bus network representation of theWestern Electricity Coordinating Council. We discuss itsperformance when implemented in both the Red Mesa/Skysupercomputer and a commodity multi-core workstation.

Francisco MunozSandia National Laboratoriesfdmunoz@sandia.gov

Jean-Paul WatsonSandia National LaboratoriesDiscrete Math and Complex Systemsjwatson@sandia.gov

MS270

QuickSched - Using Tasks for Massively Parallel

Hybrid Shared/distributed Memory Computing

Task-based parallelism is a well-known paradigm for effi-cient and scalable shared-memory parallel computing. Inthis talk, we will present QuickSched, a library for task-based parallelism which extends the usual model of tasksand dependencies by conflicts between tasks, and by speci-fying explicitly which resources are used by which task. Weshow how this approach allows us to provide good scalingfor problems with complex task hierarchies. We also showhow QuickSched extends task-based parallelism to CUDA-based GPUs. The task/resource decomposition is also use-ful for hybrid shared/distributed-memory computations,e.g. on clusters of multicores. The task graph can beused to equitably partition the work involved in a compu-tation over a set of distributed-memory nodes, as opposedto simply partitioning the data. Furthermore, the task-based system can be used to implement fully asynchronouscommunication between distributed-memory nodes on topof MPI.

Pedro GonnetUniversity of Oxfordgonnet@maths.ox.ac.uk

MS270

Parallelization Techniques for Tsunami SimulationUsing Space-Fillig-Curve Orders

Samo(oa)2 is a parallel code for element-oriented numer-ical solution of PDEs based on space-filling curve traver-sals. Heuristics and methods for adaptive, parallel gridsare gained by sequential element orders induced by theSierpinski curve, which provide an efficient approach thatwe use as basis for an application framework. We imple-mented a model that simulates tsunamis originating fromtime-dependent sea-floor displacements computed from anearthquake simulation (Galvez et al.). Parallel perfor-mance was studied with hybrid OpenMP/MPI paralleliza-tion and several load balancing techniques that exploit in-herent properties of the space-filling curve.

Michael Bader, Oliver MeisterTechnische Universitat Munchenbader@in.tum.de, meistero@in.tum.de

MS270

A Patchwork Family - Task Distribution Patternsfor Shallow Water Equations on Patch-structuredAMR Grids

Spacetrees holding regular Cartesian patches are a powerfulformalism to describe dynamically adaptive Cartesian gridsthat scale on manycores. In previous work, we successfullyused this formalism to solve shallow water equations. Thechoice of a proper block size here is delicate. While largeblock sizes foster loop parallelism and vectorisation, theyrestrict the adaptivity’s granularity. They increase the to-tal memory footprint and lower the numerical accuracy perinvested byte. Though small patches exhibit a high inter-block concurrency they are surprisingly outperformed byhuge blocks processed by a plain parallel-for on Xeon Phis.This insight from our previous work has motivated us tointroduce algorithms that automatically detect assembliesof patches that can be fused into one big patch and thento replace the assemblies by such a regular data structure.The present talk rolls back to a small-patch formulationand studies the patch performance, in particular the con-currency, en detail. We propose to formalise inter-block

CS15 Abstracts 213

parallelism as tasks each representing one patch update.These tasks then are fired into a scheduler to be deployedamong the cores. We study the arising distribution pat-terns and try to put the best-case data and task assign-ment into relation to the data access patterns of the fusedpatches.

Tobias WeinzierlDurham Universitytobias.weinzierl@durham.ac.uk

MS270

Understanding Tsunami and Hurricane Depositswith a Mess-Scale Model for Sediment Dynamics

A meaningful event history for storms and tsunamis doesnot only include the number of events, but also containsinformation of the magnitude of each event. Conventionalmethods to simulate the sediment dynamics in tsunamisand storms have so far failed to reproduce the fine de-tail that real deposits feature. We employ a meso-scaleapproach to do this with some success. Our model runson HPC platforms containing multi-CPU and multi-GPUachitectures.

Robert Weiss, Wei ChengVirginia TechDepartment of Geosciencesweiszr@vt.edu, chengwei@vt.edu

MS271

Block Adaptive MHD Simulations for Solar Coro-nal Dynamics

I will present the open source MPI-AMRVAC simulationtoolkit [Keppens et al., 2012, JCP 231, 718-744], with afocus on solar physical applications modeled by its mag-netohydrodynamic module. Spatial discretizations avail-able cover standard shock-capturing finite volume algo-rithms, but also extensions to conservative high-order fi-nite difference schemes, both employing many flavors oflimited reconstruction strategies. Multi-step explicit timestepping includes strong stability preserving high orderRunge-Kutta steppers to obtain stable evolutions in multi-dimensional applications realizing up to fourth order accu-racy in space and time. The parallel scaling of the code isdiscussed and we obtain excellent weak scaling up to 30000processors allowing to exploit modern peta-scale infrastruc-ture. Solar physics applications target the formation of fluxrope topologies through boundary-driven shearing of mag-netic arcades, following the in situ condensation of promi-nences in radiatively controlled evolutions of arcades andfluxropes, and the enigmatic phenomenon of coronal rain,where small-scale condensations repeatedly form and raindown in thermodynamically structured magnetic arcades.

Rony KeppensKU LeuvenCentre for Mathematical Plasma-Astrophysicsrony.keppens@wis.kuleuven.be

MS271

Globally Divergence-Free Projection Methods forIdeal Magnetohydrodynamics

It has been long established in the literature that control-ling magnetic field divergence errors in compressible mag-netohydrodynamic (MHD) simulations is necessary for nu-merical stability. Many approaches exist to achieve either

approximately or exactly divergence-free discrete magneticfield values, including hyperbolic divergence-cleaning, con-strained transport, and elliptic projection techniques. Inthis work we develop a high-order discontinuous Galerkinversion of the elliptic projection method that produces aglobally divergence-free magnetic field. After developingit, we show how to efficiently implement this method bothon Cartesian and unstructured grids. The resulting schemeis applied to several standard test cases.

James A. RossmanithIowa State UniversityDeparment of Mathematicsrossmani@iastate.edu

MS271

Multi-Fluid Plasma Modeling Through the Colli-sional Transition Regime

Plasmas consist of charged particles that interact throughelectromagnetic fields and collisions. Neutral particleswhen present interact only through collisions. For low col-lisionality, a multi-species kinetic model must be used. Forhigh collisionality, a fluid model with lower dimensional-ity can be used. Multi-fluid plasma models approximatethe velocity distribution function by a limited number ofmoments for each species. Models with higher momentsextend the region of validity and relax the assumption oflocal thermodynamic equilibrium.

Uri Shumlak, Andrew HoAerospace and Energetics Research ProgramUniversity of Washingtonshumlak@uw.edu, andrewh0@uw.edu

Robert LillyUniversity of Washingtonrlilly@aa.washington.edu

Sean MillerAerospace and Energetics Research ProgramUniversity of Washingtonsmiller3@uw.edu

Noah F. Reddell, Eder SousaUniversity of Washingtonreddell@uw.edu, sousae@uw.edu

MS271

Positivity-Preserving Weno Schemes with Con-strained Transport for Ideal MHD

We will present a novel positivity-preserving flux limitingtechnique developed for WENO schemes to solve idea mag-netohydrodynamic (MHD) equations. There are two mainsteps in our MHD solver: first updating conservative quan-tities by WENO scheme with positivity-preserving limiterand then correcting the magnetic field and total energy bya high-order constrained transport approach. Several ex-amples are presented to verify the order of accuracy and todemonstrate the efficiency of positivity-preserving limiter.

Qi TangDepartment of MathematicsMichigan State University

214 CS15 Abstracts

tangqi@msu.edu

MS272

A High-Order Global Discontinuous Galerkin Non-Hydrostatic Atmospheric Model Using Hevi TimeIntegration Scheme

Availability of peta-scale computing resources facilitate de-velopment of high-resolution non-hydrostatic (NH) atmo-spheric model at a global scale. Discontinuous Galerkin(DG) method is an ideal candidate for such model de-velopment because of its inherent conservation property,geometric flexibility and excellent parallel efficiency. Weconsider a NH atmospheric model based on DG spatialdiscretization on cubed-sphere grid. The model uses thehorizontally-explicit and vertical-implicit (HEVI) operator-split time integration method to overcome the CFL limi-tation resulting from the small vertical grid-spacing, andis constrained only by the minimum horizontal resolution.The performance of the DG-HEVI model will be evaluatedthrough a suite of benchmark test cases.

Ram NairNCARInstitute for Mathematics Applied to Geosciencesrnair@ucar.edu

Lei BaoUniversity of Colorado at BoulderDept. of Applied Mathematicslei.bao@colorado.edu

MS272

Vertical Discretization of Geophysical Flows withthe Hybrid Finite Element Method - Normal Modeand Wave Dispersion Properties

The Hybrid Finite Element Method is a new techniquethat takes advantage of the arbitrary order of accuracy ofthe discontinuous Galerkin and Spectral Element methodsand provides a combined, natural setting for the imple-mentation of grid staggering. We present a discrete nor-mal mode analysis of this method for the vertical directionusing the linearized Euler equations. 2-D simulations willbe shown demonstrating atmospheric waves reproduced bythe HFEM compared to traditional methods.

Jorge E. GuerraDepartment of Land, Air and Water ResourcesUniversity of California, Davisjeguerra@ucdavis.edu

Paul UllrichUniversity of California, Davispaullrich@ucdavis.edu

MS272

Toward Exa-Scale Computing in CAM-SE

Supercomputers are projected to achieve exa-flop scaleswithin the next fire years, providing enough computa-tional power to perform climate simulations with lateralresolutions approaching or exceeding the hydrostatic bar-rier. To perform accurate simulations at these resolutions,CAM-SE will require new technologies including: nonhy-drostatic dynamical solvers, increased vertical accuracy,improved variable-resolution grids, and scale-aware param-eterizations. We will discuss the need for these improve-

ments and present our progress to date in their implemen-tation.

David M. HallUniversity of Colorado at BoulderDepartment of Computer Sciencedavid.hall@colorado.edu

Henry TufoNCARUniversity of Colorado at Bouldertufo@cs.colorado.edu

MS272

Tempest: Efficient Computation of AtmosphericFlows Using High-Order Local DiscretizationMethods

The Tempest Framework composes several numericalmethods to easily facilitate intercomparison of non-hydrostatic atmospheric flow calculations on the sphere.This framework includes the implementations of Spec-tral Elements, Discontinuous Galerkin, Flux Reconstruc-tion, and Hybrid Finite Element methods with the goal ofachieving optimal accuracy and efficiency in computing thesolution of atmospheric problems. Several advantages ofthis approach are discussed such as: improved pressure gra-dient calculation, numerical stability by vertical/horizontalsplitting, arbitrary order of accuracy, etc. The local nu-merical discretization allows for high performance parallelcomputation and efficient inclusion of parameterizations.

Paul UllrichUniversity of California, Davispaullrich@ucdavis.edu

MS273

Ongoing Developments in BigDFT towards the ab-initio Computation of Resonant States

Siegert’s resonant states provide a convenient description ofunoccupied electronic states of atoms and molecules, sincefew (discrete) resonant states carry as much informationas many (in principle infinite) continuum states. The com-plex scaling method, and generalizations thereof, allowsone to compute resonant states as particular eigenstates ofcomplex-symmetric Hamiltonians. In my presentation, Iwill discuss the application of Polizzi’s FEAST eigensolverto the iterative, matrix-free extraction of resonant statesfrom complex-scaled Kohn-Sham Hamiltonians.

Alessandro CerioniInstitute of Nanosciences and CryogenyCEA - Grenoblealessandro.cerioni@gmail.com

Luigi GenoveseInstitut Nanosciences et Cryogenie, CEAluigi.genovese@cea.fr

Thierry DeutschInstitute of Nanosciences and CryogenyCEAthierry.deutsch@cea.fr

Ivan DucheminInstitute of Nanosciences and CryogenyCEA Franceivan.duchemin@cea.fr

CS15 Abstracts 215

Maxime MoriniereInstitute of Nanosciences and CryogenyCEA - Grenoblemaxime.moriniere@cea.fr

MS273

Planning the Next Generation of Electronic Struc-ture Codes

Pseudopotential density functional theory implemented inreal space provides a means for computing the properties ofmaterials in many different forms, including liquids, solids,and nanoscale structures. Current approaches yield self-consistent solutions for systems with thousands of atoms.However, there remain systems where quantum mechani-cal accuracy is desired, but scalability proves to be a hin-drance. We will present an overview of our work on algo-rithms for this problem, which performs spectrum slicingin the eigensolver.

James R. ChelikowskyInstitute for Computational Engineering and SciencesUniversity of Texas at AUstinjrc@utexas.edu

MS273

A Projected Preconditioned Conjugate GradientAlgorithm for Eigenvalue Calculation

We examine a projected gradient algorithm for computinga relatively large number of lowest eigenvalues of a Hermi-tian matrix. The algorithm performs fewer Rayleigh-Ritzcalculations than some of the existing algorithms, thus hasbetter parallel scalability. It is relatively easy to imple-ment (for example in the Quantum Espresso package). Wewill discuss a number of practical issues for implementingthis algorithm, and demonstrate its performance in Kohn-Sham density functional theory based electronic structurecalculations.

Chao Yang, Eugene VecharynskiLawrence Berkeley National Labcyang@lbl.gov, evecharynski@lbl.gov

John PaskLawrence Livemore National Labpask1@llnl.gov

MS273

Updating Strategies for Efficient Large-Scale Elec-tronic Structure Calculations

We give an introduction to our recently published BlockedHouseholder-CholeskyQR algorithm which has been devel-oped for the dense symmetric eigensolver ELPA, whereatthe QR-decomposition of tall and skinny matrices repre-sents an important substep. Further, we show the benefitsof this algorithm on today’s HPC systems in terms of par-allel efficiency. Finally, we give an outlook on modifyingthe classical ELPA solver,e.g. for updating the eigenspaceinformation in case of small changes.

Roland Wittmann, Thomas K. HuckleInstitut fuer InformatikTechnische Universitaet Muenchen

wittmanr@in.tum.de, huckle@in.tum.de

MS274

Scalable Algorithms for Optimal Control of Sys-tems Governed by PDEs under Uncertainty

We focus on optimal control of systems governed by PDEswith random coefficient functions. We seek controls thatminimize an objective function that incorporates mean andvariance of the control objective. To enable applicationsto problems with infinite-dimensional (high-dimensionalwhen discretized) parameters, we consider linearization ofthe control objective at the mean of the uncertain param-eters. As application, we consider optimal control of aporous medium flow model with a random permeabilityfield.

Alen AlexanderianUniversity of Texas at Austinalen@ices.utexas.edu

Noemi PetraUniversity of California, Mercednpetra@ucmerced.edu

Georg StadlerCourant Institute for Mathematical SciencesNew York Universitystadler@cims.nyu.edu

Omar GhattasThe University of Texas at Austinomar@ices.utexas.edu

MS274

A Scalable Compositional Approach to UncertaintyQuantification for the Optimization under Uncer-tainty of Multi-physics Systems

Complex multi-physics systems often exhibit a great dealof uncertainty due to unexpected interactions. To ensurea sufficiently reliable and robust system, rigorous designunder uncertainty must be carried out with models ca-pable of precisely representing multi-physics interactions.We propose a compositional approach to uncertainty quan-tification based on importance sampling that enables anoffline/online approach to optimization under uncertaintywith high-fidelity physics-based models. Our approach isdemonstrated on the design of a gas turbine blade.

Doug AllaireTexas A&Mdallaire@tamu.edu

Sergio AmaralDepartment of Aeronautics & AstronauticsMassachusetts Institute of Technologysamaral@mit.edu

Kaiyu LiTexas A&Mkaiyuli@tamu.edu

Karen E. WillcoxMassachusetts Institute of Technology

216 CS15 Abstracts

kwillcox@MIT.EDU

MS274

Stochastic Reduced-Order Models in Optimizationand Inverse Problems

This work presents a novel approach for inverse problemsin the presence of uncertainty using stochastic reduced or-der models (SROMs). Given the statistics of an uncertainobserved quantity, the statistics of unknown system pa-rameters are estimated through the solution of a stochasticoptimization problem. The proposed framework is basedon the representation of a random quantity using a SROMan optimal discrete approximation to a continuous randomelement that permits efficient and non-intrusive stochasticcomputations.

Wilkins AquinoAssociate ProfessorDept. of Civil and Environmental Engineering, DukeUniv.wa20@duke.edu

James WarnerNasa Langley Research Centerjw666@cornell.edu

Mircea GrigoriuCornell Universitymdg12@cornell.edu

MS274

Integration of Approximate Schur Preconditionersand SQP Algorithms for Nonlinear PDE Optimiza-tion under Uncertainty

We study the integration of Schur preconditioners for opti-mality systems and matrix-free composite-step sequentialquadratic programming (SQP) algorithms in the context ofpartial differential equation (PDE) constrained optimiza-tion under uncertainty. Our approach extends the recentlyintroduced optimal solvers for PDE-constrained optimiza-tion to a wide range of problems in optimal engineeringdesign, including those governed by PDEs with randominputs. We present numerical examples in thermal-fluidcontrol, acoustic design and topology optimization.

Denis RidzalSandia National Laboratoriesdridzal@sandia.gov

Drew P. KouriOptimization and Uncertainty QuantificationSandia National Laboratoriesdpkouri@sandia.gov

Bart G. Van Bloemen WaandersSandia National Laboratoriesbartv@sandia.gov

MS275

Recursive Multilevel Approximate Inverse-BasedPreconditioning

We present an algebraic recursive multilevel approximateinverse preconditioner based on a distributed Schur com-plement formulation, for solving systems of linear equa-tions. The proposed solver uses recursive combinatorial

algorithms to preprocess the matrix structure and to max-imize sparsity in the approximate inverse factors. We de-scribe the preordering, analysis and factorization phaseof the construction, we assess their performance, considerstrategies for automatic parameter selection, and we dis-cuss applications to preconditioning least-squares prob-lems.

Yiming BuUniversity of Groningeny.bu@rug.nl

Bruno CarpentieriInsitute for Mathematics and ComputationUniversity of Gronenginbcarpentieri@gmail.com

MS275

A Recursive Multilevel Approximate Inverse-Based Preconditioner for Solving General LinearSystems

Abstract not available at time of publication.

Bruno CarpentieriInsitute for Mathematics and ComputationUniversity of Gronenginbcarpentieri@gmail.com

MS275

Krylov Subspace Methods Preconditioned by InnerIterations for Rank-Deficient Least Squares Prob-lems

Inner-iteration preconditioning performed by several iter-ations of stationary iterative methods including the SOR-type method is applied to Krylov subspace methods suchas the CG-, MINRES-, and GMRES-type methods for solv-ing rank-deficient least squares problems. We present the-oretical justifications for using these methods. Numericalexperiments on large sparse problems show that the pro-posed methods are more robust and efficient compared toprevious methods for some problems.

Keiichi MorikuniInstiute of Computer ScienceAcademy of Sciences of the Czech Republicmorikuni@cs.cas.cz

Miroslav RozloznikInstitute of Computer ScienceCzech Academy of Sciencesmiro@cs.cas.cz

Ken HayamiNational Institute of Informaticshayami@nii.ac.jp

MS275

Global Adaptive Dropping in Incomplete Factor-izations

Incomplete factorizations represent an important compo-nent in solving large sparse systems of equations and linearleast squares problems. A new approach for SPD matricesis described. It is based on the factorized approximate in-verse that links together the inverse and direct factors. Thestrategy is motivated by the floating-point behavior of the

CS15 Abstracts 217

decomposition that implies an algorithm where droppingof the incomplete decomposition mimicks propagation ofthe rounding errors. Numerical experiments demonstrateits efficiency.

Miroslav TumaAcademy of Sciences of the Czech RepublicInstitute of Computer Sciencetuma@cs.cas.cz

Jiri KopalTechnical University in Liberecjiri.kopal@tul.cz

Miro RozloznikCzech Academy of SciencesPrague, Czech Republicmiro@cs.cas.cz

MS276

Model-Based Sketching and Recovery with Ex-panders

Linear sketching and recovery of sparse vectors with ran-domly constructed sparse matrices has numerous appli-cations in several areas, including compressive sensing,data stream computing, graph sketching, and combinato-rial group testing. This work considers the same prob-lem with the added twist that the sparse coefficients ofthe unknown vector exhibit further correlations as deter-mined by a known sparsity model. We prove that exploit-ing model-based sparsity in recovery provably reduces thesketch size without sacrificing recovery quality. We alsopresent the model-expander iterative hard thresholding al-gorithm for efficient recovery of model sparse signals fromlinear sketches.

Luca Baldassarre

Ecole Polytechnique Federale de Lausanneluca.baldassarre@epfl.ch

Volkan CevherEPFLvolkan.cevher@epfl.ch

MS276

Performance Limits of Ideal Decoders in Linear In-verse Problems

In this talk, we focus on the fundamental performance lim-its that can be expected from an ideal decoder given ageneral model in a linear inverse problem. We link theexistence of an instance optimal decoder and the NullSpace Property of the measurement operator in very gen-eral cases. We prove that in this general setting, the lower-RIP yields instance optimality with an operator-dependentnorm called the M-norm while the upper-RIP allows to up-per bound this M-norm by an operator-independent norm.

Anthony BourrierIRISAanthony.bourrier@gipsa-lab.fr

MS276

Statistical Methods in Compressive Sensing: The-ory and Experiment

This talk is concerned with compressive sensing of signals

drawn from a Gaussian mixture model (GMM) with sparseprecision matrices. Previous work has shown: (i) a signaldrawn from a given GMM can be perfectly reconstructedfrom r noise-free measurements if the (dominant) rank ofeach covariance matrix is less than r; (ii) a sparse Gaus-sian graphical model can be efficiently estimated from fully-observed training signals using graphical lasso. This paperaddresses a problem more challenging than both (i) and(ii), by assuming that the GMM is unknown and each sig-nal is only partially observed through incomplete linearmeasurements. Under these challenging assumptions, wedevelop a hierarchical Bayesian method to simultaneouslyestimate the GMM and recover the signals using solely theincomplete measurements and a Bayesian shrinkage priorthat promotes sparsity of the Gaussian precision matrices.In addition, we provide theoretical performance bounds torelate the reconstruction error to the number of signals forwhich measurements are available, the sparsity level of pre-cision matrices, and the incompleteness of measurements.The proposed method is demonstrated extensively on com-pressive sensing of imagery and video, and the results withsimulated and hardware-acquired real measurements showsignificant performance improvement over state-of-the-artmethods.

Larry CarinElectrical & Computer EngineeringDuke Universitylcarin@duke.edu

MS276

Practical Compressed Sensing: On AsymptoticStructure

Compressed Sensing allows recovery from undersampleddata, a desirable feat in many applications, e.g. MRI, mi-croscopy, tomography, imaging, interferometry etc. How-ever, a wide gap exists between practice and traditionalCS theory as some of its principles such as sparsity andincoherence are unsuitable. This talk shows how new CSprinciples, namely asymptotic sparsity, asymptotic inco-herence and multilevel sampling, provide a better fit forpractical problems and help to better understand under-lying phenomena and significantly improve results in real-world applications.

Bogdan RomanUniversity of Cambridgeabr28@cam.ac.uk

MS277

Optimal Energy Conserving Local DiscontinuousGalerkin Methods for Second-Order Wave Equa-tion in Heterogeneous Media

Abstract not available at time of publication.

Ching-Shan ChouDepartment of MathematicsOhio State Universitychou@math.ohio-state.edu

MS277

Performance Analysis of High-Order DiscontinuousGalerkin Methods for First and Second Order For-

218 CS15 Abstracts

mulation of the Wave Equation

Abstract not available at time of publication.

Julien DiazTeam-Project Magique-3DINRIA Bordeaux Sud-Ouestjulien.diaz@inria.fr

MS277

The Double Absorbing Boundary Formulation ofComplete Radiation Boundary Conditions

Complete radiation boundary conditions are local se-quences implementing optimal rational approximations tothe exact time-domain DtN map. Our original implemen-tation of CRBCs was for first order systems and was notdirectly generalizable to second order formulations. Thedouble absorbing boundary method provides an easy al-ternative formulation which can be directly applied to sec-ond order equations. We will outline the stability theory ofdouble absorbing boundaries, and demonstrate implemen-tations for a variety of volume discretizations.

Thomas M. HagstromSouthern Methodist UniversityDepartment of Mathematicsthagstrom@smu.edu

MS277

Second-Order Wave Equation with Uncertain Pa-rameters: Analysis and Computation

Abstract not available at time of publication.

Mohammed MotamedDepartment of Mathematics and StatisticsThe University of New Mexicomotamed@math.unm.edu

MS278

Adaptive Time Domain Boundary Element Meth-ods (TD-BEM) for Scattering Problems

We investigate a generalized version of the MOT methodfor TD-BEM, which allows variable time-steps in an adap-tive algorithm. The residual error estimator is based onnew regularity results. We also discuss numerical quadra-ture schemes for the evaluation of the time-dependentGalerkin elements. Our theoretical results are underlinedby several numerical examples.

Matthias Maischak, Matthias GlafkeBrunel Universitymatthias.maischak@brunel.ac.uk, m glaefke@hotmail.com

MS278

Convolution Quadrature Discretization of VolumeIntegral Equations

Time domain scattering from an inhomogeneous penetra-ble medium can be formulated as a time domain volumeintegral equation. This equation can be discretized in timeusing convolution quadrature. Using a Fourier basis inspace, the resulting integral operators can be diagonalizedto allow fast operator evaluation. The fully discrete systemcan then be solved by marching on in time and an itera-tive two grid procedure. We provide an analysis of this

approach and some numerical results.

Peter B. MonkDepartment of Mathematical SciencesUniversity of Delawaremonk@math.udel.edu

MS278

An Exponentially Convergent ConvolutionQuadrature Method for Time-Domain Bound-ary Integral Equations

The Convolution Quadrature method is a recent methodto solve time-domain wave problems with Boundary Ele-ment Methods. We present new results on the exponen-tially convergence of the CQ solution to the exact solutionof the underlying time-stepping scheme. These results relyon the analyticity of the frequency-domain solution and onthe location of the resonant poles. We study the influenceon the convergence of the scheme used for the time dis-cretisation, the contour involved in the inverse transform,and the number of frequency problems solved.

Nicolas Salles, Timo BetckeUniversity College Londonn.salles@ucl.ac.uk, t.betcke@ucl.ac.uk

MS278

Fast Galerkin Method for Parabolic Space-TimeBoundary Integral Equations

Layer potentials of the heat equation are coercive in appro-priate anisotropic Sobolev spaces. This fact implies stabil-ity and error estimates for Galerkin methods. The resultinglinear systems are block-lower triangular and can be solvedby block-forward elimination. To handle the cost of densematrix calculation a space-time version of the fast multi-pole method can be used, which allows the computationa matrix vector product with nearly optimal cost. Fur-ther, if the space-time meshwidths satisfy ht ≤ Ch2

x theconditioning of the linear system in each time step doesnot grow with mesh refinements. We will also discuss theapplication of the methodology to three-dimensional tran-sient Stokes flow. Perhaps surprisingly, this is not straightforward, because of different properties of the fundamentalsolutions of the heat and Stokes equations.

Johannes TauschSouthern Methodist UniversityDepartment of Mathematicstausch@mail.smu.edu

MS279

Overview Co-Design at the DOE NNSA Trilabs

Los Alamos, Lawrence Livermore, and Sandia Nationallaboratories, collectively know as the Department of En-ergy NNSA Trilabs, have been conducting a variety of code-sign studies. In this presentation we give an overview of arecently completed trilab milestone that focused on an ex-ploration of the capabilities and characteristics of emergingand expected future architectures.

Richard BarrettSandia National Laboratories

CS15 Abstracts 219

rfbarre@sandia.gov

MS279

The ∇-Nabla Time-Composite Approach for Multi-Physics Applications Productivity

The numerical-analysis specific ∇ language provides anew approach for integrating next generation multi-physics large-scale scientific applications. Reflectionand hierarchical-logical-time composition are combined todemonstrate productive practices and abilities for agileproduction at extreme-scale. The gain in abstraction with∇ during design improves portability, allowing composablesoftware integration for continually changing hardware ar-chitectures. This presentation will illustrate these new pos-sibilities on several proxies to build a multi-physics appli-cation within the above-cited codesign space.

Jean-Sylvain CamierCEA, DAM, DIFJean-Sylvain.Camier@cea.fr

MS279

Multi-Material ALE in the Blast Code

The goal of the BLAST project is to develop a new multi-physics ALE code based on higher-order finite elements. Inthis talk I will explain how we handle multi-material mixedcells during the Lagrangian and remap phases. The maintopics will include the application of higher-order finite ele-ments to multi-material closure models, remap approachesthat preserve monotonicity, conservation and synchroniza-tion between different fields and materials, elimination ofartificial mixing during remap.

Vladimir TomovLawrence Livermore National Laboratorytomov2@llnl.gov

MS279

Co-Design Studies Using Mini-Multifluid-Ppm

Abstract not available at time of publication.

Paul R. WoodwardLaboratory for Computational Science and EngineeringUniversity of Minnesotapaul@lcse.umn.edu

MS280

Modeling Across the Undergraduate Curriculum

We report on the findings of the undergraduate group forthe Modeling Across the Curriculum II Workshop. We dis-cuss the curricular gaps between the status quo in academiatoday and what is needed to meet the challenges of a glob-ally competitive workforce in the 21st Century. Along thelines of the two NRC reports Mathematical Sciences 2025report and its companion piece Fueling Discovery and In-novation, we discuss several recommendations that camefrom our group.

Jeffrey HumpherysBrigham Young University

jeffh@math.byu.edu

MS280

Mathematical Modeling in the Early Grades

The common core state standards for mathematics specif-ically name modeling with mathematics as a mathemati-cal practice. Applied mathematicians, especially those en-gaged in mathematical modeling are in a great positionto work with mathematics education specialists, teachers,curriculum developers and students to decide how studentswill enact this standard in the classroom. I will sharethe conclusions of such a group, describe a new three yearproject and solicit feedback from the audience about thepotential for mathematical modeling in the early grades.

Rachel LevyHarvey Mudd Collegelevy@hmc.edu

MS280

Applied and Computational Mathematics at theHigh School Level

Secondary schools in the US offer their students a varyinglevel of access to rich mathematical modeling topics. Someschools offer entire courses centered on mathematical mod-eling practices while others offer very little. Our workinggroup has developed a set of recommendations for ques-tions to investigate and tasks to carry out that might helpinfuse models and modeling across the curriculum. Pleasejoin us to explore these ideas further in a constructive con-versation.

Katherine SochaMath for Americaksocha@parkschool.net

Kathleen FowlerClarkson UniversityDepartment of Mathematicskfowler@clarkson.edu

MS280

Modeling Across the Curriculum: Introductionand Overview

This talk will begin with background information on theModeling across the Curriculum, MaC, initiative, an NSF-sponsored SIAM program aimed at advancing modelingand computational applied mathematics throughout theeducational spectrum. The main focus will be on the sec-ond MaC workshop held in January 2014 and the resultingreport and recommendations. The subsequent talks willgo more deeply into the three primary themes of the work-shops.

Peter R. TurnerClarkson UniversitySchool of Arts & Sciencespturner@clarkson.edu

MS281

Singular Values and Convex Programming forPower System Synchrophasor Data Management

This talk centers on the efficient processing of the obser-vations of phasor measurement units (PMUs) for power

220 CS15 Abstracts

system monitoring. Different from traditional PMU dataanalysis that typically analyzes individual PMU channelsseparately, we propose a spatial-temporal framework of col-lectively processing measurements of PMUs in electricallyclose regions. Leveraging the low-dimensionality of PMUdata, various data management issues such as missing datarecovery and data substitution detection can be addressedby solving computationally efficient convex programs.

Joe Chow, Meng WangRenssalaer Polytechnic Institutechowj@rpi.edu, wangm7@rpi.edu

MS281

Policy-switching Schemes for Power System Pro-tection

Current power system protection schemes have proven use-ful in order to mitigate several localized contingencies.However, there is still ample heterogeneity and uncertaintyin the design of wide-area Remedial Action Schemes (RAS)for effective restraint of large cascading outages. We pro-pose a policy-switching approach to select optimal protec-tion schemes during and after a contingency. This talkdescribes the application of the method to a benchmarkingtest case in order to achieve optimal power system perfor-mance during emergency situations.

Rich Meier, Jesse Hostetler, Eduardo Cotilla-Sanchez,Alan FernOregon State Universitymeierr@eecs.oregonstate.edu, hostetlj@onid.orst.edu,ecs@eecs.oregonstate.edu, afern@eecs.oregonstate.edu

MS281

Exploring State Estimation Techniques to Accom-modate non-Gaussian Noises

Measurement data have always been a key element of powergrid operation and planning. However, the use of measure-ment data is based on a key assumption of Gaussian noises.Driven by the investment from the American Recovery andReinvestment Act of 2009, thousands more sensors are be-ing put into the power grid. The rate and volume of theemerging measurement data are hundred times higher andlarger. Power grid operation and planning functions are be-coming more and more dependent on measurement data.More accurate understanding of the noise properties of thedata is critical and can make large impact on the outcomeof data applications. This talk will examine real phasormeasurements and present latest findings in noise proper-ties as well as potential impact on mathematical algorithmsfor power grid analysis.

Zhenyu HuangPacific Northwest National Laboratoryzhenyu.huang@pnnl.gov

Ning ZhouBinghamton Universityningzhou@binghamton.edu

Mihai AnitescuArgonne National LaboratoryMathematics and Computer Science Divisionanitescu@mcs.anl.gov

Shaobu WangPacific Northwest National Laboratory

shaobu.wang@pnnl.gov

MS281

Efficient Algorithms for N-x Contingency Analysisfor Power Grids

N-x contingency analysis on power flow evaluates the sta-bility of a power system by simulating the failures of xtransmission lines or generators. Currently each N - x con-tingency analysis is performed independently, but since thenumber of cases increases exponentially with x, this is com-putationally impractical. We propose new algorithms forthe problem by observing that only a small portion of thesystem is changed when a component is removed.

Alex PothenPurdue UniversityDepartment of Computer Scienceapothen@purdue.edu

Yu-Hong YeungPurdue Universityyyeung@purdue.edu

Mahantesh HalappanavarPacific Northwest National Laboratoryhala@pnnl.gov

Zhengyu HuangPNNLzhenyu.huang@pnnl.gov

MS282

A Low-dimensional Approximation to the Stochas-tic Elliptic Interface Problem

In this presentation, we will discuss a numerical method ofstochastic elliptic interface problem with random interface.An efficient finite element scheme is proposed to computethe covariance of the solutions by using a low-dimensionalapproximation of the random input. Error estimate is es-tablished and some numerical tests are performed.

Ju MingBeijing Computational Science Research Centerjming@csrc.ac.cn

MS282

A Finite Element Method for a Stokes InterfaceProblem

We present a higher-order finite element method for solv-ing a class of interface problems in two dimensions. Themethod is based on correction terms added to the right-hand side of the natural method. We prove optimal errorestimates of the method on general quasi-uniform meshesin the maximum norms. In addition, we apply the methodto a Stokes interface problem obtaining optimal result.

Manuel A. Sanchez-UribeBrown Universitymanuel sanchez uribe@brown.edu

MS282

Surfactant Driven Tipstreaming in a Flow Focusing

CS15 Abstracts 221

Geometry

We model a surfactant-mediated tipstreaming in a mi-crofluidic flow focusing geometry. That microfluidicmethod for production of submicrometer and potentiallynanoscale droplets and particles uses the elongational flowalong with dissolved surfactant in one of the liquid phasesto create strong surfaces tension gradient. The concentra-tion of bulk soluble surfactant was found to significantly ef-fect the mode of formation and size of the emitted droplets.By carefully controlling the surfactant concentration andother flow quantities, droplets can be created that are anorder of magnitude or more smaller than the scale of boththe device and droplets produced in the absence of surfac-tant.

Jacek WrobelDepartment of Mathematics, Tulane UniversityCenter for Computational Sciencejwrobel@tulane.edu

Michael SiegelNew Jersey Institute of Technologymisieg@njit.edu

Michael R. BootyDepartment of Mathematical Sciences, NJITbooty@njit.edu

MS282

Immersed Finite Element Methods with EnhancedStability

In this talk, we present new immersed finite element (IFE)methods for the second-order elliptic interface problems.Comparing with classic IFE schemes using Galerkin for-mulation, these new IFE methods contain either partialstabilization terms on interface edges or full stabilizationon all interior edges. A priori error estimates show thatthese new methods converge optimally in correspondingenergy norms. Numerical experiments also indicate thatthese stabilized IFE methods outperform classic IFEs atvicinity of interfaces.

Xu ZhangPurdue Universityxuzhang@purdue.edu

Tao LinDepartment of Mathematics, Virginia Techtlin@math.vt.edu

MS283

Code Generation for Higher Level Spectral Meth-ods with Spiral

The FFT is a ubiquitous tool in signal processing and forsolving large-scale PDEs. Many use cases can be builton top of the 1D FFT, which has a very simple math-ematical definition. However, extracting maximum per-formance on big parallel machines requires rethinking ofthe FFT as highest-level building block. We will investi-gate Spiral-based code generation for higher-level buildingblocks like convolution, interpolation, and Greens Func-tion approaches and their implication of FFT-based per-formance optimization and show the performance potentialof this approach.

Franz Franchetti

Department of Electrical and Computer EngineeringCarnegie Mellon Universityfranzf@ece.cmu.edu

MS283

Numerical Eigenvalue Engine towards Extreme-scale Computing Era

Towards Exa-scale computing Era, we have been study-ing next generation eigenvalue library, which must exploithigh performance, highly parallelism and high portability.EigenExa has been developed and released in August 2013as a prototype of exa-scale library. EigenExa performs onmulti-peta scale system such as K computer and a Blue-Gene/Q. We investigate key points to be innovated in theheritage stage to 10 to 100 fold-scale complex systems. Inthis mini-symposium, project overview, our goal and keytechnologies in exa-scale library will be discussed.

Toshiyuki ImamuraRIKEN Advance Institute for Computational Scienceimamura.toshiyuki@riken.jp

Takeshi FukayaRIKEN, JapanJapantakeshi.fukaya@riken.jp

Yusuke HirotaRIKEN AICSyusuke.hirota@riken.jp

Susumu Yamada, Masahiko MachidaJapan Atomic Energy Agencyyamada.susumu@jaea.go.jp,machida.masahiko@jaea.go.jp

MS283

Automatic Tuning for Parallel FFTs on GPU Clus-ters

In this talk, we propose an implementation of a parallelfast Fourier transform (FFT) with automatic performancetuning on GPU clusters. Because the parallel FFTs requireall-to-all communications, one goal for parallel FFTs onGPU clusters is to minimize the PCI Express transfer timeand the MPI communication time. Performance results ofFFTs on a GPU cluster are reported.

Daisuke TakahashiFaculty of Engineering, Information and SystemsUniversity of Tsukubadaisuke@cs.tsukuba.ac.jp

MS283

Statistical Performance Modeling and Autotuningfor Dense QR Factorization in Hybrid CPU-GPUSystems

We investigate how to adaptively and automatically choosethe block sizes of a dense QR factorization algorithm tomaximize the use of CPU and GPU on the same computingnode. The decision is based on statistical surrogate modelsof performance and an online monitor, which avoids unex-pected occasional performance drops. Numerical resultssuggest that our approaches are efficient and can lead to

222 CS15 Abstracts

near-optimal block sizes.

Ray-Bing ChenDepartment of StatisticsNational Cheng Kung Universityraybingc@gmail.com

Yaohung TsaiDepartment of MatheamticsNational Taiwan Universityev.hunter@gmail.com

Weichung WangInstitute of Applied Mathematical SciencesNational Taiwan Universitywwang@ntu.edu.tw

MS284

Multiphase Sub-Surface Flow Using Moose

Abstract not available at time of publication.

Chris GreenUniversity of Melbourne, Australiachris.green@csiro.au

Jonathan Ennis-KingCSIROjonathan.ennis-king@csiro.au

MS284

Low Mach and Two-Phase Flow Modeling withMoose Applications

A 7-equation two-phase flow fluid model has been imple-mented in the next-generation nuclear reactor safety codeRELAP-7 built upon the MOOSE multiphysics framework.The entropy viscosity method, an artificial viscosity tech-nique for hyperbolic conservation laws [Guermond et al.,Entropy viscosity method for nonlinear conservation laws,Journal of Comput. Phys. 230 (2011) 4248–4267], hasbeen extended to the low-Mach regimes for single and two-phase flows. The entropy viscosity method is a numeri-cal stabilization technique that is spatial-discretization ag-nostic and satisfies the minimum entropy principle. Thefluid flow governing equations are discretized using stan-dard continuous finite elements and an implicit BDF2 timediscretization. The resulting system of nonlinear equationsare solved using the Jacobian-free Newton Krylov solver ofMOOSE. Numerical results will be presented.

Jean C. RagusaDepartment of Nuclear EngineeringTexas A&M Universityjean.ragusa@tamu.edu

Marco DelchiniTexas A&M Universitydelcmo@tamu.edu

Ray A. BerryIdaho National Laboratoryray.berry@inl.gov

MS284

Modeling Nuclear Fuel Behavior with BISON

BISON is a modern finite-element based nuclear fuel per-

formance code that solves the coupled thermo-mechanicsand unsteady species diffusion equations using the paral-lel Jacobian-Free Newton-Krylov framework in MOOSE.BISON can be used to investigate computationally largeproblems, e.g. a full stack of discrete pellets in a fuelrod. We provide a brief overview of the material and be-havioral models and discuss successes with preconditioningand solving the large nonlinear system.

Shane StaffordIdaho National Laboratoryshane.stafford@inl.gov

MS284

Stabilization Methods for High Peclet NumberFlows in Heterogeneous Porous Media

A class of reconstructed Discontinuous Galerkin (rDG)methods are developed for fluid dynamics in heterogeneousporous media. Numerical examples demonstrate that therDG methods are able to maintain stabilization of the so-lution in the case of high Peclet number flows, while ren-dering sharp resolution at the vicinity of large gradientsor discontinuities, indicating a promising methodology forliquid convection in computational hydrogeology.

Yidong XiaIdaho National Laboratoryyidong.xia@inl.gov

Hai HuangIdaho National LaboratoryIdaho National Laboratoryhai.huang@inl.gov

Robert PodgorneyIdaho National Laboratoryrobert.podgorney@inl.gov

MS285

Reassessing the Missing Point Estimation ModelOrder Reduction Method

When applied to nonlinear systems, projection-basedmodel-order reduction requires a second-level approxima-tion to achieve its full potential. This talk introduces ageneralization of one such technique, the so-called MissingPoint Estimation, which is characterized by its simplicityand generality. A greedy sampling algorithm based on arigorous a priori error bound is proposed. The applicationto finite element discretizations will be considered.

Julien CortialSandia National Laboratories (Livermore)Quantitative Modeling and Analysisjulien.cortial@safran.fr

Kevin T. CarlbergSandia National Laboratoriesktcarlb@sandia.gov

MS285

Reduced Basis Methods for Variational Inequalities

We consider parabolic variational inequalities with differ-ent trial and test spaces and a possibly non-coercive bi-linear form. Fine discretizations that are needed for suchproblems resolve in high dimensional problems and in long

CS15 Abstracts 223

computing times. To reduce the dimensionality of theseproblems,we use the Reduced Basis Method. Error es-timators could be obtained by combining Reduced BasisMethods with a space-time formulation of the variationalinequality. We provide numerical results for a heat inequal-ity model.

Silke GlasUniversity of Ulm, Germanysilke.glas@uni-ulm.de

MS285

Parsimonious Data Acquisition for Data-drivenModel Reduction

Data-driven model reduction methods require input froman external source, such as snapshots for POD. Obtain-ing this input can be resource-intensive. This presentationwill discuss methods that limit usage of memory and com-putation time in attempting to meet user-specified errortolerances or basis sizes.

Geoffrey M. OxberryLawrence Livermore National Laboratoryoxberry1@llnl.gov

MS285

An Adaptive Parametrized-Background Data-Weak Approach to State Estimation; Applicationto Heat Transfer Companion Experiments

We present an adaptive Parametrized-Background Data-Weak (PBDW) formulation for data assimilation prob-lems modeled by parametric PDEs. PBDW combines aprior space, which approximates the solution manifold as-sociated with the parametric PDE, and M experimen-tal observations to provide real-time, in-situ state estima-tion. The adaptive procedure exploits a novel a posterioriobservation-based error estimator to refine the prior spaceusing historical data-assimilation solutions. We illustrateour method through a synthetic example and a physicalthermal patch problem.

Tommaso TaddeiMITttaddei@mit.edu

Masayuki Yano, James PennMassachusetts Institute of Technologymyano@mit.edu, pennjam@mit.edu

Anthony T. PateraMassachusetts Institute of TechnologyDepartment of Mechanical Engineeringpatera@mit.edu

MS286

Interweaving PFASST and Parallel Multigrid

The parallel full approximation scheme in space and time(PFASST) has been introduced by Emmett and Minionas an iterative method for the parallelization of ordinarydifferential equations or time-dependent PDEs. On each(time-)level the systems that arise have to be solved to thesame accuracy. The usage of lower accuracy on levels withlarger time steps is natural. In this talk different strategiesfor coupling PFASST iterations with multigrid methods are

presented.

Matthias BoltenUniversity of WuppertalDepartment of Mathematicsbolten@math.uni-wuppertal.de

Michael MinionStanford Universitymlminion@lbl.gov

Robert SpeckJuelich Supercomputing CentreForschungszentrum Juelichr.speck@fz-juelich.de

Matthew EmmettLawrence Berkeley National LaboratoryCenter for Computational Sciences and Engineeringmwemmett@lbl.gov

Daniel RuprechtInstitute of Computational ScienceUniversita della Svizzera italianadaniel.ruprecht@usi.ch

MS286

Towards a Multigrid Perspective of MLSDC

Spectral deferred corrections (SDC) are a class of itera-tive solvers for the collocation formulation of an ODE sys-tem. The multi-level extension MLSDC, which constitutesthe basis for the time-parallel method PFASST, performsSDC sweeps on a full space-time hierarchy and employs anFAS technique well-known from non-linear multigrid meth-ods. In this talk we analyze SDC’s smoothing propertiesand investigate which concepts of standard multigrid the-ory translate to MLSDC and how these can be exploitedfurther.

Dieter Moser, Robert SpeckJuelich Supercomputing CentreForschungszentrum Juelichd.moser@fz-juelich.de, r.speck@fz-juelich.de

Matthias BoltenUniversity of WuppertalDepartment of Mathematicsbolten@math.uni-wuppertal.de

MS286

Parallel in Time Multigrid for Nonlinear Equations

The multigrid reduction in time method (MGRIT) createsa multilevel hierarchy of different temporal discretizations.For nonlinear equations each iteration of the parallel-in-time method requires expensive, nonlinear, spatial solves.Using a Picard method for the nonlinear solver, we investi-gate several methods for reducing the cost of these solves,including reducing solver accuracy on coarser temporal lev-els and introducing spatial coarsening on coarse temporallevels.

Ben O’NeillUniversity of Colorado, Boulder

224 CS15 Abstracts

Ben.Oneill@Colorado.edu

MS286

An Adaptive Spectral Deferred Time Integrator forVesicle Suspensions

Vesicles are deformable and inextensible capsules, filledwith and submerged in a viscous fluid. Their dynamicsare governed by hydrodynamic and elastic forces which canbe formulated as a system of integro-differential-algebraicequations. I will describe a spectral deferred correctionalgorithm that we use to construct high-order vesicle sim-ulations. Then, I will show how we estimate the error withonly one numerical solution and use this to construct anadaptive time stepping scheme.

Bryan D. QuaifeInstitute for Computational Engineering and SciencesUniversity of Texas at Austinquaife@ices.utexas.edu

George BirosUniversity of Texas at Austinbiros@ices.utexas.edu

MS287

Maximizing Throughput on a Dragonfly Network

In this talk, I will present our analysis of a 100+ Petaflop/sprototype machine with a dragonfly network, 92,160 high-radix routers and 8.8 million cores. We compare networkthroughput for various routing strategies, job placementpolicies, and application communication patterns. Ourstudy is based on a novel model that predicts traffic onindividual links for direct, indirect, and adaptive routingstrategies. We analyze results for individual communica-tion patterns and some common parallel job workloads.

Abhinav BhateleLawrence Livermore National Laboratorybhatele@llnl.gov

Nikhil JainUniversity of Illinoisnikhil@illinois.edu

Xiang Ni, Laxmikant V KaleUniversity of Illinois at Urbana-Champaignxiangni2@illinois.edu, kale@illinois.edu

MS287

Topology Aware Mapping using Graph Models forExascale Systems

Communication time of parallel applications is limited byvarious features of the interconnection networks such aslatency or bandwidths of the links. Topology aware taskmapping methods that place application tasks on proces-sors by exploiting information about the underlying net-work can help to avoid such limitations. In this work,by using the graph models for representing the networktopology and applications communication requirements,we study topology aware task mapping methods to reducebottlenecks in the applications’ communication time.

Mehmet DeveciThe Ohio State Universitymdeveci@bmi.osu.edu

Kamer KayaCERFACS, Toulouse, Francekamer@cerfacs.fr

Umit V. CatalyurekThe Ohio State UniversityDepartment of Biomedical Informaticsumit@bmi.osu.edu

MS287

Locality for Sparse Unstructured CommunicationPatterns

In high performance computing data centers, job alloca-tion and mapping of the parallel tasks to the allocatednodes should comply with the job communication patternto reduce the execution time. We discuss the potential ofsimultaneous allocation and mapping for jobs with sparseunstructured communication, and propose a graph-basedalgorithm that is based on breadth-first expansion both innode network and in job communication domains. Simu-lations show that our method outperforms other state-of-the-art approaches.

Ozan TuncerBoston Universityotuncer@bu.edu

Vitus LeungSandia National Laboratoriesvjleung@sandia.gov

Ayse CoskunBoston UniversityElectrical and Computer Engineering Departmentacoskun@bu.edu

MS288

Fluctuating Hydrodynamics Methods for Soft Ma-terials

Many efficient implicit solvent coarse-grained (IS-CG) de-scriptions have been developed for equilibrium studies byremoving the solvent degrees of freedom and treating theircontributions implicitly in the free energy of interactions.To study many dynamic responses requires capturing mo-mentum transfer and kinetic effects involving the solventdegrees of freedom. We present fluctuating hydrodynamicmethods for extending IS-CG models. We present resultsfor dynamic studies of polymeric materials and lipid bilayermembranes.

Paul J. AtzbergerUniversity of California-Santa Barbaraatzberg@math.ucsb.edu

MS288

Temporal Integrators for Fluctuating Hydrody-namics

We develop temporal integrators for solving Langevinstochastic differential equations (SDEs) that arise in fluc-tuating hydrodynamics (FHD). These methods add fluc-tuations to standard second-order deterministic solvers ina way that maintains second-order weak accuracy for lin-earized FHD. We also construct integrators for integratingthe overdamped limit of systems of equations with a fastand slow variable in the limit of inifinite separation of the

CS15 Abstracts 225

fast and slow timescales. We illustrate these integrators onapplications involving particles suspended in a fluctuatingfluid, as well as the development of giant nonequilibriumfluctuations in diffusively-mixing fluids.

Steven D. DelongCourant Institute of Mathematical SciencesNew York Universitysteven.d.delong@gmail.com

Eric Vanden-EijndenCourant InstituteNew York Universityeve2@cims.nyu.edu

Aleksandar DonevCourant Institute of Mathematical SciencesNew York Universityaleks.donev@nyu.edu

MS288

A Fluctuating Immersed Boundary Method forBrownian Suspensions of Rigid Particles

I will describe how to model Brownian suspensions of pas-sive or active particles and rigid bodies using an immersedboundary (IB) approach. I will first discuss minimally-resolved models in which each suspended spherical parti-cle is represented by a single IB marker [F. Balboa Us-abiaga and R. Delgado-Buscalioni and B. E. Griffith andA. Donev, Computer Methods in Applied Mechanics andEngineering, 269:139-172, 2014; and S. Delong, F. BalboaUsabiaga, R. Delgado-Buscalioni, B. E. Griffith and A.Donev, J. Chem. Phys., 140, 134110, 2014]. More complexrigid bodies suspensed in fluid can be represented with dif-ferent degrees of fidelity by enforcing a rigidity constraintfor each partially- or fully-resolved body [B. Kallemov, A.Bhalla, A. Donev, and B. Griffith, in preparation]. Ther-mal fluctuations and thus Brownian motion can be consis-tently modeled by including a fluctuating (random) stressin the momentum equation, as dictated by fluctuating hy-drodynamics.

Aleksandar DonevCourant Institutedonev@courant.nyu.edu

Bakytzhan KallemovCourant Institute of Mathematical SciencesNYUkallemov@gmail.com

Boyce GriffithUniversity of North Carolina at Chapel Hillboyceg@email.unc.edu

Steven D. DelongCourant Institute of Mathematical SciencesNew York Universitysteven.d.delong@gmail.com

MS288

An Immersed Boundary Method for Rigid Bodies

We develop an immersed-boundary method for fluid-structure coupling at small and moderate Reynolds num-bers. This is important in problems involving rigid andsemi-rigid structures immersed in a fluid. We couple

an immersed-boundary Lagrangian representation of rigidbodies to a finite-volume fluid solver. Our methods (1)Do not employ time splitting and are thus suitable for thesteady Stokes (viscous-dominated or low Reynolds num-ber) regime; (2) Strictly enforce the rigidity constraint;and, (3) Ensure fluctuation-dissipation balance in theBrownian regime in the overdamped limit even in the pres-ence of nontrivial boundary conditions.

Bakytzhan KallemovCourant Institute of Mathematical SciencesNYUkallemov@gmail.com

Aleksandar DonevCourant Institute of Mathematical SciencesNew York Universityaleks.donev@nyu.edu

Boyce GriffithUniversity of North Carolina at Chapel Hillboyceg@email.unc.edu

Amneet BhallaCourant Institute of Mathematical Sciencesmail2amneet@gmail.com

MS289

Gaussian Processes in High-Dimensions

Gaussian process regression in high-dimensions is challeng-ing task. Under special circumstances, active subspacemethods can effectively deal with high-dimensions. Mostof the times, the active subspace is defined in an intuitive,albeit ad hoc manner, using gradient information. Here,we show how traditional machine learning techniques canbe used to infer the active subspace with no ad hoc as-sumptions and without gradient information.

Ilias BilionisPurdue Universityebilionis@gmail.com

Nicholas ZabarasCornell Universitynzabaras@gmail.com

MS289

Numerical Solution for the High-Dimensional JointResponse-Excitation Pdf Evolution Equations

Evolution equations of the joint response-excitation prob-ability density function (REPDF) generalize the existingPDF evolution equations and enable us to compute thePDF of the solution of stochastic systems with random ini-tial condition, coefficient, forcing, involving colored noise.An efficient algorithm by using adaptive discontinuousGalerkin method and probabilistic collocation method hasbeen developed for low dimensional systems. In this talk,we address the high-dimensionality of the REPDF sys-tem. We focus on two approximations, namely, the ProperGeneralized Decomposition (PGD) involving the separatedrepresentation and the ANOVA approximation. Both ap-proaches overcome the curse of dimensionality and cancompute the PDFs of extremely high-dimensional systems.Here, we demonstrate the effectiveness of these methods tothe Lorenz-96 model and the advection equation.

Heyrim Cho

226 CS15 Abstracts

Brown UniversityProvidence, RIheyrim cho@brown.edu

Daniele VenturiDivision of Applied MathematicsBrown Universitydaniele venturi@brown.edu

George E. KarniadakisBrown UniversityDivision of Applied Mathematicsgeorge karniadakis@brown.edu

MS289

High-Dimensional Hierarchical Uncertainty Quan-tification for Electronic Systems

We present a hierarchical uncertainty quantification ap-proach for complex electronic systems with several high-dimensional subsystems. First, we obtain a sparse surro-gate model for each subsystem, and utilize a tensor-train-based algorithm to obtain its orthonormal polynomials andGauss quadrature points. Next, we treat each subsystemas a single parameter and perform the high-level simula-tion using stochastic spectral methods. The frameworkshows 90x speedup over hierarchical Monte Carlo on anMEMS/IC oscillator circuit with 184 random parameters.

Zheng ZhangMITz zhang@mit.edu

Xiu YangPacific Northwest National Laboratoryxiu.yang@pnnl.gov

George E. KarniadakisBrown UniversityDivision of Applied Mathematicsgeorge karniadakis@brown.edu

Ivan OseledetsInstitute of Numerical MathematicsRussian Academy of Sciences, Moscowivan.oseledets@gmail.com

Luca DanielM.I.T.Research Lab in Electronicsluca@mit.edu

MS289

Adaptive Multivariate Interpolation Algorithm onNested Grids and Its Application to Stochastic Col-location

We propose an adaptive method for high dimensional poly-nomial interpolation for efficient stochastic collocation.The method utilizes least orthogonal interpolation on un-structured grids. It is based on a greedy algorithm to adap-tively induces nested grids and can be highly flexible forpractical stochastic computations. Along with numericalexamples to demonstrate its effectiveness, we also provideconvergence proof.

Xueyu Zhu

University of Utahxzhu@sci.utah.edu

Yeonjong ShinScientific Computing and Imaging InstituteUniversity of Utahshin@math.utah.edu

Dongbin XiuUniversity of Utahdongbin.xu@utah.edu

MS290

BDDC Domain Decomposition for Weak GalerkinMethods

A Balancing domain decomposition by constraints(BDDC) algorithm is studied for solutions of large sparselinear algebraic systems arising from weak Galerkin dis-cretization of second order elliptic boundary value prob-lems. The condition number for the preconditioned systemis estimated and numerical results are provided to confirmthe results.

Xuemin TuUniversity of Kansasxuemin@ku,edu

MS290

Innovative Weak Galerkin Finite Element Methodswith Application in Fluorescence Tomography

In this talk, I will discuss a new and efficient numerical al-gorithm by using weak Galerkin (WG) finite element meth-ods for a fourth order elliptic problem arising from Fluores-cence Tomography(FT) model. Fluorescence Tomographyis an emerging, in vivo non-invasive 3-D imaging techniquewhich reconstructs images that characterize the distribu-tion of molecules that are tagged by fluorophores. Weaksecond order elliptic operator and its discrete version areintroduced for a class of discontinuous functions definedon a finite element partition of the domain consisting ofgeneral polygons or polyhedra. An error estimate of op-timal order is derived in an H2-equivalent norm for theWG finite element solutions. Error estimates in the usualL2 norm are established, yielding optimal order of con-vergence for all the WG finite element algorithms exceptthe one corresponding to the lowest order (i.e., piecewisequadratic elements). Some numerical experiments are pre-sented to illustrate the efficiency and accuracy of the nu-merical scheme.

Chunmei WangGeorgia Institute of Technologycwang462@math.gatech.edu

MS290

Weak Galerkin Mixed Finite Element Methods forLinear Elasticity Problems

In the talk, I will talk about solving linear elasticity prob-lems by using Weak Galerkin mixed finite element method(WG-MFEM). It is shown that WG-MFEM provides anaccurate approximation for both the stress tensor and thedisplacement field of linear elasticity problems. The nu-merical experiments will be provided to verify that WG-

CS15 Abstracts 227

MFEM is efficient and reliable in computing.

Yujie ZhangOklahoma State University, USAyjzhang@mathdept.okstate.edu

MS290

A Weak Galerkin Finite Element Scheme for Solv-ing the Brinkman Equations

A weak Galerkin (WG) finite element method for solvingthe Brinkman equation in two or three dimensional spacesby using polynomials is introduced and analyzed. The WGmethod is designed by using the generalized functions andtheir weak derivatives which are defined as distributions.The variational form we considered is based on two gra-dient operators which is different from the usual gradient-divergence operators. The WG method is highly flexibleby allowing the use of discontinuous functions on arbi-trary polygons or polyhedra with certain shape regularity.Optimal-order error estimates are established for the cor-responding WG finite element solutions in various norms.Some computational results are presented to demonstratethe efficiency of the method.

Ran ZhangJilin University, Chinazhangran@jlu.edu.cn

MS291

Preconditioning Stochastic Gradient Algorithmswith Randomized Linear Algebra

We provide a method for combining SGD (Stochastic Gra-dient Descent) and RLA (Randomized Linear Algebra) al-gorithms. This involves reformulating a deterministic re-gression problem as a stochastic optimization problem thatis of the form of an expectation over a nontrivial data-dependent probability distribution. This permits us tocombine stochastic approximation (SA) methods and sam-ple average approximation (SAA) methods from optimiza-tion theory to develop novel RLA-SGD-hybrid randomizedalgorithms for these deterministic regression problems.

Michael MahoneyStanford UniversityApplied and Computational Mathematicsmmahoney@stat.berkeley.edu

MS291

Randomized Methods for Accelerating StructuredMatrix Computations

Methods based on randomized sampling have over the lastseveral years proven to be powerful tools for computinglow-rank approximations to matrices whose singular val-ues exhibit appropriate decay. In this talk, we describehow such techniques can be extended to certain ”rank-structured” matrices, for which only certain off-diagonalblocks (not the matrix itself) admit accurate low-rank ap-proximations. Matrices of this type often arise in the con-struction of O(N) direct solvers for elliptic PDEs.

Gunnar MartinssonUniv. of Colorado at Boulder

martinss@colorado.edu

MS291

Using Random Butterfly Transformations to AvoidPivoting in Sparse Direct Methods

Dynamic pivoting prevents parallel sparse direct solversfrom achieving high performance and scalability. In thiswork, we investigate a statistical technique based on Ran-dom Butterfly Transformations to avoid pivoting. Previousworks showed that this technique is successful in the densecase; here we investigate the sparse case. We will comparethis method with the static pivoting and the partial pivot-ing approaches in various performance metrics, includingrobustness, sparsity, and runtime in a parallel environment.

Francois-Henry RouetLawrence Berkeley National Laboratoryfhrouet@lbl.gov

Xiaoye Sherry LiComputational Research DivisionLawrence Berkeley National Laboratoryxsli@lbl.gov

Marc BaboulinUniversity of Paris-Sud/INRIAmarc.baboulin@inria.fr

MS292

A Pod Model for Resolving the Angular Dimensionof the Boltzmann Transport Equation

A new method using POD in neutral particle transportproblems is described. POD is used to represent the angu-lar direction of particle travel when solving the Boltzmannequation for time independent problems. It is based on themethod of snapshots which are of the angular flux distri-butions taken at different instances in space. The methodsubstantially reduces the number of functions required toresolve angular direction, this reduces solving times whilstretaining solution accuracy.

Andrew G. BuchanDepartment of Earth Science & EngineeringImperial Collegeandrew.buchan@imperial.ac.uk

Atyab CallooImperial College Londonatyab.calloo13@imperial.ac.uk

Christopher PainImperial Collegec.pain@imperial.ac.uk

Fangxin FangDepartment of Earth Science and EngineeringImperial College London, U.K.f.fang@imperial.ac.uk

Steven DargavilleImperial College Londons.dargaville@imperial.ac.uk

Ionel M. NavonFlorida State UniversityDepartment of Scientific Computing

228 CS15 Abstracts

inavon@fsu.edu

MS292

Automated Adjoints for Mesh-Independent PDE-Constrained Optimisation

We will present a method for automatically deriving ad-joints of finite element models with two major advantagesover algorithmic differentiation: the adjoints enjoy approx-imately optimal efficiency (crucial for optimisation and in-verse problems), and scale naturally in parallel without dif-ferentiating MPI calls or OpenMP directives. The methodis used to derive adjoints of models employing the FEniCSframework. We will further discuss how discrete adjointscan be carefully used to achieve mesh independence in op-timisation algorithms.

Patrick E. FarrellDepartment of MathematicsUniversity of Oxfordpatrick.farrell@maths.ox.ac.uk

MS292

Challenges in Assimilation of PM2.5 Observationsfor Air Pollution Forecast

Air pollution is a big issue in China. A good air qual-ity forecast is very useful and important for warning andmanagement of air pollution. More than 1,000 surface ob-servation stations for PM2.5 monitoring were establishedrecently. The big data from this observing network has thepotential to improve the air quality forecast via advanceddata assimilation techniques. Over recent years we havebeing worked on this problem. There are some progresses,and some failures too. This talk will focus on some chal-lenges and discuss some possible solutions.

Jiang JZhuInstitute of Atmospheric PhysicsChinese Academy of Sciencesjzhu@mail.iap.ac.cn

MS292

Inversion of Geothermal Heat Flux in a Thermo-mechanically Coupled Nonlinear Stokes Ice SheetModel

To project the contribution of polar ice sheets to futuresea level rise, high-resolution numerical ice sheet modelsare critical. Yet, large uncertainties remain in the bound-ary conditions at the base of the ice sheet due to the lackof direct observations. Here we study mathematical andcomputational issues in inverse problems for basal bound-ary conditions, in particular, the geothermal heat flux, ina thermomechanically coupled nonlinear Stokes ice sheetmodel, using surface velocity observations.

Hongyu ZhuInstitute for Computational Engineering and SciencesUniversity of Texas at Austinzhuhongyu@ices.utexas.edu

Georg StadlerCourant Institute for Mathematical SciencesNew York Universitystadler@cims.nyu.edu

Noemi Petra

University of California, Mercednpetra@ucmerced.edu

Toby IsaacICESThe University of Texas at Austintisaac@ices.utexas.edu

Omar GhattasThe University of Texas at Austinomar@ices.utexas.edu

Thomas HughesInstitute for Computational Engineering and SciencesThe University of Texas at Austinhughes@ices.utexas.edu

MS293

Stability and Convergence of the Co-volumeScheme for the Stokes Problem

The co-volume scheme specifies the mass at cell centers andcell vertices, and both of the normal and tangential velocitycomponents at cell edges. This scheme is extremely flexi-ble, applicable to unstructured meshes, and avoids the needto reconstruct the tangential velocity component, as theclassical C-grid scheme does. Even though the co-volumescheme has had some success in simulating geophysicalflows, there has not been much progress in the theoreticalanalysis of the scheme. In this talk, we present stabilityand convergence results concerning the scheme applied tothe classical Stokes problem on unstructured meshes. Boththe linear and nonlinear cases will be discussed.

Qingshan ChenClemson Universityqsc@clemson.edu

MS293

Semi-Analytical Time Differencing Methods forStiff Problems

A semi-analytical method is developed based on conven-tional integrating factor (IF) and exponential time differ-encing (ETD) schemes for stiff problems. The latter meansthat there exists a thin layer with a large variation in theirsolutions. The occurrence of this stiff layer is due to themultiplication of a very small parameter ε with the tran-sient term of the equation. Via singular perturbation anal-ysis, an analytic approximation of the stiff layer, which iscalled a corrector, is sought for and embedded into the IFand ETD methods. These new schemes are then used toapproximate the non-stiff part of the solution. Since thestiff part is resolved analytically by the corrector, the newmethod outperforms the conventional ones in terms of ac-curacy. In this paper, we apply our new method for bothproblems of ordinary differential equations and some par-tial differential equations.

Chang-Yeol JungUlsan National Institute of Science and TechnologySouth Koreachangyeoljung@gmail.com

Thien Binh NguyenUNIST

CS15 Abstracts 229

ngthienbinh@gmail.com

MS293

A New Adaptive Weighted Essentially Non-oscillatory WENO-θ Scheme for Hypberbolic Con-servation Laws

A new adaptive WENO-θ scheme is proposed. Depend-ing on the smoothness of the large stencil used in the re-construction procedure, a parameter θ is set adaptively toswitch the scheme between a 5th-order upwind and 6th-order central approximation. A new set of smoothness in-dicators for both the sub-stencils and the large one is intro-duced. These are constructed symmetrically around xj inTaylor expansions. Numerical results show that WENO-θsubstantially improves other comparing WENO schemes.

Chang-Yeol JungUlsan National Institute of Science and TechnologySouth Koreachangyeoljung@gmail.com

Thien Binh NguyenUNISTngthienbinh@gmail.com

MS293

The Effective Resolution of Advection Schemes

Typical classification of numerical schemes concerns theconvergence order of the scheme and the relative accuracyin the limit of an infinitesimal grid (in either space or time).We define and analyze the effective resolution of numericalschemes designed for the advection equation by calculat-ing the smallest spatial scale that is completely resolved bythat scheme. This is done via dispersion relation analysisand numerical testing. We also briefly discuss the impactof these novel approaches to quantify the utility of a nu-merical algorithm at accurately representing the influenceof waves on mean flow for nonlinear evolution equations influids that incorporate a three-wave interaction.

James KentUniversity of Michiganjdkent@umich.edu

Jared P. WhiteheadBrigham Young Universitywhitehead@mathematics.byu.edu

Christiane JablonowskiUniversity of MichiganAnn Arbor MI 48109-2143cjablono@umich.edu

Richard RoodUniversity of MichiganAnn Arbor, MI 48109-2143rbrood@umich.edu

MS294

Flooding with Equelle: A Domain Specific Lan-guage for Finite Volume Methods

Modern hardware is increasingly complex and difficult toutilize for researchers and scientists. Peak performance isonly acquired through mastering a huge set of fields, includ-ing the physical problem at hand, the mathematical formu-

lation, the numerical discretization, and the parallel imple-mentation. As most simulator writing teams consist of onePh.D. student, acquiring peak performance can be a daunt-ing task. We address this challenge with a new open sourcedomain specific language called Equelle. The language di-vides the different fields into different software componentsin order to maximize productivity of each researcher. Forexample, a parallelization expert would mostly contributeto the compiler back-end, and an expert in numerical meth-ods would contribute with Equelle programs.

Andre R. BrodtkorbSINTEF ICT, Department of Applied MathematicsAndre.Brodtkorb@sintef.no

MS294

High Performance High Order Numerical Methodfor Tsunami Wave Propagation

We present a high order discontinuous Galerkin method forthe accurate simulation of tsunami wave propagation. Wediscuss the acceleration of the method on modern manycore hardware architectures such as GPUs, for the fasterthan real time predictions. The developed algorithms usea unified multi-threading approach OCCA. A computa-tional kernel written in OCCA can be executed on sev-eral hardware architectures that support multi-threadingapproaches OpenCL, CUDA, OpenMP, Pthreads and IntelCOI.

Rajesh GandhamRice UniversityDepartment of Computational and Applied Mathematicsrg20@rice.edu

Timothy WarburtonDepartment of Computational And Applied MathematicsRice Universitytimwar@rice.edu

David MedinaRice Universitydsm5@rice.edu

MS294

FEM Integration with Quadrature on the GPU

Efficient integration of low-order elements on a GPU hasproven difficult. We have previously shown how to inte-grate a differential form (such as Laplace or elasticity) ef-ficiently using algebraic simplification and exact integra-tion. This, however, breaks down for multilinear formsor when using a coefficient. In this work, we show howto efficiently integrate an arbitrary form using quadrature.We introduce a technique we call ”thread transposition”which matches the work done during evaluation at quadra-ture points to that done during basis coefficient evaluation.We are able to achieve more than 300GF/s for the variable-coefficient Laplacian, and provide a performance model toexplain these results.

Matthew KnepleyUniversity of Chicagoknepley@gmail.com

Karl RuppInstitute for Analysis and Scientific Computing, TU WienInstitute for Microelectronics, TU Wienrupp@iue.tuwien.ac.at

230 CS15 Abstracts

Andy R. TerrelInstitute for Computational Engineering and SciencesUniversity of Texas at Austinandy.terrel@gmail.com

MS294

Thermal Comfort Simulations on Massive ParallelSystems

Many engineering-based problems, which were deemed un-solvable a decade ago, can be simulated today using mod-ern supercomputers such as SuperMUC installed at LRZ,Germany. Computational fluid dynamics play a dominantrole in simulating urban floods or complex indoor air flowscenarios. We will present our multi-scale CFD approachbased on hierarchic, block-structured Cartesian grids forsolving a coupled thermal simulation together with a hu-man manikin model, running on up to 140,000 cores inparallel.

Ralf-Peter MundaniTUM, Faculty of Civil, Geo and EnvironmentalEngineeringChair for Computation in Engineeringmundani@tum.de

Jerome FrischChair for Computation in EngineeringTechnische Universitat Munchenfrisch@tum.de

MS295

Scalable Solvers for Extended MHD in the Low-βRegime

Extended MHD (XMHD) is a very challenging hyperbolicPDE system for implicit integration techniques due to theill-conditioning introduced by fast dispersive waves. In thistalk, we will describe our physics-based preconditioning ap-proach for XMHD in the low-β regime, when a large guidefield is present. The method exploits the nature of thehyperbolic couplings in XMHD to produce a block diag-onally dominant PDE system, well-conditioned for multi-level techniques. Numerical experiments will demonstratethe scalability of the approach.

Luis ChaconLos Alamos National Laboratorychacon@lanl.gov

MS295

Multi-Fluid Magnetohydrodynamic Models forPartially-Ionized Non-Equilibrium AnisotropicPlasmas

A multi-fluid extended magnetohydrodynamic model andnumerical solution method are proposed and describedfor the treatment of partially-ionized non-equilibriumanisotropic and strongly-magnetized plasmas. The Gaus-sian moment closure is used to describe the non-equilibriumtransport of the neutral, ion, and electron components ofthe plasma in the multi-fluid model. The Gaussian clo-sure is a maximum-entropy-based, strictly-hyperbolic clo-sure providing approximate solutions to the Boltzmannequation which allow for strong pressure/temperatureanisotropies. The treatment of reactive collisions is incor-porated to allow for the effects of ionization-recombinationand charge-exchange. The moment equations are cou-

pled with Maxwells equations to complete the descriptionfor magnetized plasmas. A Godunov-type finite-volumemethod is proposed for the solution of the multi-fluid modelby numerical means and results are described for both one-and two-dimensional problems.

Clinton P. GrothUniversity of Toronto Institute for Aerospace StudiesCanadagroth@utias.utoronto.ca

Ken MiuraUniversity of Toronto Institute for Aerospace Studiesken.miura@gmail.com

MS295

A High-order Block-adaptive Simulation Frame-work for Ideal and Resistive MHD Equations onCubed-sphere Grids

Numerical simulations of large-scale space-physics prob-lems typically require the computation of discrete solu-tions of complex multiphysics phenomena characterizedby disparate spatial and temporal scales. Adequate nu-merical algorithms capable to resolve the wide range ofdynamic scales of such simulations at reduced computa-tional cost are highly desirable. This talk presents anadaptive, conservative, high-order CENO finite-volume ap-proach for space-plasma phenomena described by the setof ideal and resistive MHD equations. Results for sev-eral benchmark problems are presented to illustrate theaccuracy and computational performance of the fourth-order accurate method used in combination with a paral-lel, dynamically-adaptive, simulation framework on cubed-sphere grids.

Lucian Ivan, Hans De Sterck, Andree SusantoUniversity of WaterlooApplied Mathematicslucian.ivan@utoronto.ca, hdesterck@uwaterloo.ca,asusanto@uwaterloo.ca

Clinton P. GrothUniversity of Toronto Institute for Aerospace StudiesCanadagroth@utias.utoronto.ca

MS295

Block Preconditioners for 3D Incompressible MHD

The scalable iterative solution of strongly coupled3Dincompressible resistive magnetohydrodynamics (MHD)equations is very challenging. This study considers mixedFE integration for velocity/pressure (Q2/Q1) and edge-elements for magnetic induction and presents anew approx-imate block factorization (ABF) preconditioner for thissystem. The ABF preconditioner reduces the system toap-proximate Schur complement systems that are solved bynodal and edge-element based AMG methods.

Eric C. CyrScalable Algorithms DepartmentSandia National Laboratotorieseccyr@sandia.gov

Edward PhillipsSandia National Laboratoriesegphill@sandia.gov

CS15 Abstracts 231

John ShadidSandia National LaboratoriesAlbuquerque, NMjnshadi@sandia.gov

MS296

An HDG Method for Non-Hydrostatic Atmosphere

Abstract not available at time of publication.

Tan Bui-ThanhThe University of Texas at Austintanbui@ices.utexas.edu

MS296

Towards a Fully 3D Compressible Atmosphere Dy-namical Core with Compatible Finite Elements

We have recently been developing compatible finite elementmethods (i.e., mixed finite element methods using familiesof spaces forming discrete de Rham complexes) as an ex-tension of the C-grid staggered finite difference approach.These methods lead to higher-order discretisations on ar-bitrary meshes with flexibility to adjust the global DOFratio between pressure and velocity in order to minimisethe impact of spurious mode branches. These methods arebeing developed as part of the GungHo dynamical coreproject in the UK, a collaboration between the Met Of-fice, STFC and several UK universities. In Phase I of theproject, we successfully developed finite element discretisa-tions for the nonlinear rotating shallow-water equations onthe sphere, which serves as a useful testbed for the horizon-tal discretisation in dynamical cores. The compatible finiteelement structure allows for numerical schemes with sta-ble advection of the implied diagnostic potential vorticityfield, which is important for stable long-time integrationswith minimal numerical dissipation. We are now develop-ing these ideas in the context of a full 3D dynamical core,via vertical slice models. This talk will discuss our progressin addressing the following issues: * What is the finite ele-ment analogue of the Charney-Phillips vertical staggering(necessary for good representation of hydrostatic balancein the vertical)? What is the correct choice of finite ele-ment space for temperature? * How to obtain stable andaccurate advection schemes for temperature in this case?* How to extend the velocity advection scheme to threedimensions? Can the 3D vorticity equation be incorpo-rated? * How to discretise the nonlinear pressure gradientterm in the theta-pi formulation? Proposed solutions tothese questions will be illustrated with numerical exper-iments implemented using Firedrake, a high-performancefinite element library targetting geophysical fluid dynam-ics applications.

Colin J. CotterImperial College LondonDepartment of Aeronauticscolin.cotter@imperial.ac.uk

MS296

A Higher-Order Finite Volume Nonhydrostatic Dy-namical Core with Space-Time Refinement

We present an adaptive non-hydrostatic dynamical corebased on a higher-order finite volume discretization on thecubed sphere. Adaptivity is both in space, using nestedhorizontal refinement; and in time, using subcycling in re-fined regions. The algorithm is able to maintain scalar

conservation with careful flux construction at refinementboundaries, as well as conservative coarse-fine interpola-tion. We show results for simple tests as well as morechallenging ones that highlight the benefits of refinement.

Hans JohansenLawrence Berkeley National LaboratoryComputational Research Divisionhjohansen@lbl.gov

MS296

Optimization-based Spectral Element Semi-Lagrangian Tracer Transport

Transport algorithms are highly important in atmosphericmodeling where hundreds of tracer species must be ef-ficiently transported while maintaining conservation oftracer mass and preservation of physical bounds. Wepresent a new transport algorithm that combines a high-order spectral element semi-Lagrangian scheme with anoptimization algorithm to enforce mass conservation andbounds preservation. We evaluate the new method us-ing several standard two- and three-dimensional trans-port problems on the sphere and compare to existing ap-proaches.

Kara PetersonSandia Natl. Labskjpeter@sandia.gov

Mark A. TaylorSandia National Laboratories, Albuquerque, NMmataylo@sandia.gov

MS297

Linear Response Eigenvalue Problem and ExcitedState Calculations

Linear response (LR) eigenvalue problems arise from exci-tation state calculations of collective motion of many par-ticle systems. In this talk, we first present theoretical re-sults for the LR eigenvalue problems such as minimizationprinciples. Although the LR eigenvalue problems are non-symmetric, these results mirror the well-known theoreticalresults for symmetric eigenproblems. Then we will discussthe best approximation of the few smallest positive eigen-values via a structure-preserving projection, and describeconjugate gradient-like algorithms for simultaneously com-puting these eigenvalues.

Zhaojun BaiDepartments of Computer Science and MathematicsUniversity of California, Davisbai@cs.ucdavis.edu

Ren-Cang LiUniversity of Texas - Arlingtonrcli@uta.edu

MS297

Accelerating Quantum Transport CalculationsThrough the Feast Algorithm

In Quantum Transport the scattering region of a de-vice is connected to semi-infinite leads, where the energy-dependent reflected modes must be determined by solvinga polynomial eigenvalue problem. As fast decaying modesdo not significantly contribute, it is sufficient to compute

232 CS15 Abstracts

only those eigenvalues with a small or vanishing imaginarypart. The FEAST algorithm allows for drastically reduc-ing the system size by specifically searching for the desiredeigenvalues and for efficiently parallelizing the computa-tional workload.

Sascha Brueck, Mauro CalderaraIntegrated Systems LaboratoryETH Zurichbruecks@iis.ee.ethz.ch, mcalderara@iis.ee.ethz.ch

Hossein Bani-Hashemian, Joost VandeVondeleNanoscale SimulationsETH Zurichhossein.banihashemian@mat.ethz.ch,joost.vandevondele@mat.ethz.ch

Mathieu LuisierIntegrated Systems LaboratoryETH Zurichmluisier@iis.ee.ethz.ch

MS297

Parallel Solution of Eigenvalue Problems fromGraphene Modeling with Solvers Based on Inte-gration and Approximation

Graphene is a material that recently attracts a lot of in-terest among researchers. Studying its electronic proper-ties involves solving (typically large scale) sparse eigen-value problems. In this talk we will present FEAST-likeand polynomial based solvers for the solution of theseeigenvalue problems. We will also discuss approaches tothe solution of the arising inner linear systems. We fi-nally present numerical examples involving the solution ofgraphene eigenvalue problems.

Bruno Lang, Lukas KramerUniversity of Wuppertallang@math.uni-wuppertal.de,lukas.kraemer@math.uni-wuppertal.de

Martin GalgonYniversity of Wuppertalgalgon@math.uni-wuppertal.de

MS297

Polynomial Techniques and Primme for the Com-putation of Large Number of Eigenvalues

A computationally challenging task is the computation ofa large number, M, of eigenvalues and their eigenvectors.Enforcing orthogonality of a Krylov subspace larger thanM becomes a bottleneck, and computing eigenvectors afew at a time increases the iteration cost linearly with M.Polynomial filters have been used to trade orthogonaliza-tion for matrix-vector multiplications. We discuss polyno-mial filters both for single and multivectors on top of thePRIMME eigenvalue software.

Andreas StathopoulosCollege of William & MaryDepartment of Computer Scienceandreas@cs.wm.edu

MS298

Optimal Control Problems With Uncertain Model

Parameters

I demonstrate solving stochastic optimal control problemsby adding minimal modifications to their correspondingdeterministic optimization solvers using Trilinos packages.The process of modifying the deterministic solver to astochastic one can be done systematically and automati-cally given suitable code structure. I illustrate this processby solving optimal control problems with uncertain modelparameters arising in heat-flux control and oil reservoir op-timization.

Xiaodi DengRice Universityxiaodi.deng@rice.edu.

MS298

On Risk-averse PDE-constrained Optimization us-ing Convex Risk Measures Inspired by ConditionalValue-at-risk

We consider a class of PDE-constrained optimization prob-lems in which the underlying PDE-system contains uncer-tain parameters. In order to obtain robust controls that areboth deterministic and risk-averse, we consider the mini-mization of the conditional value-at-risk (CVaR) of the re-duced objective functional. In order to develop efficient nu-merical schemes, regularization approaches are suggestedfor the primal and the dual formulation of the minimiza-tion problem. The regularized CVaR is shown to be aconvex risk measure. Sensitivity and consistency results ofthe regularized problems are derived. Finally, we presentnumerical results for several example problems.

Thomas M. SurowiecDepartment of MathematicsHumboldt University of Berlinsurowiec@math.hu-berlin.de

MS298

Optimization under Uncertainty: Application toElectrical Circuits

This presentation will demonstrate the application ofstochastic optimization algorithms to the problem of modelcalibration and optimal control under uncertainty for sim-ple electrical circuits. Our implementation uses the RapidOptimization Library (ROL) from the Trilinos frameworkto solve optimization under uncertainty problems with al-gebraic and partial differential equation constraints. Ournumerical experimentation considers the Shockley idealdiode equation and drift-diffusion model.

Timur TakhtaganovRice UniversityHouston, Txtat3@rice.edu

MS298

Maximizing AUC and Buffered AUC in Classifica-tion

We propose an alternative to the Area Under the ReceiverOperating Characteristic Curve (AUC) performance met-ric called Buffered AUC (bAUC). We show that bAUCis an intuitive counterpart to AUC. We then show thatbAUC, compared to AUC, can be a more informative mea-sure of a classifiers ranking quality. In addition, we show

CS15 Abstracts 233

that bAUC is much easier to handle in optimization frame-works than AUC, specifically reducing to convex and linearprogramming. We use these friendly optimization proper-ties to introduce the bAUC Efficiency Frontier, a conceptthat serves to partially resolve the incoherency that ariseswhen misclassification costs need be considered. We con-clude that bAUC avoids many of the numerically trouble-some issues encountered by AUC and integrates much moresmoothly into the general framework of model selection andevaluation.

Stan UryasevUniversity of Floridauryasev@ufl.edu

MS299

Facilitating Learners Cognitive Presence In A Self-Directed Online Course

The study will report our study on students self-directedlearning and inquiry in a 15-week graduate-level onlinecourse. We will investigate learners cognitive presence andfacilitating behaviors that help create higher-level cogni-tive presence. Online discussion transcripts, semi-structureinterviews, and learning records (i.e. view frequencies,grades) will be used as the primary data sources. Thepurpose of this study is to reveal the effective facilitatingstrategies that trigger or promote learners critical thinkingand deep reflection.

Ye Chen, Jing LeiSyracuse Universityychen129@syr.edu, jlei@syr.edu

MS299

Towards Automating Analysis of MidtermSemester Feedback Surveys for Improving CourseEffectiveness

This talk will report on the use of midterm semester feed-back survey for improving teaching and learning effective-ness in college courses, including data from the Computa-tional Modeling courses discussed during this session. Ef-forts to expand and partially automate analysis and feed-back from these surveys will be explored, with some initialresults.

Douglas HoltonEmbry-Riddle Aeronautical Universitydouglas.holton@erau.edu

MS299

Tri-Located Course in Mathematical Modeling andComplementary Reu Summer Workshop

This talk will report the summative evaluation for theproject funded by NSF TUES to create a cluster of collab-orating institutions that combine students into commonclasses and use cyberlearning technologies to deliver andmanage instruction. We will also share the course-basedresearch experience that was complemented by innovativeundergraduate research summer workshops. We will dis-cuss ideas how to advance CSE Education through MOOC,project-based learning, and deep learning assessment tech-nology.

Hong LiuDepartment of MathematicsEmbry-Riddle Aeronautical University

liuho@erau.edu

Andrei LuduEmbry-Riddle Aeronautical UniversityMathematics Departmentludua@erau.edu

MS299

Deep Learning Assessment for Near Real-time,Formative Feedback during Complex Problem-solving Activities

A critical factor for progress in cyberlearning involvesassessment, especially near real-time, formative feedbackduring complex problem-solving activities. Detecting mis-conceptions early is important to help learners gain compe-tence and build confidence. This presentation will demon-strate one approach to assessing learning in complex do-mains that involves the analysis of student conceptualiza-tions of the problem space over time and in comparisonwith those of experienced persons. These conceptualiza-tions can be gathered explicitly in the form of annotatedconcept maps or through student models created usingtools such as MATLAB.

Michael SpectorUniversity of North TexasMike.Spector@unt.edu

MS300

Weighted Sparsity and Function Interpolation ViaInfinite-dimensional Compressed Sensing

We introduce a framework for function interpolation usingweighted l1 minimization. Two advantages of this frame-work over existing approaches are: (i) in the absence ofnoise it leads to interpolatory approximations, and (ii) itdoes not require a priori estimates on the expansion tail.We explain the critical role weighted sparsity plays in func-tion interpolation; namely, that of regularizing the problemand removing aliased solutions. Finally, we present a num-ber of near-optimal recovery guarantees.

Ben AdcockPurdue Universityben adcock@sfu.ca

MS300

Representation Using the Weyl Transform

The Weyl transform is introduced as a powerful frameworkfor representing measurement data. Transform coefficientsare connected to the Walsh-Hadamard transform of multi-scale autocorrelations, and different forms of dyadic peri-odicity in a signal are shown to appear as different featuresin its Weyl coefficients. A large group of multiscale trans-formations is shown to support very fast pooling since theWeyl coefficients are unique up to permutation and phasechanges when the original signal is transformed by any ele-ment of this group. The effectiveness of the Weyl transformis demonstrated through the example of textured imageclassification.

Robert CalderbankMathematicsDuke University

234 CS15 Abstracts

robert.calderbank@duke.edu

MS300

Compressive Parameter Estimation via Approxi-mate Message Passing

The literature on compressive parameter estimation hasbeen mostly focused on the use of sparsity dictionariesthat encode a sampling of the parameter space; these dic-tionaries, however, suffer from coherence issues that mustbe controlled for successful estimation. We propose theuse of statistical parameter estimation methods within theapproximate message passing (AMP) algorithm for signalrecovery. Our proposed work leverages the recently high-lighted connection between statistical denoising methodsand the thresholding step commonly used during recovery.As an example, we consider line spectral estimation byleveraging the well-known MUSIC algorithm. Numericalexperiments show significant improvements in estimationperformance.

Shermin HamzeheiUniversity of Massachusettsshamzehei@engin.umass.edu

Marco F. DuarteUniversity of Massachusetts Amherstmduarte@ecs.umass.edu

MS300

Fast and Robust Dictionary Learning, with Invari-ances and Multiresolution

We introduce a novel dictionary learning procedure forlearning sparsifying representations for images. Sparserepresentations have been used successfully for a varietyof imaging tasks, from denoting to imprinting to super-resolution. Key features of our construction are (1) theability of seamlessly construct a dictionary for patches ofimages at different scales, rather than on patches of a fixedsize; (2) the ability to produce representations that areinvariant under a known, given desired invariances (e.g.translations, rotations); (3) having fast algorithms for boththe construction of the dictionary, and for computing thesparse representation of a signal onto the dictionary; (4)theoretical finite sample guarantees on the learning algo-rithm.

Mauro Maggioni, Samuel GerberDepartment of MathematicsDuke Universitymauro@math.duke.edu, sgerber@math.duke.edu

MS301

Upwind DG for Acoustic and Elastic Wave Equa-tions

We develop and analyze a new strategy for the spatial dis-continuous Galerkin discretization of wave equations in sec-ond order form. The method features a direct, parameter-free approach to defining interelement fluxes. Both energy-conserving and upwind discretizations can be devised. Wederive a priori error estimates in the energy norm for cer-tain fluxes and present numerical experiments showing thatoptimal convergence in L2 is obtained.

Daniel AppeloUniversity of New Mexico

appelo@unm.edu

Thomas M. HagstromSouthern Methodist UniversityDepartment of Mathematicsthagstrom@smu.edu

MS301

High-Order Upwind Methods for Second-OrderWave Equations on Curvilinear and OverlappingGrids

In this talk I will present preliminary results for a promisingnew technique to PDE discretization. The approach, calledGalerkin finite differences, blends the attractive featuresfrom finite differences and finite elements to yield schemeswith provable energy stability, high-order accuracy, andwell-conditioned discrete systems even for very high order.Results are presented for the wave equation using bothcontinuous and discontinuous representations.

Jeffrey W. BanksLawrence Livermore National Laboratorybanksj3@rpi.edu

MS301

A Discontinuous Galerkin Method for the Spher-ically Reduced Einstein Field Equations withSecond-Order Operators

A discontinuous Galerkin (dG) method for evolving aspherically reduced formulation of the Einstein field equa-tions of general relativity is proposed. The system is dis-cretized in its natural first-order in time second-order inspace form. I will discuss in some detail our scheme aswell as our treatment of the second-order spatial operatorswhich appear in this particular system. By approximatingthe second-order spatial derivatives of the system, we avoidthe need to introduce extra fields and equations which canlead to new challenges. We demonstrate stable, long-timeevolutions achieved by our scheme, which also constitutesthe first use of dG methods in computational general rel-ativity. I will conclude with a brief overview of currentstatus of dG methods within the computational relativitycommunity.

Scott FieldDepartment of AstronomyCornell Universitysfield@astro.cornell.edu

Jan HesthavenEPFLjan.hesthaven@epfl.ch

Stephen LauMathematicsThe University of New Mexicolau@math.unm.edu

Abdul MroueCanadian Institute for Theoretical Astrophysicsmroue@cita.utoronto.ca

MS301

Uncertainty Quantification for High Frequency

CS15 Abstracts 235

Waves

We consider the wave equation with highly oscillatory ini-tial data, where there is uncertainty in the wave speed, ini-tial phase and/or initial amplitude. To estimate quantitiesof interest related to the solution, and their uncertainty,we combine a high frequency method based on Gaussianbeams with stochastic collocation. We show that this isan efficient approach for quadratic quantities of interest,since they vary smoothly with respect to the random vari-ables, with derivatives bounded independently of the wavefrequency.

Olof RunborgKTH, Stockholm, Swedenolofr@nada.kth.se

MS302

A Consistent and Robust Discrete Adjoint Solverfor the SU2 Framework

In this talk we discuss the development of a discrete adjointsolver, which enables the computation of consistent gradi-ents in a robust way based on the exploitation of the fixed-point structure of the flow solver. All occurring derivativesin this formulation can be calculated using advanced tech-niques of Algorithmic Differentiation so that the extensionto arbitrary complex flow models can be performed alongwith the development of the primal code.

Tim AlbringTU Kaiserslauterntim.albring@rhrk.uni-kl.de

Nicolas R. GaugerRWTH Aachen Universitynicolas.gauger@rhrk.uni-kl.de

MS302

High-Performance Optimizations of the Unstruc-tured Open-Source SU2 Suite

Strategies and lessons learned from applying high-performance optimizations to an open-source computa-tional fluid dynamics suite, SU2, are presented. We fo-cus on performance optimizations of solver execution withemphasis on parallelization and on finding well-suited algo-rithms. The resulting code modifications are geared towardachieving high scalability with edge-based CFD solverssuch as SU2, making efficient use of memory, and choosingappropriate algorithms for maximizing parallelism, espe-cially for solving linear systems arising from implicit timediscretizations.

Thomas EconomonDepartment of Aeronautics and AstronauticsStanford Universityeconomon@stanford.edu

Francisco PalaciosStanford Universityfpalacios@stanford.edu

Juan J. AlonsoDepartment of Aeronautics and AstronauticsStanford Universityjjalonso@stanford.edu

Gaurav Bansal

Software and Services GroupIntel Corporation, Hillsboro, OR, USAgaurav2.bansal@intel.com

Anand DeshpandeParallel Computing LaboratoryIntel Corporation, Bangalore, Indiaanand.m.deshpande@intel.com

Alexander HeineckeParallel Computing LaboratoryIntel Corporation, Santa Clara, CA, USAalexander.heinecke@intel.com

Dheevatsa MudigereParallel Computing LaboratoryIntel Corporation, Bangalore, Indiadheevatsa.mudigere@intel.com

Mikhail SmelyanskiyIntel Corporationmikhail.smelyanskiy@intel.com

MS302

Large Scale Design Using Su2 and a ContinuousAdjoint Rans Approach

Abstract not available at time of publication.

Francisco PalaciosStanford Universityfpalacios@stanford.edu

MS302

A Discrete Adjoint Framework for Lift-Constrained Noise Minimization Using SU2

This talk presents an discrete adjoint-based frameworkfor aeroacoustic shape optimization. The unsteady ad-joint solver is developed by applying algorithmic differen-tiation (AD) to the open source SU2 code. A practical lift-constrained noise minimization formulation is presented inwhich the acoustic signal is minimized at a far-field obser-vation point while a lift constraint is imposed to ensureadequate aerodynamic performance in low speed operatingconditions.

Beckett ZhouTU Kaiserslauternyuxiang.zhou@rhrk.uni-kl.de

Nicolas R. GaugerRWTH Aachen Universitynicolas.gauger@rhrk.uni-kl.de

Thomas EconomonDepartment of Aeronautics and AstronauticsStanford Universityeconomon@stanford.edu

Francisco PalaciosStanford Universityfpalacios@stanford.edu

Juan J. AlonsoDepartment of Aeronautics and AstronauticsStanford University

236 CS15 Abstracts

jjalonso@stanford.edu

MS303

Time-Domain Simulation of Two Dimensional Elas-tic Scattering

We show how a combination of a simple Nystromdiscretization in the Laplace domain and ConvolutionQuadrature can be used for simulation of transient elas-tic waves around a finite number of obstacles and cracks intwo dimensions. The implementation of most of the inte-gral operators is based on naive quadrature formulas andwell chosen mixing parameters. Only the hypersingularintegral operator requires the careful use of a regulariza-tion formula that is known in the literature. The CalderonCalculus thus defined can be used for exterior scatteringproblems, transmission problems in locally homogeneousmaterials, and even in problems in wave-structure interac-tion.

Victor DominguezUniversidad Publica de NavarraSpainvictor.dominguez@unavarra.es

Tonatiuh Sanchez-VizuetUniversity of Delawaretonatiuh@math.udel.edu

Francisco J. J. SayasDepartment of Mathematical SciencesUniversity of Delawarefjsayas@math.udel.edu

MS303

Variable Order Fast Multipole Method for an Elas-todynamic BEM

A fast time domain BEM based on the CQM is understudy. Chebyschev polynomials are used as kernel expan-sion within the Fast Multipole Method. Furthermore, a di-rectional clustering schema is applied to establish the hier-archical cluster tree. A variable order FMM is implementedto obtain optimal complexity while ensuring convergence.Some examples show the suitability of the proposed ap-proach.

Thomas TraubGraz Univeristy of TechnologyInstitute of Applied Mechanicsthomas.traub@tugraz.at

Martin SchanzTechnical University of Grazm.schanz@tugraz.at

MS303

Accuracy of the Marching-on-in-Time Scheme forTd-Bie Methods

The marching-on-in-time (MOT) scheme is a popular dis-cretization technique for Time Domain Integral Equationmethods. The choice of temporal basis function has a pro-found impact on the computational characteristics. Wewill present an analysis of the accuracy in time of the MOTscheme based on the interpolation accuracy of the tempo-ral basis functions. Surprisingly, a higher order of accuracy

has been observed in numerical experiments with splinesthan for Lagrange basis functions with equal support.

Elwin Van ’t WoutUniversity College LondonCentre for Medical Image Computinge.wout@ucl.ac.uk

MS303

Recent Advances in the Convolution Quadratureand Temporal Galerkin Approaches to TransientElectromagnetics

Time domain integral equation based methods for the so-lution of electromagnetics and scattering problems havebeen increasing in popularity in recent years. Two meth-ods, convolution quadrature and temporal Galerkin, havebecome popular for the discretization of these equations,and have spawned many variants. This talk will compareand contrast these methods, especially in their most recentincarnations in electromagnetics, with respect to stability,accuracy, and efficiency.

Daniel WeileUniversity of Delawareweile@ee.udel.edu

Balasubramaniam ShankerDepartment of Electrical and Computer EngineeringMichigan State Universityshanker@egr.msu.edu

MS304

Development of a Contact MiniApplication UsingKokkos

We present a new approach at the contact global search al-gorithm, targeted at providing high performance on many-core computer architectures. Sandias ACME contact li-brary was chosen to serve as the reference implementa-tion. A new global search algorithm was implemented, us-ing the Kokkos performance portable programming model,that is based on a Morton-code linearized Bounding Vol-ume Hierarchy (BVH) developed by Nvidia for executionon GPU co-processors. We conclude with results that com-pare the reference ACME search approach using MPI withthe new Morton algorithm using MPI and multicore pro-cessing within each MPI rank.

Glen Hansen, Patrick Xavier, Sam MishSandia National Laboratoriesgahanse@sandia.gov, pgxavie@sandia.gov,smish@sandia.gov

MS304

Co-Designing Hierarchical Algorithms: Applica-tion to Vlasov-Maxwell Particle-in-Cell Methods

Often, multiscale mathematical descriptions admit a multi-layered (hierarchical) description based on a systematiccoarse-graining procedure. Recently, such hierarchical de-scriptions have been demonstrated to provide significant al-gorithmic acceleration in a number of challenging applica-tions. Moreover, the layered nature of these algorithms hasopened novel opportunities for co-design, which can be ex-ploited to maximize FLOPs and minimize communication.In this presentation, we will discuss our co-design strat-egy for hierarchical algorithms, exemplified with a particle-

CS15 Abstracts 237

based implementation of the Vlasov-Maxwell system.

Joshua Payne, Luis Chacon, Guangye Chen, ChrisNewman, Dana Knoll, Allen McPhersonLos Alamos National Laboratorypayne@lanl.gov, chacon@lanl.gov, gchen@lanl.gov, cnew-man@lanl.gov, nol@lanl.gov, mcpherson@lanl.gov

MS304

Uintah/Wasatch: Addressing Multiphsyics Com-plexity in a High-Performance Computing Envi-ronment

To address the coding and software challenges of modernhybrid architectures, we propose a modern approach tomultiphysics code development. The approach is based onusing a Domain Specific Language in tandem with runtimealgorithm generation. When coupled with a large-scaleparallel framework, the result is an architecture-proof codecapable of executing on hybrid platforms. We share ourexperience developing such a code - an effort that spans aninterdisciplinary team of engineers and computer scientists.

Tony SaadThe Institute for Clean and Secure EnergyDepartment of Chemical Engineering, University of Utahtony.saad@utah.edu

Christopher EarlUniversity of Utahearl.christopher@gmail.com

Abhishek BagusettyChemical EngineeringUniversity of Utahabhishek.bagusetty@utah.edu

Matthew MightThe University of Utahmight@cs.utah.edu

James C. SutherlandDepartment of Chemical EngineeringThe University of Utahjames.sutherland@chemeng.utah.edu

PP1

Lid Driven Cavity Simulations in 2d and 3d UsingHigh Accurate Methods

in this poster, numerical simulations of two-dimensionaland three-dimensional partial differential equations arepresented by solving the steady navier-stokes equationsin a lid driven cavity at high Reynolds numbers whereit becomes difficult. in two dimensions, we use thestreamfunction-vorticity formulation to solve the problemin a square domain. a numerical computational method isemployed to discretize the problem in the x and y directionswith a spectral collocation method. the problem is codedin the matlab programming environment. solutions at highreynolds numbers are obtained up to re=20000 on a finegrid. Also in this poster, the numerical computational sim-ulation for the three-dimensional lid-driven cavity problemare obtained by solving the velocity-vorticity formulationof the navier-stokes equations (which is the first time thatthis has been simulated with special boundary conditions)for various Reynolds numbers.

Badr Alkahtani

King Saud Universityalhaghog@gmail.com

PP1

Numerical Study of Thin Viscoelastic Films onSubstrates

We numerically study the interfacial dynamics and insta-bility of a thin viscoelastic film on a substrate. We use thelong wave approximation to describe the non-linear evo-lution of the interface. We consider different regimes ofslippage, and in each regime, we investigate the role of theliquid viscoelasticity and of the contact angle on the thinfilm break-up. Numerical solutions of the full non-linearequations are compared with the results of the linear sta-bility analysis.

Valeria BarraNew Jersey Institute of Technologyvb82@njit.edu

Shahriar AfkhamiDepartment of Mathematical SciencesNew Jersey Institute of Technologyshahriar.afkhami@njit.edu

PP1

A Novel Modeling Approach for Multiscale, Mul-tiphysics Flow

Turbulent combustion simulation remains a challengingproblem due to the wide range of time and length scalesassociated with the governing physics. We propose a novelmethodology, termed Lattice-Based Multiscale Simulation(LBMS) that creates a 3D network of widely spaced lineswith fully resolved 1D physics along each line. Local tur-bulence along a line is modeled stochastically while lattice-scale advection is captured directly. LBMS is ideal for sit-uations where multiscale coupling is key like wall-boundedflows, reacting flows, etc.

Derek A. ClineUniversity of UtahChemical Engineering Departmentderek.cline@chemeng.utah.edu

PP1

Flusepa - a Navier-Stokes Solver for UnsteadyProblems with Bodies in Relative Motion : Towarda Task-Based Parallel Version over a Runtime Sys-tem for Large Simulations

FLUSEPA code is designed to handle unsteady prob-lems with bodies in relative motion (stage separation) andstrong shocks. A finite volume formulation is used to solvethe RANS equations. Time integration consists on an ex-plicit temporal adaptive solver. We present a task basedparallel version of the aerodynamic solver designed fromthe previous MPI/OpenMP one and using a modern run-time system to schedule the tasks. An Ariane 5 boosterseparation computation will be presented.

Jean Marie Couteyen CarpayeAirbus Defence and SpaceInriajean-marie.couteyen@inria.fr

Jean Roman

238 CS15 Abstracts

INRIAJean.Roman@inria.fr

Pierre BrennerAirbus Defence and Spacepierre.brenner@astrium.eads.net

PP1

Efficiency of an Adjoint Industrial CFD Code

We apply Algorithmic Differentiation on the commercialflow solver CFD-ACE+ to derive a discrete adjoint code.The objective is to assess its performance and to improveits efficiency in terms of memory consumption and runtime.To achieve that, we combine the flexibility of an operatoroverloading tool with the efficiency of an adjoint code gen-erated by source transformation. In addition, we speed upthe adjoint computation by exploiting the mathematicalaspect of the involved fixed-point iteration.

Zahrasadat DastouriSTCE,RWTH Aachen Universitydastouri@stce.rwth-aachen.de

Johannes LotzSTCE, RWTH Aachen UniversityGermanylotz@stce.rwth-aachen.de

Uwe NaumannRWTH Aachen UniversitySoftware and Tools for Computational Engineeringnaumann@stce.rwth-aachen.de

PP1

Production of Dissipative Vortices by Solid Bodiesin the Inviscid Limit of Incompressible Fluid Flows:Comparison Between Prandtl, Navier-Stokes andEuler Solutions

We revisit the problem posed by Euler in 1748 that leadd’Alembert to formulate his paradox and we address thefollowing question: does energy dissipate when boundarylayer detaches from a solid body in the vanishing viscositylimit? To trigger detachment we consider a vortex dipoleimpinging onto a wall and we compare the numerical solu-tions of Euler, Prandtl, and Navier-Stokes equations. Weobserve the formation of two opposite-sign boundary layerswhose thickness scales as predicted by Prandtl’s 1904 the-ory. But after a certain time Prandtl’s solution becomessingular, while the Navier-Stokes solution collapses downto much finer thickness for the boundary layers, in accor-dance with Kato’s 1984 theorem. Then the boundary layersroll up and form vortices which detach from the wall anddissipate a finite amount of energy, even in the vanishingviscosity limit.

Marie FargeLMD-CNRSEcole Normale Superieurefarge@lmd.ens.fr

Romain Nguyen van yenFreie University, Berlin, Germanyromain.nguyenvanyen@gmail.com

Matthias WaidmannFreie University, Berlin (Germany

matthias.waidman@math.fu-berlin.de

Kai SchneiderUniversite de Provence, Aix-MarseilleCentre de Mathematiques et Informatiquekschneid@cmi.univ-mrs.fr

Rupert KleinFreie Universitat Berlinrupert.klein@math.fu-berlin.de

PP1

A Numerical Study of Shock-Induced Cavity Col-lapse in a Solid Explosive

The shock-induced collapse of a gas-filled cavity in a solidexplosive is examined. The system is modeled as a multi-material compressible fluid with a mixture equation ofstate and an ignition-pressure reaction rate. The govern-ing equations are solved numerically using a Godunov-typescheme designed to accommodate the large impedance mis-match at the fluid-solid interface. Results are described forellipsoidal cavities of various shapes to determine whetherthe collapse initiates a detonation in the reactive material.

James R. GambinoRPIgambij@rpi.edu

Ashwani K. KapilaRensselaer Polytechnic Inst.kapila@rpi.edu

Donald W. SchwendemanRensselaer Polytechnic InstituteDepartment of Mathematical Sciencesschwed@rpi.edu

William HenshawRensselaer Polytechnic Institutehenshw@rpi.edu

PP1

Scalable Advection Algorithms for Multi-Tracers inClimate Codes

One of the important goals of ACES4BGC project (Apply-ing Computationally Efficient Schemes for BioGeochemicalCycles) is to implement and optimize new computationallyefficient advection algorithms for large number of tracerspecies. This work demonstrates a framework that uses in-tersection algorithms developed in MOAB (Mesh OrienteddatABase), linked with a HOMME dynamical core driver.

Iulian GrindeanuArgonne National Laboratoryiulian@mcs.anl.gov

Kara PetersonSandia Natl. Labskjpeter@sandia.gov

Vijay Mahadevan, Navamita Ray, Rajeev JainArgonne National Laboratoryvijay.m@gmail.com, navamitaray@gmail.com,

CS15 Abstracts 239

jain@mcs.anl.gov

PP1

Fast Ship Hydrodynamics Via Novel Methods

An existing high-order finite difference, potential flowsolver for large-scale ocean wave modeling is extendedto include interaction with floating bodies via a newimmersed-boundary technique based on weighted leastsquares. High-order WENO schemes are used for the free-surface boundary conditions to obtain stable solutions forthe linear seakeeping response of a ship at forward speed.The code is implemented on massively parallel GPU archi-tectures using the CUDA API.

Stavros KontosDTU - Technical University of Denmarkstakon@mek.dtu.dk

Ole LindbergFORCE Technologyold@force.dk

Allan Engsig-KarupThe Technical University of Denmarkapek@dtu.dk

Harry BinghamTechnical University of DenmarkDTU MECHANICAL ENGINEERINGhbb@mek.dtu.dk

PP1

A Conservative, Positivity Preserving Scheme forReactive Solute Transport Problems in Moving Do-mains

We study the mathematical models and numerical schemesfor reactive transport of a soluble substance in deformablemedia. The problem is modeled by a convection-diffusionadsorption-desorption equation in moving domains. Wepresent a conservative, positivity preserving, high resolu-tion ALE-FCT scheme for this problem in the presenceof dominant transport processes and wall reactions on themoving wall. A Patankar type time discretization is pre-sented, which provides conservative treatment of nonlinearreactive terms. Consequences of this result are significantin the area of, e.g., nano-particle cancer drug delivery. Ourresult shows that periodic excitation of the cancerous tissueusing, e.g., ultrasound, may enhance adsorption of cancerdrugs carried by nano-particles via the human vasculature.

Sibusiso MabuzaUniversity of Houstonsmabuza@math.uh.edu

PP1

Singly-Periodic Stokes Flow with a Wall

A closed formula for the 2D singly-periodic laminar veloc-ity field near a solid straight boundary is derived using themethod of images. The flow is induced by regularized peri-odic forces. This result provides a model, for instance, forthe modeling of cilia.

Forest O. MannanTulane University

fmannan@tulane.edu

Ricardo CortezTulane UniversityMathematics Departmentrcortez@tulane.edu

PP1

Computational Hydrodynamics: How Portableand Scalable Are Heterogeneous ProgrammingParadigms?

Many-core era applications at the interface of mathemat-ics and computer science adopt modern parallel program-ming paradigms and expose parallelism through proper al-gorithms. We present results for a novel massively parallelfree surface wave model suitable for advanced experimentsin Numerical Wave Tanks. Our application exhibits ex-cellent performance portability and scalability using hy-brid MPI-OpenCL/CUDA and running on arbitrary sys-tem sizes including desktops, superclusters and cloud uti-lizing heterogeneous devices like multi-core CPUs, GPUs,and Xeon Phi coprocessors.

Wojciech PawlakDTU Compute, Technical University of DenmarkAllan P. Engsig-Karup Associate Professor, Ph.D.wojciechpawlak@gmail.com

Allan Engsig-KarupThe Technical University of Denmarkapek@dtu.dk

Stefan GlimbergLloyd‘s Register Consultingstefan.glimberg@lr.org

PP1

A Fully Discrete Derivation of a Direct Ale Conser-vative Scheme for Compressible Hydrodynamics

Lagrange plus remap schemes have been used for years inindustrial applications. However, this kind of scheme canlead to some difficulties with conservativity and computa-tional cost. In this work, a direct ALE scheme is providedusing a least action principle to a discretized action inte-gral in both space and time. The internal energy equationfollows from the conservation of the total energy. Thismimetic procedure guarantees the physical compatibilitybetween the thermodynamical variables.

Thibaud Vazquez-GonzalezCEA Bruyeres le Chatelthibaud.vazquez-gonzalez@cea.fr

Antoine Llor, Christophe FochesatoCEAantoine.llor@cea.fr, christophe.fochesato@cea.fr

PP2

A Non Standard Scheme for Nagumo Type Differ-ential Equations

In this work, we design explicit difference schemes for theNagumo reaction-diffusion and the Allen-Cahn equations.The Nonstandard exact schemes that we design for thespace-independent sub-equations help to reduce the com-putational cost common with difference schemes approx-

240 CS15 Abstracts

imation of singularly perturbed equations like the Allen-Cahn. A careful assemblage of these schemes with the en-ergy preserving scheme of the steady state equation yieldsa uniformly convergent difference scheme for the equations.

Adebayo A. AderogbaUniversity of PretoriaSouth Africaaderogba adebayo@yahoo.com

Michael Chapwanya, Pius ChinDepartment of Mathematics and Appl Math.University of Pretoriamichael.chapwanya@up.ac.za, pius.chin@up.ac.za

PP2

Reduced Basis Methods for Calibration and OptionPricing

We present reduced basis approximations for parametrizedtime-dependent variational (in-)equalities with the specialfocus on applications from finance. In particular, we con-sider the case of calibrating European and American op-tions with the Heston model. With the use of an offline-online computational procedure, we significantly reducethe computational cost of the calibration phase. Numericaltests illustrate the approximation quality and convergenceof the reduced basis methods and it’s advantage in appli-cation to the calibration algorithms.

Olena BurkovskaTechnical University of Munichburkovsk@ma.tum.de

Kathrin GlauTechnical University Munichkathrin.glau@tum.de

Mirco MahlstedtTechnical University of MunichChair of Mathematical Financemirco.mahlstedt@tum.de

Barbara WohlmuthTechnical University of Munichbarbara.wohlmuth@ma.tum.de

PP2

A Fast and Stable Explicit Operator SplittingMethod for Phase-Field Models

We propose a combined finite difference and pseudo-spectral method for one- and two-dimensional nonlineardiffusion equations for thin film epitaxy with slope selectionand Cahn-Hilliard equation. Equations are split into non-linear part, solved using the method of lines approach to-gether with an efficient large stability domain ODE solver;and linear part, solved by a pseudo-spectral method, whichis based on the exact solution and thus has no stability re-striction on the size of time step. Finally, an adaptivetime-stepping strategy is introduced for long time simula-tion.

Yuanzhen ChengTulane Universityycheng5@tulane.edu

Alexander KurganovTulane UniversityDepartment of Mathematicskurganov@math.tulane.edu

Zhuolin QuTulane Universityzqu1@tulane.edu

Tao TangHong Kong Baptist Universityttang@math.hkbu.edu.hk

PP2

Method of Lines Transpose Schemes for ParabolicProblems

We present a novel numerical scheme suitable for solv-ing parabolic differential equation model using the Methodof Lines Transpose (MOLT ) combined with the successiveconvolution operators. The primary advantage is that theoperators can be computed quickly in O(N) work, to highprecision; and a multi dimensional solution is formed bydimensional sweeps. We demonstrate our solver on theAllen-Cahn and Cahn-Hilliard equation.

Hana ChoMichigan State Universitychohana@math.msu.edu

Andrew J. ChristliebMichigan State UniverityDepartment of Mathematicsandrewch@math.msu.edu

Matt CausleyKattering Universitymatt.causley@gmail.com

David SealMichigan State Universityseal.david@gmail.com

PP2

Comparison of Nonlinear and Linear StabilizationSchemes for Advection-Diffusion Equations

Standard finite element discretizations of advection-diffusion equations introduce unphysical oscillationsaround steep gradients. Therefore, stabilization must beadded to the discrete formulation to obtain correct solu-tions. The SUPG, dCG91, and Entropy Viscosity schemesare compared using stationary and non-stationary testequations. Differences in maximum overshoot and under-shoot, smear, and convergence orders are compared usingcode written using deal.ii

Ryan R. GroveSIAM Webmaster at Clemson Universityrgrove@clemson.edu

Timo HeisterClemson UniversityMathematical Sciences

CS15 Abstracts 241

heister@clemson.edu

PP2

A Task-Parallel Approach for Solving PDEs on aLattice

We solve PDE’s on a lattice. This creates a unique set ofcommunication patterns, at the intersections of the lineson the lattice, creating a coarse mesh, and between parallellines, creatine overlapping fine meshes. We use a directeda-cyclical graph to order the execution and communicationin parallel across the lattice, via sender-poller; allowing, inparallel, different pieces of the problem to be solved con-currently while communication is happening.

John T. HutchinsBoise State University‘Hutchinsjh@hotmail.com

Derek A. ClineUniversity of UtahChemical Engineering Departmentderek.cline@chemeng.utah.edu

James C. SutherlandDepartment of Chemical EngineeringThe University of Utahjames.sutherland@chemeng.utah.edu

PP2

Finite Element Analysis of Free Material Optimiza-tion Problems

In Free Material Optimization, the design variable is thefull material tensor of an elastic body. Written in matrixnotation one obtains a control-in-the-coefficients problemfor the material tensor. With this poster we present re-cent results in the finite element analysis in Free MaterialOptimization. We employ the variational discretization ap-proach, where the control (i.e., material tensor) is only im-plicitly discretized. Numerical examples supplement ouranalytical findings.

Tobias JordanUniversity of HamburgDepartment of Mathematicstobias.jordan@uni-hamburg.de

Michael HinzeUniversitat HamburgDepartment Mathematikmichael.hinze@uni-hamburg.de

PP2

Higher Order Numerical Schemes for Convec-tion Diffusion Equation Based on B-Spline Quasi-Interpolation

In the present work, we propose B-Spline Quasi-Interpolation (BSQI) based higher order numerical schemefor convection-diffusion equation in one and two space di-mensions. The linear stability of BSQI scheme is establishusing the von-Neumann analysis. We find the CFL con-dition under which BSQI scheme is stable. Numerical ex-periments are performed for the non-linear problems likeBurgers’ equation, Buckley-Leverett, and the incompress-ible flow to measure the accuracy and rate of convergence

of the BSQI scheme.

Rakesh KumarIIT Bombayrakeshk@math.iitb.ac.in

Sambandam BaskarIndian Institute of Technology Bombaybaskar@math.iitb.ac.in

PP2

NIST AMR Benchmarks

Adaptive mesh refinement (AMR) techniques for the nu-merical solution of PDEs have been under development formany years. Most research papers conclude with numeri-cal results to demonstrate the effectiveness of a proposedmethod. Although there are some commonly used prob-lems, like the L-domain problem, many disparate test prob-lems have been used. NIST has mined the AMR literatureto create a collection of standard test/benchmark problemsfor AMR. The resulting web resource will be demonstrated.

William F. MitchellNIST, Gaithersburg, MDwilliam.mitchell@nist.gov

PP2

Finite Element Methods for the Evolution Problemin General Relativity

Gravitational waves can be understood as small ripples inthe fabric of the Universe, caused by moving masses. Todetect such weak waves, several new gravitational waveobservatories are being built. Computer simulations areessential for determining expected signals and interpretingthe data. This project consists of the design and implemen-tation of a new mixed finite element method for the prop-agation of gravitational waves, by adapting the recentlydeveloped Finite Element Exterior Calculus framework.

Vincent Quenneville-BelairSchool of MathematicsUniversity of Minnesotavqb@umn.edu

PP2

Massively Parallel Radiation Transport Sweeps onUnstructured Grids

The massively parallel radiation transport code PDT hasrecently scaled to 432,000 processes with an efficiencygreater than 70%. The discretization techniques employa Discontinuous FEM method in space and a discrete-ordinate collocation in angle. The algorithm is based ona transport sweep, whereby the solution for a given an-gle is done one cell at a time. The parallel transportsweep algorithm is provably optimal for logically Cartesianmeshes. However, complex geometries cannot be efficientlymeshed with regular grids, even with point motion. In thiswork, we present an unstructured mesh generation capa-bility that satisfies most of the requirements for optimalsweeps. Notably, the subdomain partitions remain convexand pipe-filling within a subdomain is preserved; however,a load imbalance in terms of spatial unknowns may ex-ist between subdomains due to local geometrical features.Numerical results are presented and strategies to mitigate

242 CS15 Abstracts

spatial load imbalance are discussed.

Jean C. Ragusa, Tarek GhaddarDepartment of Nuclear EngineeringTexas A&M Universityjean.ragusa@tamu.edu, tghaddar92@gmail.com

Michael AdamsTexas A&M Universityi.am.michael.adams@gmail.com

PP2

The Discrete Maximum Principle in the Family ofMimetic Finite Difference Methods

The Maximum Principle is the important property ofPDEs. To mimic this property in simulations is very de-sirable in wide range of applications. The mimetic finitedifference method produces a family of schemes with equiv-alent properties such as the stencil, stability region, andconvergence order. Each member is defined by parameterswhich can be chosen locally for every cell. We presenta new adaptation methodology that identifies memberswhich satisfies the discrete maximum principle.

Daniil SvyatskiyLos Alamos National Laboratorydasvyat@lanl.gov

Gianmarco ManziniLANLgmanzini@lanl.gov

Konstantin LipnikovLos Alamos National Laboratorylipnikov@lanl.gov

PP2

A Locally Adaptive RBF-FD Method

Conventional Radial Basis Function (RBF) methods fornumerically solving partial differential equations use globalapproximations resulting in dense matrices that grow insize if the algorithm refines. The Radial Basis Function –Finite Difference (RBF-FD) approach is a local approxima-tion method that utilizes nearest neighbor nodes and yieldsa sparse implementation. Unfortunately RBF-FD matriceshave fixed stencils and the approximations can lose accu-racy. In this paper we propose using local approximationswith locally adaptive stencils that take advantage of bothglobal and local approximations. In this approach the sten-cil sizes stay fixed where the solution is smooth but growin size only where refinement is needed. The advantage ofthis method is that it is computationally efficient and sta-ble offering comparable accuracy to global approximationswith significantly lower computational cost.

Wade MeyersUniversity of Wisconsin - Stoutmeyersw3476@my.uwstout.edu

Talin MasihimirzakhanianCal Poly Pomonatalinm@csupomona.edu

Keith WojciechowskiUniversity of Wisconsin - Stout

wojciechowskik@uwstout.edu

PP2

A Second-Order Maximum Principle PreservingLagrange Finite Element Technique for NonlinearScalar Conservation Equations

Based on one of our accepted paper (J.-L. Guermond etal.), this poster will show an explicit, (at least) second-order and maximum principle satisfying lagrange finite el-ement method for solving nonlinear scalar conservationequations. The algorithm works for arbitrary meshes inany space dimension and for all Lipschitz fluxes. The for-mal second-order accuracy and the convergence propertiesare tested on a series of linear and nonlinear benchmarkproblems.

Jean-Luc GuermondDepartment of MathematicsTexas A&M, USAguermond@math.tamu.edu

Murtazo NazarovTAMUmurtazo@math.tamu.edu

Bojan PopovDepartment of MathematicsTexas A&M Universitypopov@math.tamu.edu

Yong YangTexas A&M Universityyytamu@math.tamu.edu

PP3

A New Test for Exclusion Algorithm to Find theOptimum Value of Function in Rn

The problem of finding the global minimum of a vectorfunction is very common in science, economics and engi-neering. One of the most notable approaches to find theglobal minimum of a function is that based on intervalanalysis. In this area, the exclusion algorithms (EAs) area well-known tool for finding the global minimum of a func-tion over a compact domain. There are several choices forthe minimization condition. In this paper, we introduce anew exclusion test and analyze the efficiency and compu-tational complexity of exclusion algorithms based on thisapproach. We consider Lipschitz functions and give a newminimization condition for the exclusion algorithm. Thenwe study the convergence and complexity of the method.

Ibraheem AlolyanKing Saud Universityialolyan@ksu.edu.sa

PP3

Approximation and Error Estimation in High Di-mensional Space for Stochastic Collocation Meth-ods on Arbitrary Sparse Samples

We have develop a fast method that can capture piece-wise smooth functions in high dimensions with high orderand low computational cost. This method can be used forboth approximation and error estimation of stochastic sim-ulations where the computations can either be guided or

CS15 Abstracts 243

come from a legacy database. We demonstrate how thismethod compares to Gaussian processes.

Richard ArchibaldComputational Mathematics GroupOak Ridge National Labratoryarchibaldrk@ornl.gov

PP3

Rational Least Squares Fitting using Krylov Spaces

For given square matrices A,F and a vector v, we considerthe problem of finding a rational function Rmin

m of type(m,m) such that

‖Fv −Rm(A)v‖22 → min,

and propose an iterative algorithm for its solution. In thespecial case when A = diag(λj) and F = diag(ψj) arediagonal we have a weighted rational least squares fittingproblem

∑Nj=1 |vj |2 · |ψj −Rm(λj)|2 → min, and compare

our method to the popular vector fitting algorithm.

Mario BerljafaSchool of MathematicsThe University of Manchesterm.berljafa@maths.man.ac.uk

Stefan GuettelThe University of Manchesterstefan.guettel@manchester.ac.uk

PP3

A Hybrid Openmp/mpi Cg Iterative Eigensolverfor First-Principles Plane Wave Materials ScienceCodes

First-principles materials science codes based on densityfunctional theory (DFT) and using plane waves (PW) havebecome the largest user (by method) of computer cycles atscientific computer centers around the world. We presenta hybrid OpenMP/MPI Conjugate Gradient based itera-tive eigensolver that allows this approach to scale to tensof thousands of cores on modern many core parallel com-puters. Performance results will be presented for the CrayXE6 and XC30 architectures.

Andrew M. CanningLawrence Berkeley National Laboratoryacanning@lbl.gov

PP3

All Real Eigenvalues of Symmetric Tensors

This poster displays how to compute all real eigenvaluesof a symmetric tensor. As is well known, the largest orsmallest eigenvalue can be found by solving a polynomialoptimization problem, while the other middle eigenvaluescan not. We propose a new approach for computing all realeigenvalues sequentially, from the largest to the smallest.We show that each eigenvalue can be computed by solvinga finite hierarchy of semidefinite relaxations. Numericalexperiments are presented.

Cui Chunfeng, Dai Yu-HongAcademy of Mathematics and Systems Science,Chinese Academy of Sciencescuichf@lsec.cc.ac.cn, dyh@lsec.cc.ac.cn

Nie JiawangDepartment of Mathematics,University of California San Diegonjw@math.ucsd.edu

PP3

A Python Toolbox for Shape Optimization in Imag-ing and Data Analysis

Many data analysis and image processing problems are nat-urally expressed as shape optimization problems, e.g. im-age segmentation, surface reconstruction. The shape opti-mization approach is a great fit for such problems becauseof its intuitiveness and the ?exibility to easily incorporatedata ?delity, geometric regularization and statistical priorterms. However, carrying out the actual minimization inan ef?cient and reliable manner requires overcoming manytechnical challenges. In this work, we introduce a Pythontoolbox that implements a diverse collection of shape ener-gies for image processing, and state-of-the-art optimizationmethods to compute their solutions.

Gunay DoganTheiss Research, NISTgunay.dogan@nist.gov

PP3

Discovering Block Structure in Graphs with Ap-proximate Eigenvectors

Graphs and Networks are important in modeling structureacross disciplines. We demonstrate that graph partition-ing in a minimum cut sense can be improved with an en-semble of low-fidelity eigenvectors which can outperforma single high-fidelity eigenvector. These ensembles can becomputed faster and be more helpful than one high-fidelityeigenvector. Since the individual ensemble members are in-dependent they can be computed in parallel.

James FairbanksGeorgia Institute of Technologyjames.fairbanks@gatech.edu

Geoffrey D. SandersCenter for Applied Scientific ComputingLawrence Livermore National Labsanders29@llnl.gov

PP3

Efficient Multigrid Methods for Distributed Opti-mal Control Problems Constrained by ParabolicEquations

In this work we present numerical computations in sup-port of our theoretical results regarding convergence prop-erties of multigrid preconditioners for linear systems aris-ing in the solution process of space-time distributed opti-mal control problems constrained by linear and semi-linearparabolic equations. As for elliptic-constrained problems,the number of preconditioned linear iterations per opti-mization iteration is shows to decrease with increasing res-olution, but the rate of decrease is suboptimal by half anorder.

Mona HajghassemDepartment of Mathematics and StatisticsUniversity of Maryland, Baltimore Countymona4@umbc.edu

244 CS15 Abstracts

Andrei DraganescuDepartment of Mathematics and Statistics, UMBCUniversity of Maryland, Baltimore Countydraga@umbc.edu

PP3

Computing the Heat Kernel of a Graph for a LocalClustering Algorithm

We present an efficient local clustering algorithm that findscuts in large graphs by performing a sweep over a heatkernel pagerank vector. We show that for a subset S ofCheeger ratio φ, many vertices in S may serve as seedsfor a heat kernel random walk which will find a cut ofconductance O(

√φ). Further, the random walk process is

performed in time sublinear in the size of the graph.

Olivia SimpsonUniversity of California, San Diegooliviamsimpson@gmail.com

PP4

Reduced Order Modelling for Optimal CancerTreatment

We study reduced order modelling for optimal radiother-apy treatment plan. Boltzmann equation is used to modelthe interaction between radiative particles with tissue. Atfirst, we solve optimization problems: minimizing the de-viation from desired dose distribution. Then we consider aparameterized geometry. In offline stage we solve a prob-lem for sampled parameter values. The online phase thenconsists of solving the reduced problem for the actual setof parameters. Numerical results are presented.

Bahodir AhmedovAachen Institute for Advanced Study inComputational Engineering Science (AICES)ahmedov@aices.rwth-aachen.de

Michael Herty, Martin GreplRWTH Aachen Universityherty@igpm.rwth-aachen.de, grepl@igpm.rwth-aachen.de

PP4

A Mesh Free Method for Numerical Simulation ofCalcium Dynamics In Ventricular Myocytes

We consider a coupled system of non-linear reaction-diffusion equations that model the spatio-temporal vari-ation of intracellular calcium concentration in ventricularmyocytes. We introduce a modified mesh free method andutilize exponential time differencing to significantly reducethe simulation time. At the end we present numerical re-sults demonstrating the stability of the method when usedon uneven distribution of nodes.

Emmanuel O. Asante-AsamaniDepartment of Mathematical SciencesUniversity of Wisconsin-Milwaukeeeoa@uwm.edu

Bruce WadeDepartment of Mathematical Sciences, UW-MilwaukeeMilwaukee, Wisconsin 53201-0413wade@uwm.edu

Zeyun Yu

University of Wisconsin-Milwaukeeyuz@uwm.edu

PP4

Computed Tear Film and Solute Dynamics on AnEye-Shaped Domain

The concentration of ions (osmolarity) in the tear film isa key variable to understanding its dynamics. We derivea system of nonlinear partial differential equations (PDEs)that couples solutes and fluid dynamics on a 2D eye-shapeddomain. We solve these PDEs using the Overture computa-tional framework with a hybrid BDF/RKC time-steppingscheme. Our results agree with existing 1D models andprovide new insight into the osmolarity distribution andfluorescence imaging for in vivo experiments.

Richard BraunUniversity of DelawareDepartment of Mathematical Sciencesbraun@math.udel.edu

Longfei LiDepartment of Mathematical SciencesUniversity of Delawarelongfei@udel.edu

Tobin DriscollUniversity of DelawareMathematical Sciencesdriscoll@udel.edu

William Henshaw, Jeffrey BanksRensselaer Polytechnic Institutehenshw@rpi.edu, banksj3@rpi.edu

P. Ewen King-SmithOhio State Universityking-smith.1@osu.edu

PP4

The Transcriptomic Clock of Human Cerebral Cor-tex Development

Singular value decomposition and clustering analysis ofstem cell RNA transcription data reveals the genes associ-ated with the stages of human embryonic cerebral cortexdevelopment. The method discovered a previously uniden-tified stage between pluripotency and neural differentia-tion containing distinct transcriptional patterns for overtwo thousand differentially expressed genes. Enrichmentanalyses of genes associated with neurological diseases withrespect to the resulting corticogenesis clock reveal distinctstages of development associated with root causes of thedisease.

Elisabeth M. BrownRensselaer Polytechnic Institutebrowne6@rpi.edu

Kristin BennettMathematical SciencesRensselaer Polytechnic Institutebennek@rpi.edu

Hannah De Los Santos, Joey LeaRensselaer Polytechnic Institutedelosh@rpi.edu, leaj2@rpi.edu

CS15 Abstracts 245

Nathan Boles, Thomas Kiehl, Sally Temple, ChristopherFasanoNeural Stem Cell Institutenathanboles@neuralsci.org, tomkiehl@neuralsci.org, sal-lytemple@neuralsci.org, chrisfasano@neuralsci.org

PP4

Computational Methods to Study the Coordina-tion of Mechanical Forces Involved in AmoeboidCell Migration

We present a computational model to study the interplayof cellular mechanics, substrate mechanics and cell-matrixinteraction and the resulting migration. Our mathemat-ical framework considers a porous viscoelastic cytoplasm,adhesion dynamics, and substrate mechanics. Our modelintroduces a novel way of simulating a viscoelastic deform-ing network. Using our methodology we present insightinto the 3D cell-substrate forces for cells migrating on flatsubstrates. The development and maintenance of multi-cellular organisms relies on cell migration. During theseprocesses, cells encounter a wide range of extracellular en-vironments and adapt their migration strategy in responseto mechanical properties of their environment. One of thecurrent challenges in cellular biology is to understand howthe extracellular environment modulates the deploymentof the cells’ molecular machinery to produce different mi-gratory behaviors.

Calina A. CoposUniversity of California Davisccopos@math.ucdavis.edu

Robert D. GuyMathematics DepartmentUniversity of California Davisguy@math.ucdavis.edu

PP4

Segmentation and Processing of Brain Images ofMultiple Modalities in 2 and 3 Dimensions

Medical imaging of various modalities continues to ad-vance, providing higher resolution and higher signal tonoise ratios than ever before. Software must keep up bynot only accounting for better quality images, but also withlarger and larger datasets. We present work on segment-ing and processing Magnetic resonance (MRI) and Elec-tron microscopy (EM) images using advanced algorithmsdesigned to scale in both 2 and 3 dimensions.

John Edwards, Brian SummaScientific Computing and Imaging InstituteUniversity of Utahjedwards@sci.utah.edu, bsumma@sci.utah.edu

Valerio PascucciSCI Institute - University of Utahpascucci@sci.utah.edu

Christopher JohnsonUniversity of UtahDepartment of Computer Sciencecrj@sci.utah.edu

PP4

Improving Performance of Multi-Level NonrigidRegistration of Two Ct-Based Lung Images With

Use of Gpu Computing

Graphics Processing Units (GPUs) have been successfullyemployed to accelerate scientific computing applicationsin several disciplines, including medical image process-ing. We demonstrate a novel computation- and memory-efficient diffeomorphic multi-level B-Spline transform com-posite method on GPUs for improving performance of non-rigid registration of two CT lung images. The GPU methodis compared against its CPU counterpart, with GPU per-formance 112 times faster than the single-threaded CPUversion occurring at highest resolutions while preservingaccuracy.

Nathan Ellingwood, Youbing YinUniversity of Iowanathan.ellingwood@gmail.com, youbing.yin@gmail.com

Matthew SmithNational Cheng Kung Universitymsmith@mail.ncku.edu.tw

Ching-Long LinUniversity of Iowaching@engineering.uiowa.edu

PP4

Reaction of a Solid Tumor According to the Injec-tion of Medical Supplies into Heart and Liver

A mathematical model is developed to describe the varia-tion of a solid tumor cells density in response to medicalsupplies. Two factors, random motility and chemotaxis inresponse to TAF gradients are considered for the equationof tumor cells motion. The flow rate of medicines exertsinfluence on tumor cells density and tumor cells react sen-sitively to the medical supplies at the first second, and thedensity decreases to around 20% of the initial amount.

Jaegwi GoChangwon National Universityjggo@changwon.ac.kr

PP4

Shear Wave Filtering in Bouligand Structures

We propose that the presence of Bouligand-like structurein the dactyl club of the Stomatopod lead to wave filter-ing. The (nearly) periodicity of the microstructure suggestan interaction between the microstructure and propagat-ing stress waves. The propose model use a combination ofpropagator matrix approach and the Floquet-Bloch theo-rem. From these combined analyses we compute the trans-mitted energy for different microstructural configurations.

Nicolas Guarin ZapataPurdue Universitynicoguarin@gmail.com

Juan GomezUniversidad EAFITjgomezc1@eafit.edu.co

Nick Yaraghi, David KisailusUniversity of Californianyaraghi@gmail.com, david@engr.ucr.edu

Pablo Zavattieri

246 CS15 Abstracts

Purdue Universityzavattie@purdue.edu

PP4

Newtonian and Non-Newtonian Fluid Dynamics inAbdominal Aortic Aneurysms

Biomedical research has recently indicated that some spe-cific dynamic characteristics, such as the blood wall shearstress and oscillatory shear index, of the blood flow insidearteries with aneurysms are risk factors for both the en-largement and rupture of the associated aneurysm. Theprimary objective of the project is to determine the influ-ence that the geometry of an abdominal aortic aneurysmand the fluid constitutive model have on these specific char-acteristics.

Danielle D. Masse, Jason HowellCollege of Charlestonmassedd@g.cofc.edu, howelljs@cofc.edu

PP5

Adaptive Spectral Tensor-Train Decomposition forthe Construction of Surrogate Models

We present a novel method for approximating high-dimensional functions, the cost of which scales linearlywith the input parameter dimensionality. It hingeson the combination of the low-rank approximation offunctions through the functional form of the tensor-train decomposition and on the theory of polynomialapproximation [D. Bigoni, Y. M. Marzouk, and A.P. Engsig-Karup, Spectral tensor-train decomposition,arXiv preprint arXiv:1405.5713], using anisotropic adap-tive strategies to meet the desired accuracy. The methodis relevant for high-dimensional Uncertainty Quantificationand inference. Synthetic and real applications will be pre-sented.

Daniele Bigoni, Allan Engsig-KarupThe Technical University of Denmarkdabi@dtu.dk, apek@dtu.dk

Youssef M. MarzoukMassachusetts Institute of Technologyymarz@mit.edu

PP5

A Posteriori Error Estimation for a Cut Cell FiniteVolume Method in the Presence of Uncertainty

We consider a posteriori error estimates for interface prob-lems. These are differential equations whose data is definedpiecewise across a curve, or interface, partitioning the do-main into two sections. Often, this interface is determinedfrom a small number of measurements, each of which hasuncertainty associated with it, giving a stochastic interfaceproblem. We develop a method of computing the error foreach sample interface that is independent of the number ofsamples.

James B. Collins, Simon Tavener, Don EstepColorado State Universityjbcolli2@gmail.com, tavener@math.colostate.edu, es-

tep@stat.colostate.edu

PP5

Probability Measures on Numerical Solutions ofOdes for Uncertainty Quantification and Inference

Deterministic ODE solvers are widely used, but charac-terizing the error in numerical solutions within a coher-ent statistical framework is challenging. We successfullyaddress this problem by constructing a probability mea-sure over functions consistent with the ODE solution thatprovably contracts to a Dirac measure on the unique so-lution at rates determined by an underlying deterministicsolver. The measure straightforwardly derives from im-portant classes of numerical solvers and is illustrated onuncertainty quantification and inverse problems.

Patrick R. ConradMassachusetts Institute of Technologyp.conrad@warwick.ac.uk

Mark GirolamiUniversity College Londonm.girolami@warwick.ac.uk

Simo SarkkaAalto Universitysimo.sarkka@aalto.fi

Andrew StuartMathematics Institute,University of Warwicka.m.stuart@warwick.ac.uk

Konstantinos ZygalakisUniversity of Southamptonk.zygalakis@soton.ac.uk

PP5

Adaptive Bayesian Selection, Calibration, and Vali-dation of Coarse-Grained Models of Atomistic Sys-tems

The predictive power of coarse-grained (CG) approxima-tions of atomistic systems is explored. Bayesian methodsfor statistical calibration, validation, and model selectionusing model plausibilities are used to develop basic princi-ples for developing CG and, eventually, macro-scale mod-els. An adaptive algorithm for Bayesian calibration andselection of CG models is described and examples of appli-cation to polymer chains is presented.

Kathryn FarrellInstitute for Computational Engineering and SciencesUniversity of Texas at Austinkfarrell@ices.utexas.edu

J. Tinsley OdenThe University of Texas at AustinICESoden@ices.utexas.edu

Danial FaghihiInstitute for Computational Engineering and SciencesUniversity of Texas at Austin

CS15 Abstracts 247

danial@ices.utexas.edu

PP5

Emgr - Empirical Gramian Framework

Gramian-based model reduction is a well establishedmethod for linear state-space systems. Beyond linear sys-tems, empirical gramians expand the scope of gramian-based methods to nonlinear systems. Furthermore, empir-ical gramians can also be used for parametric model orderreduction, parameter identification and parameter reduc-tion. The empirical gramian framework is a Matlab soft-ware toolbox enabling the computation of seven types ofempirical gramians, which have applications in model re-duction, system identification and uncertainty quantifica-tion.

Christian HimpeInstitute for Computational und Applied MathematicsUniverstiy of Muensterchristian.himpe@uni-muenster.de

Mario OhlbergerUniversitat MunsterInstitut fur Numerische und Angewandte Mathematikmario.ohlberger@uni-muenster.de

PP5

Kernel Density Estimation for Implicit MonteCarlo Radiation Transport

We use kernel density estimation in the Fleck-and-Cummings implicit Monte Carlo method to obtain smoothsolution estimates in thermal radiative transfer problems.The kernel density estimators obtain conservative esti-mates when using reflective boundary corrections and re-solve steep gradients with locally adaptive bandwidths. Weshow that solutions obtained using kernel density estima-tors are smoother and exhibit substantially less statisticalnoise than traditional histogram tallies.

Aaron M. HolgadoTexas A&M Universityamholgado1@gmail.com

Robert HolladayVirginia Polytechnic Institute and State Universityrholla24@vt.edu

Allan WollaberLANLwollaber@lanl.gov

Mathew Cleveland, Todd UrbatschLos Alamos National Laboratorycleveland@lanl.gov, tmonster@lanl.gov

Ryan McClarrenTexas A&M UniversityUSArgm@tamu.edu

PP5

Distribution Functions of Water Saturation forthe Stochastic Buckley-Leverett Problem Via the

Streamline Method

We give an analytical expression for the one-point distribu-tion functions of the water saturation for the 1D stochas-tic Buckley-Leverett problem with uncertainty in porosityand in the total Darcy flux. These distribution functionsparticularly lead to any one-point statistics of the watersaturation. Comparisons with both MC simulations and alow order approximation approach are provided. Finally,based on the streamline concept, a generalization to mul-tiple spatial dimensions is outlined.

Fayadhoi IbrahimaStanford Universityfibrahim@stanford.edu

Daniel W. MeyerInstitute of Fluid Dynamicsmeyerda@ethz.ch

Hamdi TchelepiStanford UniversityEnergy Resources Engineering Departmenttchelepi@stanford.edu

PP5

Hybridized Reduced Basis Method and General-ized Polynomial Chaos for Solving Partial Differ-ential Equations

The generalized Polynomial Chaos(gPC) method is a popu-lar method for solving partial differential equations (PDEs)with random parameters. However, when the probabil-ity space has high dimensionality, the solution ensemblesize required for an accurate gPC approximation can belarge.We show that this process can be made more ef-ficient by closely hybridizing gPC with Reduced BasisMethod(RBM).

Jiahua JiangUniversity of Massachusetts, Dartmouthjjiang@umassd.edu

PP5

Kriging and Spatial Design Accelerated by Ordersof Magnitude: Combining Low-Rank CovarianceApproximations with FFT-Techniques

Computational power poses heavy limitations to theachievable problem size for Kriging. In separate researchlines, Kriging algorithms based on FFT and low-rank rep-resentations of covariance functions have been developed,both leading to drastic speedup factors. The current studycombines these ideas, reducing the computational complex-ity of Kriging to O(kqmdL

∗ logL∗), where kq is the rankof approximation, m the number of measurements, d di-mension, L∗ the number of lattice points along the longestedge of the regular d-dimensional lattice. These benefitscan be fully exploited when leaving the final result in low-rank format, or when further low-rank operations follow.The current study assumes second-order stationarity andsimple Kriging on a regular, equispaced lattice.

Alexander LitvinenkoSRI-UQ Center, King Abdullah University of Science andTechnalexander.litvinenko@kaust.edu.sa

Wolfgang Nowak

248 CS15 Abstracts

Institute for Modelling Hydraulic and EnvironmentalSystemsUniversity of Stuttgartwolfgang.nowak@iws.uni-stuttgart.de

PP5

A Nonlinear Non-Gaussian Smoother for Continu-ous Stochastic Dynamical Systems

We present a novel non-Gaussian smoothing methodol-ogy for high-dimensional stochastic fields governed by gen-eral nonlinear dynamics. The history of the system isquantitatively estimated using its stochastic dynamics andinformation gathered from noisy observations. Uncer-tainty is quantified using the reduced-order Dynamically-Orthogonal equations, and smoothing is performed by ef-ficiently carrying out Bayesian-inference in an evolvinglow-dimensional dominant subspace. Various examplesfrom computational-fluid-dynamics are provided, illustrat-ing the superior performance of the smoother compared toits Gaussian/Monte-Carlo counterparts.

Tapovan Lolla, Pierre LermusiauxMITltapovan@mit.edu, pierrel@mit.edu

PP5

Uncertainty Quantification in Incompressible FlowUsing Sparse Grids

This work based on a bachelor thesis introduces a sparsegrid stochastic collocation method for uncertainty quantifi-cation. We adapted the C++ sparse grid library SGpp forbenchmark scenarios in Matlab. The method was testedon a simple ODE example as well as on an incompress-ible flow scenario in 1-D and 3-D random parameter space.The sparse grid collocation solutions show promising re-sults with respect to accuracy and runtime compared toMonte Carlo methods.

Friedrich MenhornDepartment of Informatics, Technische UniversitatMunchenmenhorn@in.tum.de

Tobias NeckelTechnische Universitat Munchenneckel@in.tum.de

PP5

Matrix Splitting Techniques for Sampling a High-Dimensional Gaussian

Langevin and Hamiltonian proposals in the Metropolis-Hastings algorithm applied to Gaussian target distribu-tions correspond to matrix splittings, similar to station-ary iterative methods for solving systems of linear equa-tions such as Gauss-Seidel and SSOR. We prove a result forhow the efficiency of the Metropolis-Hastings algorithm de-pends on a general matrix splitting in high dimensions, re-vealing new efficient proposals for the Metropolis-Hastingsalgorithm.

Richard A. Norton, Colin FoxUniversity of OtagoDepartment of Physics

richard.norton@otago.ac.nz, colin.fox@otago.ac.nz

PP5

Time Series Estimation of a Stochastic ProcessesCoupled to Pdes for Multiscale Modeling

The well-studied molecular mechanics of atomic irradia-tion damage have long-standing simulation codes model-ing binary collision cascades. Long range spatial correla-tions between damages are generally modeled using phase-field models. However, we propose a simulation schemeto model the meso-scale void accumulation damages us-ing a stochastic cellular automata. This model allows usto bridge the gap between the micro and macro scales bymodeling the stochastic cellular automata process using atime series. This time series can then be run at a muchless computationally intensive simulation until reaching asteady state. The statistical properties of the steady statecan then be coupled to the macro scale pde, ie continuummodels, in a form that it can better understand.

Charlie Vollmer, Don EstepColorado State Universitycharlesv@rams.colostate.edu, estep@stat.colostate.edu

Anter A. El-AzabPurdue Universityaelazab@purdue.edu

PP5

Fast Stochastic Simulation of Non-Gaussian Corre-lated Process Variations

The recently developed stochastic spectral methods can es-timate more efficiently the process variations effects com-pared with Monte-Carlo. However, existing publicationsmostly assume variation-parameters to be independent andGaussian. In this paper, we develop an efficient simu-lation technique based on stochastic collocation for non-Gaussian and correlated random parameters. The tech-nique is applied to silicon photonic process variations andshows 124-times speedup compared with Monte-Carlo.

Tsui-Wei WengMITResearch Lab of Electronicstwweng@mit.edu

Zheng ZhangMITz zhang@mit.edu

Luca DanielM.I.T.Research Lab in Electronicsluca@mit.edu

PP5

Uncertainty Quantification for Integrated Circuitsand MEMS

We present a simulator to quantify the uncertainties ofnano-scale integrated circuits and microelectromechanicalsystems (MEMS). We show the stochastic spectral methodsfor stochastic static, transient and periodic steady-state(i.e., limit cycle) analysis, as well as some techniques tohandle high parameter dimensionality and design hierar-

CS15 Abstracts 249

chy.

Zheng ZhangMITz zhang@mit.edu

Ibrahim ElfadelMicrosystem EngineeringMasdar Institute of Science and Engineeringielfadel@masdar.ac.ae

Luca DanielM.I.T.Research Lab in Electronicsluca@mit.edu

PP6

Reproducible Numerical Computing withHashDist

HashDist provides a critical component of the devel-opment workflow, enabling highly customizable, source-driven, and reproducible builds for scientific softwarestacks. HashDist features intelligent caching of sourcesand builds, parametrized build specifications, and theability to interoperate with system compilers and pack-ages. HashDist enables the easy specification of ”softwarestacks”, which allow both the novice user to install a de-fault environment and the advanced user to configure everyaspect of their build in a modular fashion. All HashDistbuilds are reproducible, with a unique build hash identify-ing exactly how each component of the software stack wasinstalled.

Aron AhmadiaUS Army Engineer Research and Development Centeraron@ahmadia.net

Ondrej CertikDepartment of Mathematics and StatisticsUniversity of Nevada, Renoondrej@certik.cz

Christopher KeesUS Army Engineer Research and Development Centerchristopher.e.kees@usace.army.mil

Dag Sverre SeljebotnUniversity of Oslod.s.seljebotn@astro.uio.no

Andy R. TerrelInstitute for Computational Engineering and SciencesUniversity of Texas at Austinandy.terrel@gmail.com

PP6

A Scalable Fast Method for N-Body ProblemsBased on Exact Finite Element Basis Screen Func-tions

We introduce a fast method for computing N-body inter-actions based on the particle-particle–particle-mesh (P3M)approach in which the calculation is split into rapidly de-caying short-range interactions and mesh-resolvable long-range interactions. Our method employs screening func-tions designed to yield a long-range component that isfound exactly by a finite element method, increasing the

locality of the method compared to traditional FFT-basedmethods. Multigrid methods efficiently solve the resultingsparse matrix problem.

Natalie N. BeamsUniversity of Illinois at Urbana-Champaignbeams2@illinois.edu

Luke OlsonDepartment of Computer ScienceUniversity of Illinois at Urbana-Champaignlukeo@illinois.edu

Jonathan B. FreundUniversity of Illinois at Urbana-Champaignjbfreund@illinois.edu

PP6

Boltzmann Collision Operator for CylindricallySymmetric Velocity Distributions in Plasmas

We develop a model for collision processes in industriallyrelevant plasmas. To reduce the computational cost of solv-ing the Maxwell-Boltzmann equations, we assume that thevelocity distribution function is cylindrically symmetric invelocity space and only axially dependent in physical space.We show that if the external force is only axially dependent,then the Boltzmann collision operator is also cylindricallysymmetric, which reduces the Maxwell-Boltzmann systemto two velocity and one spatial dimensions.

Yanping Chen, Yannan Shen, John Zweck, MatthewGoecknerUniversity of Texas at Dallasyxc110030@utdallas.edu, yxs135630@utdallas.edu,jwz120030@utdallas.edu, goeckner@utdallas.edu

PP6

Analysis of a Heterogeneous Multiscale Method forPoroelasticity

In this paper, we develop a highly parallelizable numeri-cal method to solve the heterogeneous linear poroelastic-ity equations in multiple dimensions via operator splittingand a finite-volume based heterogeneous multiscale methodfor the linear elasticity and reaction diffusion equations.We demonstrate convergence both analytically and numer-ically, and analyze its computational complexity on highperformance computers.

Paul M. DelgadoUTEPpmdelgado2@utep.edu

Vinod Kumar, Son Young YiUniversity of Texas at El Pasovkumar@utep.edu, syi@utep.edu

PP6

Cell List Algorithms for Nonequilibrium MolecularDynamics

A common approach in the molecular simulation of ho-mogeneous linear background flow is the use of boundaryconditions that deform with the flow. Recent developmentshave been made in finding long-term compatible boundaryconditions for a general class of three-dimensional flows.We present two modifications of the standard cell list algo-

250 CS15 Abstracts

rithm for nonequilibrium molecular dynamics. The modi-fied algorithms handle the dynamic, deforming simulationgeometry and reduce the computational complexity of forcecomputations from O(N2) to O(N) in the number of par-ticles N .

Matthew DobsonUniversity of Massachusetts Amherstdobson@math.umass.edu

PP6

Convex-Hull Classification of Molecular Data on aCluster

There has been considerable interest in understanding vari-ations in molecular signatures between normal and diseasestates using novel classification approaches. The proposedstudy will elucidate the choice of convex-hull ensemble clas-sification for discerning distinct disease groups. The al-gorithms were implemented in R and parallelized across ahigh-performance computing cluster using readily availablewrappers.

Sally R. Ellingson, Radha NagarajanUniversity of Kentuckysally@kcr.uky.edu, rnagarajan@uky.edu

PP6

Spectral Noise Filtering for Fourier Transform Pro-filometry

In Fourier transform profilometry, an optical systemprojects light with a sinusoidally-varying pattern on a 3-Dsurface and records the resulting image. The spectrum ofthe depth-modulated sinusoid is overlapped by other com-ponents of the spectrum, limiting accurate reconstructionof the surface. We present a new noise removal method toestimate the obscuring spectral components and filter themout. Surfaces reconstructed using this de-noising methodfeature increased precision and suffer from fewer aberra-tions.

Thomas HoftUniversity of St. ThomasDepartment of Mathematicshoft@stthomas.edu

PP6

Direct Evaluation of Unified Extended Splines

In this poster we demonstrate a method for direct eval-uation of unified extended spline basis functions, whichwere first introduced by Wang and Fang in 2008. We alsodemonstrate the advantages of Bezier extraction of unifiedextended splines in Isogeometric analysis.

Ian D. HenriksenBrigham Young Universityinsertinterestingnamehere@gmail.com

PP6

Numerical Modeling of Wave Propagation inPoroelastic Media Using Optimal Staggered Im-plicit Finite Differences

We apply a recently proposed optimal staggered implicit fi-nite difference scheme to model wave propagation in poroe-lastic media. The advantage of this method is that it has

high accuracy and only requires to solve tridiagonal linearsystems of equations (to compute the spatial derivatives).The instabilities that arise in high contrast media are al-leviated when using these schemes. We show examples fordifferent media configurations.

Ursula Iturraran-Viveros, Reymundo ItzaFacultad de CienciasUniversidad Nacional Autonoma de Mexicoursula.iturraran@gmail.com, reymundo.itza@gmail.com

PP6

Graph-Based Analysis of Three-Dimensional,Large Scale Phase-Field Simulations

In large scale phase-field simulations of ternary eutecticsolidification, multiple patterns emerge and evolve whilegrowing. To study the transformation of patterns depend-ing on thermodynamical properties or processing condi-tions and to analyze the respective microstructure charac-teristics, algorithms exploiting large datasets are discussed.Basic features of the arrangement of the three solid phasesare derived from the voxel data via graph representations.The targeted reduction of the data allows to visualize singlethree-dimensional structures and evaluate the correlationsof different patterns effectively. Thereby it is possible toaugment current 2D statistics and analyze projections ofthe data.

Marcus JaintaKarlsruhe Institute of Technology (KIT)Institute of Applied Materials (IAM-ZBS)marcus.jainta@kit.edu

Daniel Stubenvoll, Johannes HotzerKarlsruhe University of Applied Sciences (HSKA)Institute of Materials and Processes (IMP)stubenvoll.daniel@gmx.de,johannes.htzer@hs-karlsruhe.de

Phillip Steinmetz, Britta NestlerKarlsruhe Institute of Technology (KIT)Institute of Applied Materials (IAM-ZBS)philipp.steinmetz@kit.edu, britta.nestler@kit.edu

PP6

Uncertainty Quantification for the Estimation ofthe Diffusion Coefficient from Md Simulations

The diffusion coefficient D of a tracer particle suspendedin a fluid is estimated either from the time integral of thevelocity autocorrelation (VACF) or from the slope of themean-squared displacement (MSD). We derive relations be-tween the statistical errors present in VACF or MSD andin D and show that the statistical errors in D estimated byboth methods have the same variance if VACF and MSDare calculated from the same MD trajectories.

Changho Kim, George E. KarniadakisBrown UniversityDivision of Applied Mathematicschangho kim@brown.edu, george karniadakis@brown.edu

PP6

Adaptive Model Order Reduction in Forward andInverse Multi-Frequency Problem for Maxwell’s

CS15 Abstracts 251

Equations

A model order reduction method is developed for solutionof a forward and inverse multi-frequency problem for mag-netotellurics. The Helmholtz decomposition allows to ex-tend the MOR method to the case of a on-trivial operator’snull space. We use Pade approximation of the forward re-sponse and the jacobian, which are analytic functions offrequency. An adaptive choice of interpolating frequencies,based on minmax optimization of several error estimates,uses a fast calculation of the residual across a frequencyrange.

Michal A. KordyDepartment of Mathematics, University of UtahEnergy & Geoscience Institute, University of Utahkordy@math.utah.edu

Elena CherkaevUniversity of UtahDepartment of Mathematicselena@math.utah.edu

Phil WannamakerUniversity of Utahpewanna@egi.utah.edu

PP6

Sparse Spectral Tau-Method for Binary NeutronStars

We describe ongoing work toward construction of initialdata for binary neutron stars via a multidomain modaltau-method. Sparse systems are achieved through the useof “integration preconditioning”. We focus on (i) realiza-tion of the low-regularity interface between the stellar sur-face and exterior through tau conditions and (ii) necessaryfurther preconditioning beyond the “integration precondi-tioning”.

Stephen LauMathematicsThe University of New Mexicolau@math.unm.edu

PP6

Time-Parallel Approaches for Complex RotorcraftCalculations

Unsteady rotorcraft CFD calculations may require hun-dreds of thousands of timesteps to resolve the flow of spin-ning rotors. Spatial decomposition alone limits the num-ber of processors that can be effectively utilized; exploitingparallelism in the temporal dimension could significantlyincrease the degree of scalability. We demonstrate sev-eral approaches to achieve temporal parallelism, includingthe Time-Spectral method for periodic and quasi-periodiccases and a Parallel in Time (PIT) approach for the generalcase of fully unsteady flow.

Joshua I. LeffellUnited States Army Aeroflightdynamics DirectorateNASA Ames Research Centerjoshua.i.leffell@nasa.gov

Jay SitaramanUniversity of Wyomingjsitaram@uwyo.edu

Andrew WissinkUnited States Army Aeroflightdynamics DirectorateNASA Ames Research Centerandrew.m.wissink.civ@mail.mil

PP6

Matched Asymptotic Analysis to Solve the NarrowEscape Problem in a Domain with a Long Neck

In this study, we mainly consider the narrow escape prob-lem in a two-dimensional domain Ω with a long neck, whichis the two-dimensional analogue of a dendritic spine geom-etry. The narrow escape problem requires the computa-tion of the mean escape time of a Brownian particle start-ing from the head until it exits from the end of the neck,where the particle is absorbed. We divide the domain intothe neck part Ωn and the head part Ωh, with the commonboundary Γε. The escape time in Ωh can be considered tobe the time from the head to the end of the neck, while theescape time in Ωn can be considered to be the time from theneck to the end of the neck. We compute the two exit timesseparately and match them by considering some boundaryvalue problem with an impedance boundary condition onΓε, which we refer to as the Neumann-Robin boundarymodel.

Xiaofei LiDepartment of Mathematics, Inha Universityxiaofeili@inha.edu

Hyundae LeeInha UniversityDepartment of Mathematicshdlee18@gmail.com

PP6

Computational Homogenization for the Modelingof Soft Matter Materials

This contribution outlines the development of mathemat-ically rigorous and computationally efficient homogeniza-tion frameworks for soft matter with intrinsic network mi-crostructures. Those are commonly encountered in mate-rials such as elastomers, hydrogels, soft biological tissues,non-woven fabrics, cellular foams, and muscles and are allmicroscopically composed of elongated 1D fibers. Whenthese soft materials are subject to a macroscopic strain,the underlying microstructure undergoes a peculiar defor-mation and highly affect the macroscopic stress responseof the material.

Christian LinderStanford Universitylinder@stanford.edu

PP6

Precice – Flexible Parallel Multi-Physics Coupling

Flexible and extensible partitioned multi-physics simula-tion environments require efficient and modular tools witha broad coupling functionality. preCICE is a library forflexible numerical coupling of single-physics solvers. Ituses a partitioned black-box coupling scheme, thus requir-ing only minimal modifications to existing solvers. Codescurrently coupled with preCICE comprise both commer-cial and academic solvers, with a particular focus on fluid-structure interaction. preCICE features a clean and mod-ern software design with extensive unit and integration

252 CS15 Abstracts

testing while maintaining minimal external dependencies.Inter-solver parallelism, parallel communication and datamapping techniques will help to max out future exa-scalecomputers.

Florian Lindner, Miriam MehlUniversitat Stuttgartflorian.lindner@ipvs.uni-stuttgart.de,miriam.mehl@ipvs.uni-stuttgart.de

Benjamin UekermannTU Munichuekerman@in.tum.de

PP6

A Sparse Interpolation Algorithm for DynamicalSimulations in Computational Chemistry

We present an implementation of Smolyak’s sparse gridinterpolation algorithm designed for simulating reactionpaths of photo-induced molecular transformations. Cur-rent reaction path methods are computationally burden-some, but Smolyak’s algorithm yields a cheap surrogatemodel. Furthermore, our implementation of Smolyak’s al-gorithm facilitates the computation of several thousand re-actions paths simultaneously. We describe our new imple-mentation of Smolyak’s algorithm and compare its perfor-mance to MATLAB’s Sparse Grid Interpolation Toolbox.We also present simulation results for 2-butene.

James NanceNorth Carolina State Univjdnance2@ncsu.edu

ELENA JakubikovaNorth Carolina State Universityejakubi@ncsu.edu

C.T. KelleyNorth Carolina State UnivDepartment of Mathematicstim kelley@ncsu.edu

PP6

P2NFFT - A Versatile Framework for ComputingNFFT-based Fast Ewald Summation

The Particle-Particle–NFFT (P2NFFT) is a framework forcomputing the long range Coulomb interactions of the clas-sical N-body problem with O(N logN) arithmetic opera-tions on massively parallel architectures. Recently, it hasbeen generalized to 2d- and 1d-periodic boundary condi-tions by a combination of P3M and fast summation tech-niques based on nonequispaced fast Fourier transforms(NFFT). We review these new algorithms and present per-formance results of our publicly available implementation.

Michael Pippig, Franziska NestlerChemnitz University of TechnologyDepartment of Mathematicsmichael.pippig@mathematik.tu-chemnitz.de,franziska.nestler@mathematik.tu-chemnitz.de

PP7

Fields That Cause Elastic Breakdown in Inhomo-geneous Media

We study the inverse problem of an elastic two phase

body of unknown interior geometry. We investigate whichboundary fields will cause failure in the material, eitherfracture or plastic yielding for brittle and ductile materialsrespectively. Using knowledge of volume fractions and ma-terial properties, bounds are obtained on the fields whichthe material can safely support. From this we are able todetermine which boundary fields may be sustained by thebody.

Nathan C. Briggs, Graeme Milton, Zoe Last Koch,Andrew Boyles, Jonathan Boyle, Michael Primrose,Michael ZhaoUniversity of Utahnathancbriggs@gmail.com, milton2505@yahoo.com,kochzoe@gmail.com, eldrewomagnifico@gmail.com,jonathan.boyle@utah.edu, michael.s.primrose@gmail.com,mz84092@gmail.com

PP7

Charge Transfer Processes at Semiconductor-Electrolyte Interfaces in Solar Cell Modeling

This project discusses results from the numerical ap-proximation and simulation of reactive semiconductor-electrolyte interfaces in solar cells using a drift-diffusion-Poisson model. A mixed finite element method is employedto approximate the potential and the electric field, while alocal discontinuous Galerkin method is employed to com-pute the densities and currents. The non-linear reactiveinterface conditions are treated using a Schwarz domaindecomposition method applied to the semiconductor andelectrolyte regions.

Michael D. HarmonInstitute for Computational and Engineering Sciencesmharmon@ices.utexas.edu

PP7

Student Chapter Develops Future Professionals

SIAM at Embry-Riddle Aeronautical University has fos-tered an unrelenting passion for professional developmentof its student body. From K-12 outreach to robotics re-search, members of our organization have gained skills thattranslate to industry-level capabilities. The talk describesthe components of the organization that creates an envi-ronment for growth and enriches each student and industrypartner connection.

Stacey Joseph-EllisonEmbry-Riddle Aeronautical Universityellisos1@my.erau.edu

PP7

Optimal Control of Miscible Displacement Equa-tions Using Discontinuous Galerkin Methods

In the energy industry, reservoir simulators enable oil com-panies to optimize oil and gas production. I analyze the ac-curacy of the discontinuous Galerkin method when solvingan optimal control problem for the miscible displacementequations, which model a tertiary oil recovery process. Thecontrol variables are the flow rates at the injection wellsand the state variables are the fluid mixture pressure andvelocity, as well as the concentration of the injected fluid.

Brianna LynnRice University

CS15 Abstracts 253

bkl3@rice.edu

PP7

Elastic Deformation Due to Dislocations in a Trans-versely Isotropic Viscoelastic Halfspace

Many materials in nature have transversely isotropic (TI)viscoelastic behavior and this time-dependent phenomenoncan be addressed by advanced continuum mechanics andcomputational analysis. A model is developed to repre-sent the viscoelastic behavior of a TI media due to polyg-onal dislocation loops. Applying the Laplace transform tothe constitutive equations and adopting the algorithm pro-posed by Honig and Hirdes for the inverse transform, thedeformation fields in the physical domain will be obtained.

Amirhossein Molavi Tabrizi, Ernian Pan, Ali SangghalehUniversity of Akronam142@zips.uakron.edu, pan2@uakron.edu,as147@zips.uakron.edu

PP7

Identifying and Tracking Multiple UnderwaterAcoustic Sources Using Characteristic Signatures

When using passive sonar to locate sound sources, the gen-eral practice is to implement a particle filter to track thesource using its previous locations. Our goal is to improvethis method by including discrete characteristics to the fil-ter and calculating the likelihood that the source falls un-der one or a set of these characteristics. This will improveour estimates of source location by narrowing down move-ment patterns, will help us distinguish between multiplesources, and can give us valuable information such as whatthe source type is.

Zoi-Heleni Michalopoulou, Jacob Moorman, Jake Brusca,Shan FungDepartment of Mathematical SciencesNew Jersey Institute of Technologymichalop@njit.edu, jdm47@njit.edu, jb327@njit.edu,ssf22@njit.edu

PP7

Simulation and Modeling of Unmanned Systems forHumanitarian Applications in Industry

Unmanned systems are a burgeoning technology in therobotics and autonomy space. Utilized for decades in themilitary and defense complex, unmanned systems are nowpoised to play a key role in solving some of the most press-ing international capacitance issues. With notable appli-cations across the agricultural space, we will demonstratethe importance and utility of simulation and modeling ofcomplex systems to solve real-world problems.

Courtney E. ThurstonCommonwealth Connections Academythurscon@gmail.com

PP8

AWM Workshop: Sampling and Reconstruction inInite-Dimensional Reproducing Kernel Subspace

We will introduce quasi-optimal signal reconstruction ofadmissible sampling schemes in Banach space setting. Wewill investigate the admissibility of sampling schemes forinite-dimensional reproducing kernel subspaces of Lp. At

last, we will propose an iterative approximation-projectionalgorithm with boundary adjustment for signals to live ina inite-dimensional reproducing kernel subspaces.

Cheng ChengUNIVERSITY OF CENTRAL FLORIDAcheng.cheng@knights.ucf.edu

PP8

AWM Workshop: A Lattice of Poincare DualityAlgebras with Acyclic Annihilators and Finite Di-mension Associated to a Manifold

One is motivated by the algebraic theory of surgery tostudy finite dimensional differential commutative algebraswith an invariant nondegenerate pairing. Using Hodge de-compositions, we show there is a lattice of such algebras,which share many familiar algebraic properties of differen-tial forms on manifolds. We hope to use these ideas to solvedifferential equations on manifolds, which use d, *, and ,and to give a straightforward combinatorial description ofwhat it means to be a manifold.

Cameron CroweStony Brook Universitycameroncrowe1@gmail.com

PP8

AWM Workshop: Residual Based Aposteriori Er-ror Estimation in a Fully Automatic Hp –fem forthe Stokes Equations

Aposteriori error estimator as a computable quantity interms of known quantities gives a tool to assess the approx-imation quality in order to improve the solution adaptively.In This work we present a fully automatic hp-adaptive re-finement strategy using a residual based aposteriori errorestimation which is based on the solution of local boundaryvalue problems. The reliability and efficiency for estima-tor has been proved. Implementation for Stokes problemshows the convergence of our algorithm.

Arezou GhesmatiTexas A&M Universityaghesmati@math.tamu.edu

Markus BuergTexas A&M UniversityVisiting Professorbuerg@math.tamu.edu

Wolfgang BangerthTexas A&M Universitybangerth@math.tamu.edu

PP8

AWM Workshop: Residual-Based A Posteriori Er-ror Estimate for Interface Problems: Nonconform-ing Linear Elements

The residual-based a posteriori error estimation for thenon-conforming linear finite element approximation to theinterface problem is studied. We introduce a new and di-rect approach, without using the Helmholtz decomposition,to analyze the reliability of the estimator. It is proved thata slightly modified estimator is reliable with the constantindependent of the jump of the interfaces, with- out the as-sumption that the diffusion coefficient is quasi-monotone.

254 CS15 Abstracts

Numerical results are also presented.

Cuiyu HePurdue Universityhe75@math.purdue.edu

Zhiqiang CaiPurdue UniversityDepartment of Mathematicscaiz@purdue.edu

Shun ZhangCity University of Hong Kongshun.zhang@city.edu.hk

PP8

AWM Workshop: Enhancements for Reduced Ba-sis Methods: Reducing Offline ComputationalCosts

The reduced basis method (RBM) is a new technique forfinding approximate solutions to parametric partial differ-ential equations. It tries to reduce the total cost of com-putation, by approximating the solution space by a linearcombination of pre-- computed solutions. However, thecurrent algorithm (greedy algorithm) is still costly. So weare designing a more efficient greedy algorithm. The im-plementation of our new approach also opens the power ofparallel computing into the world of RBM.

Jiahua JiangUniversity of Massachusetts, Dartmouthjjiang@umassd.edu

PP8

AWM Workshop: Combinatorial Navier-StokesEquation

Form the cubical grid of three space. Replace differen-tial forms, exterior d and wedge product by cochains, thecoboundary operator and cup product. Replace the hodgestar by the Poincare dual cell operation followed by trans-lation. Now one can form the combinatorial analog of thecontinuum Navier-Stokes equation.

Aradhana KumariCity University Of New Yorkaradidi87@gmail.com

PP8

AWM Workshop: An Adaptive Gmsfem for High-Contrast Flow Problems

In this paper, we derive an a-posteriori error indicator forthe Generalized Multiscale Finite Element Method (GMs-FEM) framework. This error indicator is further used todevelop an adaptive enrichment algorithm for the linearelliptic equation with multiscale high-contrast coefficients.We consider two kinds of error indicators where one isbased on the L2-norm of the local residual and the other isbased on the weighted H-1-norm of the local residual wherethe weight is related to the coefficient of the elliptic equa-tion. We show that the use of weighted H-1-norm residualgives a more robust error indicator which works well forcases with high contrast media. The convergence analysisof the method is given.

Guanglian Li

Texas A&M Universitylotusli0707@gmail.com

PP8

AWM Workshop: Propagation Failure in DiscreteInhomogeneous Media Using a Caricature of theCubic

We consider a bistable differential-difference equation withinhomogeneous diffusion across an interval lattice. Previ-ous research uses a discontinuous nonlinearity to constructexact solutions. We employ a continuous piecewise lin-ear nonlinearity, a caricature of the cubic, to derive exactsteady-state front solutions. Diffusion coefficients are var-ied on a finite interval, representing the inhomogeneous me-dia. The interval of propagation failure, dependent uponthe diffusion coefficients and wave speed, determines whenand where stationary front solutions occur.

Elizabeth LydonUniversity Central Floridaelydon@knights.ucf.edu

PP8

AWM Workshop: Nontrivial Structure in Top Ho-mology of a Space

The top homology of a reasonable compact topologicalspace X is naturally sitting inside a vector space V witha canonical coordinate system. The position of this sub-space relative to the axes is a non-trivial invariant of thehomeomorphism type of X. The canonical coordinate axesof V are given by oriented components of the set of topdimensional manifold points.

Chandrika SadanandStony Brook Universitychandrika@math.sunysb.edu

PP9

A Synchronized Co-Volume Scheme for the Large-Scale Shallow Water Equations

The co-volume scheme specifies the mass at cell centers andcell vertices, and both of the normal and tangential veloc-ity components at cell edges. This scheme is extremelyflexible, applicable to unstructured meshes, and avoids theneed to reconstruct the tangential velocity component, asthe classical C-grid scheme does. But the co-volume hasbeen shown to be a generalization of the Z-grid scheme,and therefore inherits all the known defects of the latter.From another point view, a recent study shows that, forthe co-volume scheme on the f-plane, the mass-vorticity-divergence fields on the primary are completely decoupledfrom the mass-vorticity-divergence fields on the dual mesh.We propose to periodically synchronize the fields on theprimary mesh and the fields on the dual mesh. In this pre-sentation, we explore approaches for the synchronization,and the effects of them.

Qingshan ChenClemson Universityqsc@clemson.edu

PP9

Physics-Based Preconditioning and DualTimestepping for Stiff Combustion Problems

CS15 Abstracts 255

with Detailed Chemical Mechanisms

Time-accurate simulation of low-Mach combustion is chal-lenging due in part to the wide range of tightly-coupledphysical time scales. Traditional integration techniquesare severely constrained when strongly nonlinear and stiffchemistry is introduced to the Navier-Stokes equations atlow Mach number. Kinetic stiffness is exceptionally de-manding when detailed, fine-grained reaction mechanismsare utilized. We are developing local physics-based precon-ditioning techniques for detailed chemical mechanisms andextending dual timestepping for high-fidelity combustionsimulation on next-generation platforms.

Michael A. HansenUniversity of UtahSandia National Laboratoriesmike.hansen.utah@gmail.com

PP9

Rods with Bend and Twist in a Brinkman Fluid

We develop a Lagrangian algorithm to model an elasticrod in a porous medium. The three dimensional fluid isgoverned by the incompressible Brinkman equation andthe Kirchhoff rod model captures bend and twist of therod. Regularized solutions are derived and we comparenumerical results to asymptotics for swimming speeds ina Brinkman fluid. Numerical results showing bendingand twisting energies in fluids of different porosity will beshown.

Nguyenho HoMathematical Sciences DepartmentWorcester Polytechnic Institutenho@wpi.edu

Sarah D. OlsonWorcester Polytechnic Institutesdolson@wpi.edu

PP9

Discrete Exterior Calculus Solution of Incompress-ible Flows

Navier-Stokes equations are discretized using discrete ex-terior calculus (DEC) on simplicial meshes. The govern-ing equations are first rewritten, using the smooth exteriorcalculus notation, in terms of velocity and pressure forms.The smooth forms and operators are then substituted withtheir corresponding discrete definitions based on the DECframework. Several numerical test cases are presented todemonstrate numerical convergence, stability, and conser-vation properties of the developed numerical scheme.

Mamdouh S. MohamedPhysical Sciences and Engineering DivisionKAUSTmamdouh.mohamed@kaust.edu.sa

Sudantha BalagePhysical Sciences and Engineering DivisionKAUST, Jeddah, KSAsudantha.balage@kaust.edu.sa

Anil HiraniDepartment of MathematicsUniversity of Illinois at Urbana-Champaign, IL, USAhirani@illinois.edu

Ravi SamtaneyKAUSTravi.samtaney@kaust.edu.sa

PP9

Adaptive Wavelet Simulation for Weakly Com-pressible Flow Bounded by Solid Walls of ArbitraryShape

We develop an adaptive simulation method for comput-ing compressible flow bounded by solid walls of arbitraryshape. A finite volume approach is coupled with waveletanalysis for local grid refinement. A volume penalizationmethod is employed to compute the flow in Cartesian coor-dinates. We assess the quality and efficiency of the methodfor a flow in a channel with an expanded section. The re-sults are compared with a reference flow computed on auniform grid.

Naoya OkamotoNagoya Universityokamoto@ccs.engg.nagoya-u.ac.jp

Margarete DominguesInstituto Nacional de Pesquisas Espaciaismargarete.domingues@inpe.br

Katsunori YoshimatsuNagoya Universityyosimatu@esi.nagoya-u.ac.jp

Kai SchneiderUniversite de Provence, Aix-MarseilleCentre de Mathematiques et Informatiquekschneid@cmi.univ-mrs.fr

PP9

Multiple Solutions in Curved-Pipe Flow

The project deals with fluid flows in uniformly curved pipesdriven by a steady axial pressure gradient, with focus onblood flow in arteries. The problem is known to havemultiple solutions and the primary solution involving theformation of two-vortices(Dean vortices) was found andvalidated. Bifurcation was found for curved pipes witha square cross-section. In addition, wall shear stresses,stream function and vorticity were computed for differentcurvature ratios and Dean numbers.

Harsh RanjanIndian Institute of Technology Guwahatiharshranjan21@gmail.com

PP9

Cooperation and Efficiency in Sperm Motility Pat-terns

To fertilize the egg, sperm of certain species engage in co-operative swimming behaviors. These cooperative motil-ity patterns result in differences in velocity and efficiency.We employ a preferred curvature flagellum model and themethod of regularized Stokeslets to simulate the viscousfluid environment sperm encounter. Using these methods,we compare a single flagellum with two flagella systems tounderstand the empirical effects of cooperative swimming.

Owen RichfieldTulane University

256 CS15 Abstracts

Center for Computational Scienceorichfie@tulane.edu

Paul CripeTulane Universitypcripe@tulane.edu

Julie SimonsTulane UniversityDepartment of Mathematicsjsimons@tulane.edu

PP9

Efficient Simulation of Fluid-Structure InteractionsModeled by Regularized Stokes Formulation UsingKernel-Independent Fast Multipole Method

Regularized Stokes formulation has been shown to be veryeffective at modeling fluid-structure interactions when thefluid is highly viscous. However, its computational costgrows quadratically with the number of particles immersedin the fluid. We demonstrate how kernel-independent fastmultipole method can be applied to significantly improvethe efficiency of this method, and present numerical resultsfor simulating the dynamics of a large number of elasticrods immersed in 3D Stokes flows.

Minghao W. Rostami, Sarah D. OlsonWorcester Polytechnic Institutemwu@wpi.edu, sdolson@wpi.edu

PP9

Scalable Parallel Solvers for Highly HeterogeneousNonlinear Stokes Flow Discretized with AdaptiveHigh-Order Finite Element

We present scalable parallel solvers for convection-drivenflow in Earth’s mantle with associated plate motions,which is governed by nonlinear Stokes equations. Crucialsolver components are parallel geometric multigrid meth-ods for preconditioning the linearized Stokes systems thatarise upon discretization with high-order finite elementson adaptive meshes (resolution below 1km) and improvedBFBT/LSC preconditioners for the Schur complement. Weshow robustness with respect to extreme viscosity varia-tions and carry out global mantle flow simulations withreal Earth data as we progress towards solving realisticglobal mantle flow inverse problems.

Johann Rudi, Toby IsaacICESThe University of Texas at Austinjohann@ices.utexas.edu, tisaac@ices.utexas.edu

Georg StadlerCourant Institute for Mathematical SciencesNew York Universitystadler@cims.nyu.edu

Michael GurnisCaltechgurnis@caltech.edu

Omar GhattasThe University of Texas at Austin

omar@ices.utexas.edu

PP9

Discrete Adjoint Openfoam and Applications

A discrete adjoint version of OpenFOAM obtained usingAlgorithmic Differentiation[1] by operator overloading isapplied to obtain derivatives based on external aerodynam-ics of a Volkswagen Polo Car. The results are validatedqualitatively against a ’frozen turbulence’ continuous ad-joint implementation[2]. We demonstrate the robustnessand flexibility of differentiating a turbulence model dis-cretely to obtain exact derivatives. Strategies to tacklespatial and temporal complexities characteristic to discreteadjoint methods are also discussed. References: [1] Nau-mann, U., The Art of Differentiating Computer Programs,SIAM, 2012. [2] Othmer, C., A continuous adjoint for-mulation for the computation of topological and surfacesensitivities of ducted flows,Int. J. Num. Meth. Fluids,2006

Arindam SenSoftware and Tools for Computational Engineering, STCERWTH Aachen Universitysen@stce.rwth-aachen.de

Markus TowaraSTCE, RWTH Aachen Universitytowara@stce.rwth-aachen.de

Uwe NaumannRWTH Aachen UniversitySoftware and Tools for Computational Engineeringnaumann@stce.rwth-aachen.de

PP9

Strategy for Efficiently Simulating Reactive Flowswith Large Detailed Chemical Kinetics

A highly efficient numerical approach for simulating reac-tive flows with large detailed chemical kinetics is proposed.The present approach consists of a robust and fast explicittime integration method for chemical reaction equationsand a species building technique for diffusion coefficientcalculations. The computational results with a realisticcombustion problem verify the high efficiency of the presentapproach.

Hiroshi TerashimaThe University of Tokyohtera@rocketlab.t.u-tokyo.ac.jp

Youhi MoriiJapan Aerospace Exploration Agencymorii.yuuhi@jaxa.jp

Mitsuo KoshiYokohama National Universitykoshim@jcom.home.ne.jp

PP9

An Exact and Consistent Adjoint Method for High-Fidelity Unsteady Compressible Flow Simulations

We consider high-resolution discretizations commonly usedfor compressible turbulent flows. A corresponding discrete-adjoint can produce gradients that include spurious numer-ical modes, restricting its utility. A continuous-adjoint ap-

CS15 Abstracts 257

proach does not, but provides an inaccurate gradient. Weintroduce a dual-consistent finite-difference discretizationbased on common workhorse methods for compressible tur-bulent flows, which enjoy the benefits of both approaches.Demonstrations with an unsteady mixing layer show thatthe gradient is both exact up to roundoff and consistent.

Ramanathan VishnampetDepartment of Mechanical Science and EngineeringUniversity of Illinois at Urbana-Champaignvishnam2@illinois.edu

Daniel J. BodonyUniversity of Illinois at Urbana-ChampaignDepartment of Aerospace Engineeringbodony@illinois.edu

Jonathan B. FreundUniversity of Illinois at Urbana-Champaignjbfreund@illinois.edu

PP9

Periodic Stokes Flow in 2 Dimensional Space

We present a new boundary integral method to solve in-compressible Stokes flow with low Reynolds number in aperiodic background with high accuracy and efficiency.

Lin ZhaoDartmouth Collegelin.zhao.gr@dartmouth.edu

Alex H. BarnettDepartment of MathematicsDartmouth Collegeahb@math.dartmouth.edu

PP10

Etd Spectral Deferred Correction Methods

We introduce a new class of arbitrary-order exponentialtime differencing (ETD) methods based on spectral de-ferred correction. We study the stability and accuracyproperties of these methods and conduct numerical experi-ments against existing ETD and implicit-explicit schemes.We find that our new high-order ETD spectral deferredcorrection schemes outperform state-of-the-art time inte-grators for computations requiring high accuracy, makingthem well-suited to work in conjunction with spatial spec-tral methods.

Tommaso BuvoliDepartment of Applied Mathematics, University ofWashingtonSeattle, WA 98195 USAbuvoli@uw.edu

PP10

Adaptive Multigrid Methods for An IntegratedStructural Health Monitoring (SHM) Systems forComposite Material with Fluid-Structure Interac-tion (FSI) Effect

To design a SHM system, it is important to understandphenomenologically and quantitatively the wave propaga-tion in composite material and the influence of the geo-material and mechanical properties of the structures. Toaccelerate the design of SHM systems, the FSI effect on

the wave propagation has to be considered. Combiningfluid dynamics with structural analysis traditionally posesa formidable challenge for even the most advanced numer-ical techniques due to the disconnected, domain-specificnature of analysis tools. We present the state-of-the-art incomputational methods and techniques for wave propaga-tion with FSI effect that go beyond the fundamentals ofcomputational fluid and solid mechanics. Also this projectaims to develop efficient numerical methods for wave prop-agation phenomena in composite material with FSI effect,which combine modern techniques from PDE-constrainedoptimization, adaptive and multigrid simulation methods.

Bhuiyan Shameem M. Ebna HaiNumerical Methods for Computational Science andEngineering,Mechanical Engineering Department, Helmut SchmidtUniversityebnahaib@hsu-hh.de

Markus BauseHelmut-Schmidt-UniversityUniversity of the Federal Armed Forces Hamburgbause@hsu-hh.de

PP10

Reducing the Impact of the Cfl Condition for Dis-persive Wave Propagation Problems

To solve dispersive wave propagation problems in complexgeometries efficiently and accurately, it is attractive to useexplicit time-integration and high-order unstructured spec-tral element discretization in space. This combination mayhave a severe global conditional CFL time-step restriction.For specific models, we describe conditions placed on dis-persive terms for making the CFL condition independentof discretisation method and meshsizes. In this sense theCFL condition impose a minimal constraint on the effi-ciency without compromising accuracy.

Allan P. Engsig-KarupTechnical University of DenmarkDepartment of Informatics and Mathematical Modelingapek@imm.dtu.dk

Claes EskilssonChalmars University of TechnologyGothenburg, Sweden.claes.eskilsson@chalmers.se

PP10

Explicit Strong Strong Stability Preserving MultiStep Runge-Kutta Methods

High-order spatial discretizations of hyperbolic PDEs areoften designed to have strong stability properties, such asmonotonicity. We study explicit multistep RungeKuttastrong stability preserving (SSP) time integration methodsfor use with such discretizations. We prove an upper boundon the SSP coefficient of explicit multistep RungeKuttamethods of order two and above.Numerical optimizationis used to find optimized explicit methods of up to fivesteps, eight stages, and tenth order. These methods aretested on the advection and Buckley-Leverett equations,and the results for the observed total variation diminish-ing and positivity preserving time-step are presented.

Zachary J. Grant

258 CS15 Abstracts

University of Massachusetts at Dartmouthzgrant@umassd.edu

PP10

Robust Residual-Based A Posteriori Error Esti-mate for Interface Problems: Nonconforming Lin-ear Elements

A robust residual-based a posteriori error estimation forthe non-conforming linear finite element approximation tothe interface problem is studied. We introduce a new anddirect approach, without using the Helmholtz decomposi-tion, to analyze the reliability of the estimator. It is provedthat our estimator is reliable with the constant indepen-dent of the jump of the interfaces, without the assumptionthat the diffusion coefficient is quasi-monotone. Numericalresults are also presented.

Cuiyu HePurdue Universityhe75@math.purdue.edu

Zhiqiang CaiPurdue UniversityDepartment of Mathematicscaiz@purdue.edu

Shun ZhangCity University of Hong Kongshun.zhang@city.edu.hk

PP10

Monolithic Multi-Time-Step Coupling Methods forFirst and Second-Order Transient Systems

New frameworks for coupling different integration meth-ods (either temporal or spatial) for first- and second-ordertransient systems will be introduced. These methods al-low different numerical time-integrators, time-steps, andnumerical formulations in different regions of the compu-tational domain. Unique features of the proposed methodswill be demonstrated through several numerical examples.

Saeid KarimiUniversity of Houstonskarimi@central.uh.edu

Kalyana NakshatralaUniversity Of Houston - Main Campusknakshatrala@uh.edu

PP10

Total Order Function Space Spectral CollocationMethods Using the Padua Points

Multivariate Chebyshev spectral collocation methods typ-ically are implemented using Lagrange interpolating poly-nomials corresponding to tensor products of Chebyshevnodes. The Padua points are an analogue of the Cheby-shev nodes that interpolate the smaller bivariate total orderfunction space P2

n. These points can be used to implementa spectral collocation scheme, however careful treatment ofboundary conditions is required. This issue is explored forPoisson and Helmholtz problems with arbitrary, variablecoefficient, Robin boundary conditions.

Scott MoeUniversity of Washington

smoe@uw.edu

PP10

Numerical Investigation of Influence of NodeAlignment on Stable Calculation for Meshless TimeDomain Method

The meshless time domain method (MTDM) is one ofmeshless methods. The shape function derived from theradial point interpolation method (RPIM) is adopted fordiscretization process instead of meshes in MTDM. In addi-tion, the radial basis function (RBF) is employed in RPIM,and the multi quadratic function is adopted for the presentstudy. The purpose of the present study is to investigateinfluence of node alignment and RBF on stable calculation.

Yoshiharu OhiRIKEN Advanced Institute for Computational Scienceyoshiharu.ohi@riken.jp

Yoshihisa FujitaNagoya Universityfujita.yoshihisa@nifs.ac.jp

Taku Itoh, Soichiro IkunoTokyo University of Technologytaku@m.ieice.org, ikuno@cs.teu.ac.jp

PP10

Asymptotics of High-Frequency Scattering Prob-lems

Various strategies for simulating wave scattering problemsthrough the Helmholtz equation typically become compu-tationally expensive for high frequencies. The solution ofits integral representation exhibits asymptotic behaviourq(�y) ∼ keikφ(�y)

∑∞j=0 aj(�y)k

−j as the wave number k tendsto ∞, which can reduce costs. Oscillatory integrals aris-ing when solving for q(�y) on the boundary, can be ap-proximated asymptotically using the (numerical) methodof steepest descents. We explain this method, the case ofmultiple reflections and the extension to 3D.

Peter OpsomerKU Leuvenpeter.opsomer@cs.kuleuven.be

Daan HuybrechsDepartment of Computer ScienceK.U. Leuvendaan.huybrechs@cs.kuleuven.be

PP10

Accurate Derivative Computation for Finite Ele-ment Codes

It is common in physics to solve a PDE for some poten-tial, while the physically relevant quantities are actuallyderivatives of said potential. Classical finite element meth-ods, however, lose an order of accuracy for every derivativetaken. We present an integral equation-based techniquethat, in the case of 2-D semilinear Poisson equations, en-ables the computation of arbitrary derivatives to the sameorder as a given FEM solution. We present particular ap-plications to the Grad-Shafranov equation.

Lee F. Ricketson

CS15 Abstracts 259

UCLAlfr224@cims.nyu.edu

Antoine CerfonNYUcerfon@cims.nyu.edu

Manas RachhCourant InstituteNYUmanasrachh@gmail.com

PP10

Comparison of Weak Galerkin Finite ElementMethod with Dgfem and Mfem

This poster presents a comparative study on thenewly introduced weak Galerkin finite element meth-ods (WGFEMs) with the widely accepted discontinu-ous Galerkin finite element methods (DGFEMs) andthe classical mixed finite element methods (MFEMs) forsolving second-order elliptic boundary value problems.We examine the differences, similarities, and connectionamong these methods in scheme formulations, implemen-tation strategies, accuracy, and computational cost. Thecomparison and numerical experiments demonstrate thatWGFEMs are viable alternatives to MFEMs and hold someadvantages over DGFEMs, due to their properties of localconservation, normal flux continuity, no need for penaltyfactor, and definiteness of discrete linear systems.

Farrah Sadre-MarandiColorado State Universitysadre@math.colostate.edu

PP10

A Weighted Sequential Splitting Method for the3D Maxwell’s Equations

We present a Weighted Sequential Splitting (WSS) methodfor Maxwell’s equations in 3D. The solution obtained bythe WSS scheme in a given time step is a weighted aver-age of solutions of several 1D Maxwell systems, discretizedusing a Crank Nicolson method. We prove convergence ofthe scheme for all weights 0 ≤ θ ≤ 1, and show that it isunconditionally stable of first order in time when θ �= 0.5,and second order when θ = 0.5.

Puttha SakkaplangkulOregon State Universitysakkaplp@onid.oregonstate.edu

PP10

Asymptotically Compatible Schemes for RobustDiscretization of Nonlocal Models

Nonlocality is ubiquitous in nature. While partial differ-ential equations (PDE) have been used as effective mod-els of many physical processes, nonlocal models and non-local balanced laws have become possible alternatives totreat anomalous process and singular behavior. In thistalk, we use a recently developed nonlocal vector calcu-lus and nonlocal calculus of variations to study a class ofconstrained value problems associated with nonlocal op-erators. In addition, we present asymptotically compati-ble discretizations that provide convergent approximationsto both nonlocal models and their local limit. Such dis-cretizations are useful for model validation and multiscale

simulations.

Qiang Du, Xiaochuan TianColumbia UniversityDepartment of Applied Physics and Applied Mathematicsqd2125@columbia.edu, xt2156@columbia.edu

PP11

The Sparse Grid Combination Technique for Solv-ing Eigenvalue Problems

Identifying microinstabilities in hot fusion plasmas can bedone by solving the gyrokinetic eigenvalue problem which isa computationally demanding task. Our approach for solv-ing this problem is the combination technique. It combinesseveral solutions of the eigenvalue problem from differentgrid-sizes. That can diminish the curse of dimensionality,since it creates a sparse grid approximation. It also in-creases the scalability by introducing an additional layerof parallelism which is reusing the current parallelism.

Christoph KowitzTU Munichkowitz@in.tum.de

Markus HeglandAustralian National UnversityMarkus.Hegland@anu.edu.au

Hans-Joachim BungartzTechnische Universitat Munchen, Department ofInformaticsChair of Scientific Computing in Computer Sciencebungartz@in.tum.de

PP11

A Tangential Interpolation Framework for MIMOEigensystem Realization Algorithm

The Eigensystem Realization Algorithm (ERA) is a com-monly used data- driven method for system identificationand model reduction of dynamical systems. The main com-putational difficulty in ERA arises when the system underconsideration has large number of inputs and outputs, thusrequiring to compute a full SVD of a large-scale dense Han-kel matrix. In this work, we present an algorithm that aimsto resolve this computational bottleneck via tangential in-terpolation. A numerical example is presented.

Boris KramerVirginia Techbokr@vt.edu

Serkan GugercinVirginia Tech.Department of Mathematicsgugercin@math.vt.edu

PP11

Multi-Set Data Analysis and Simultaneous MatrixBlock Diagonalization: Models and Algorithms

We present joint independent subspace analysis (JISA) ofstationary sources as a statistical signal processing ap-proach to multi-set data analysis. From an algebraic per-spective, JISA may be viewed as a set of coupled block di-agonalization (CBD) problems. We evoke some new resultsfor JISA-CBD, and linkage to recent results on ISA of non-

260 CS15 Abstracts

stationary sources based on joint block diagonalization ofcovariance matrices. We focus on algorithms, performance,identifiability and the associated matrix factorizations.

Dana Lahat, Christian JuttenGIPSA-LabDana.Lahat@gipsa-lab.grenoble-inp.fr,christian.jutten@gipsa-lab.grenoble-inp.fr

PP11

Overcoming the Gibbs Phenomenon : Fast FourierExtension

Fourier series of smooth functions on an interval [−1, 1] areknown to exhibit the Gibbs phenomenon, and have overallslow convergence. The Fourier extension technique over-comes these problems by constructing a Fourier approxima-tion on an extended interval [−T, T ], through least-squaresoptimization. We present FE algorithms for approxima-tions from equidistant points that match the O(N logN)complexity of the discrete Fourier transform, and commenton the associated difficulties.

Roel MatthysenKULeuvenroel.matthysen@cs.kuleuven.be

PP11

Big Graph Analytics of Human Connectome Net-works

Analyzing the very dense human connectome network withbillions of links has become a central and challenging topicin computational neuroscience. Yet, it offers neuroscien-tists great opportunities to understand the complex struc-ture and functionality of the human brains. In this projectwe demonstrate how to use big data technology and tools,such as Spark GraphX and SAP HANA, to approximatevarious graph measurements from the brain connectivitygraphs released by the Human Connectome Project.

Jurgen Ommen, Chih Lai, Yulin YangUniversity of St. ThomasGraduate Programs in Softwareomme0003@stthomas.edu, clai@stthomas.edu,yang9594@stthomas.edu

PP11

Componentwise Sensitivity of Matrix Functionsand Applications

Matrix functions, such as the exponential, are used in a va-riety of applications. Previous sensitivity analyses involvemainly normwise condition numbers. Componentwise con-dition numbers and perturbation bounds are more appro-priate when sensitivity with respect to particular compo-nents is of interest. We develop such analysis and ap-ply it to a parameterized ODE problem arising in physicswhere the matrix components are flux coefficients describ-ing chemical interaction.

Samuel ReltonUniversity of Manchester, UKsamuel.relton@manchester.ac.uk

PP11

Inducing Approximately Optimal Flow Via Truth-

ful Mediators

The classical approach to have selfish agents route opti-mally in network congestion games is to impose edge tollsthat depend on agents’ demands. However, this fails whendemands are unknown to the mechanism designer. We de-sign a weak mediator that can impose tolls such that itis an asymptotic ex-post Nash equilibrium for agents totruthfully report their demands to the mediator and faith-fully follow its suggested route, which results in an approx-imately optimal flow.

Ryan M. RogersUniversity of Pennsylvaniaryrogers@sas.upenn.edu

Aaron RothUniversity of Pennsylvania, USAaaroth@cis.upenn.edu

Jonathan UllmanColumbia Universityjullman@cs.columbia.edu

Steven WuUniversity of Pennsylvaniawuzhiwei@cis.upenn.edu

PP11

Security in Data Mining Through Cloud Comput-ing Using Expert System

This study presents an expert system to optimize the secu-rity of data mining in cloud computing.These systems stillsuffer from privacy and security concerns. The main se-curity issues in cloud computing are identifying identity,access control, confidentiality, integrity, availability andnon-repudiation. The main goal of this investigation isdesigning an expert system to increase the security of datamining in cloud computing systems. To do this, the effi-ciency of these techniques is examined for the same dataset .Subsequently, an inference engine has been developedand this engine automatically selects the model which hasbest efficiency by using artificial intelligence techniques.

Ana Sadeghitohidi, Azadeh RoozbehiAzad Tehran Universityanasadeghii1@yahoo.com, azadeh.roozbehi@gmail.com

PP11

Big Data Analytics Application in Genomics DataProcessing

Genomics datasets are large. In this project we are process-ing genomics data on a HPC cluster using Hadoop. Ourgoal is to identify from the genome data any disease pat-tern. Eventually we plan to have access to clinical data forminorities that will help identify risk factors when com-bined with genomics data. Our processing at this timeis experimental and as such no patient privacy issues areinvolved because the clinical data will be anonymized.

S SrinivasanTexas Southern UniversityJHJ School of Businesssrinis@tsu.edu

Hector MirandaTexas Southern University

CS15 Abstracts 261

mirandahc@tsu.edu

Daniel VrinceanuTexas SOuthernvrinceanud@tsu.edu

Terence VaughnTexas Southern Universityvaughntt@tsu.edu

PP11

Generalized Low Rank Models

Principal components analysis (PCA) is a well-known tech-nique for approximating a data set represented by a matrixby a low rank matrix. Here, we extend the idea of PCA tohandle arbitrary data sets consisting of numerical, Boolean,categorical, ordinal, and other data types. This frameworkencompasses many well known techniques in data analysis,such as nonnegative matrix factorization, matrix comple-tion, sparse and robust PCA, k-means, k-SVD, and max-imum margin matrix factorization. The method handlesheterogeneous data sets, and leads to coherent schemesfor compressing, denoising, and imputing missing entriesacross all data types simultaneously. It also admits a num-ber of interesting interpretations of the low rank factors,which allow clustering of examples or of features. We pro-pose several parallel algorithms for fitting generalized lowrank models, and describe implementations and numericalresults.

Madeleine R. UdellStanford UniversityStanford Universitymadeleine.udell@gmail.com

Corinne Horn, Reza ZadehStanford Universitycehorn@stanford.edu, rezab@stanford.edu

Stephen BoydStanford UniversityDepartment of Electrical Engineeringboyd@stanford.edu

PP11

A Structured Cholesky Factorization for Fock Ma-trix Construction

The bottleneck of Fock matrix construction is computa-tion and storage of Electron Repulsion Integrals (ERIs).We present new high performance software implemented inGTFock which pre-computes a structured lazy evaluationpivoted Cholesky factorization of the matrix unfolding ofthe fourth-order ERI tensor. In addition to reducing ERIcomputation and storage by an order of magnitude, thisnew approach utilizes symmetry and sparsity structure.

Joseph VoktCornell Universityjoseph.vokt@gatech.edu

Edmond ChowSchool of Computational Science and EngineeringGeorgia Institute of Technology

echow@cc.gatech.edu

PP11

Parallel Bayesian Global Optimization, With Ap-plication To Metrics Optimization at Yelp

We consider parallel global optimization of expensive-to-evaluate functions, and propose an efficient method basedon stochastic approximation for implementing a conceptualBayesian optimization algorithm proposed by Ginsbourgeret al. (2010). We also introduce an open-source softwareimplementation of this algorithm, called Metrics Optimiza-tion Engine, developed in collaboration with engineers atYelp Inc. and used internally at Yelp to optimize predic-tion models and performance metrics.

Jialei Wang, Peter I. FrazierCornell Universityjw865@cornell.edu, pf98@cornell.edu

Scott Clark, Eric LiuYelp Incsclark@yelp.com, eliu@yelp.com

PP12

The Modified Bidomain Model with Periodic Dif-fusive Inclusions

Bidomain equations are the standard way to model theelectric potential in cardiac tissue. We propose the modifi-cation of this model for the case of the diseased heart, e.g.fibrosis of the heart tissue. On microscale, we assume tohave periodic diffusive inclusions embedded in the healthytissue modelled by the bidomain equations. We derivethe macroscale model using the homogenisation technique.We recover a bidomain model with modified conductivi-ties, that depend on the volume fraction of the diffusiveinclusions but also on their geometries.

Andjela DavidovicINRIA Bordeaux Sud-Ouest, Bordeaux, FranceUniversity Bordeaux, Bordeaux, Franceandjela.davidovic@inria.fr

Yves CoudiereUniversite Bordeaux 1Inria & IMB (UMR 5251)yves.coudiere@inria.fr

Clair PoignardINRIA Bordeaux Sud-OuestUniversity Bordeauxclair.poignard@inria.fr

PP12

Simulation-Based Solute Transport in Kidney Cells

Based on solute and water conservation and electroneu-trality constraints, we developed mathematical modelsof kidney cells. With the models, we computed intra-cellular Na+ concentration and membrane hyperpolariza-tion/depolarization behavior as a function of extracellularNaCl. Mathematical models like these can be adapted toformulate hypotheses of a system response after a pertur-bation. Furthermore, they can help in the developmentof new drugs prior to in vivo testing, thereby minimizing

262 CS15 Abstracts

research costs, and time.

Monica Nadal-QuirosUniversity of Puerto Rico, Rio Piedras CampusDepartment of Biologymonica.nadal@upr.edu

Aniel Nieves-GonzalezUniversity of Puerto RicoInstitute of Statistics and Information Systemsaniel.nieves@upr.edu

Leon MooreSUNY HSCDepartment of Physiology and Biophysicsleon.moore@stonybrook.edu

Mariano MarcanoUniversity of Puerto Ricomariano.marcano@upr.edu

PP12

An Adaptive Markov Chain Monte Carlo MethodApplied to Simulation of a Tumor Growth Model

The inference of mechanistic descriptions of oncogenesis isoften a challenge due to limited experimental data. MarkovChain Monte Carlo (MCMC) methods have been developedand widely used in Bayesian analysis. This project appliesan adaptive MCMC technique based on the Metropolis-Hastings algorithm to calibrate the parameters of a tumorgrowth model to experimental data. The study is sup-ported by the NIGMS of NIH grant as part of the WestVirginia INBRE (P20GM103434).

Qing Wang, Zhijun WangDept. of Computer Science, Math and EngineeringShepherd University, Shepherdstown, WVqwang@shepherd.edu, zwang@shepherd.edu

David KlinkeDept. of Chemical EngineeringWest Virginia University, Morgantown, WVdavid.klinke@mail.wvu.edu

PP12

Numerical Simulation of a Tumor Cell PopulationGrowth Dynamics Model Using Genetic Algorithm

Tumor cell growth models involve high-dimensional param-eter spaces that require computationally tractable methodsto solve. Genetic algorithm is applied to search for parame-ter values that fit experimental data from mice cancel cells.Dynamically variable crossover and mutation methods areused to produce new generations. Fitness functions, whichmeasure the difference between calculated results and ex-perimental data, are minimized. This study is supportedby the NIGMS of NIH grant as part of the WV INBRE(P20GM103434).

Zhijun Wang, Qing WangDept. of Computer Science, Math and EngineeringShepherd University, Shepherdstown, WVzwang@shepherd.edu, qwang@shepherd.edu

PP12

”Allostery”: A Python Package for Network Anal-

yses of Biomolecular Simulations

Allosteric interaction network is an intrinsic complex prob-lem in computational bio-molecular researches and veryscarce analysis tools are available. Here I present a pythonpackage named “Allostery” for calculation of biomolecu-lar interaction networks using Lange-Grubmuller general-ized correlation coefficient, based on Kraskov-Stogbauer-Grassberger Mutual Information estimator. It features:distance and k-d tree based implementation, memory ef-ficient serial and cluster level parallel execution and user-friendly tools for data IO and visualization.

Yuhang WangUniversity of Illinois, Urbana-Champaignywang148@illinois.edu

Emad TajkhorshidUniversity of Illinois, Urbana-Chamnpaignemad@life.illinois.edu

PP12

Numerical Methods for Protein Adsorption inPorous Membranes

Protein therapeutics are used as treatments for various ill-nesses (diabetes, cancer, hemophilia, infectious diseases).Most of the cost of protein production is associated withthe downstream separation/purification. Developing moreefficient purification methods would decrease the cost ofprotein therapeutics. In this presentation, we will dis-cuss protein separation using multi-modal membranes de-veloped in Clemson University’s chemical engineering de-partment. We will present numerical simulations of theadvection-diffusion-reaction equation, comparing and con-trasting solution methods and adsorption models.

Anastasia B. WilsonClemson UniversityDepartment of Mathematical Sciencesanastas@clemson.edu

PP12

Modeling Core Body Temperature during Exercise

Dynamics of core body temperature of rats running ontreadmills with varied speeds at different ambient temper-atures were modeled. The model was used to estimate heatgenerated in the body for thermoregulation and additionalheat produced by the muscles during exercise. We foundthat the latter grows with exercise intensity in ambienttemperature independent way. In contrast, the thermoreg-ulatory component reduces at room temperature, while re-maining unchanged at high temperature implying existenceof compensatory mechanisms.

Yeonjoo YooIndiana University-Purdue University IndianapolisIUPUIyjyoo@iupui.edu

PP12

Ensemble Kalman Filters for Dynamic Dipole Es-timation from Magnetoencephalography

We discuss the dynamic imaging of electromagnetic cere-bral activity based on magnetoencephalography (MEG)data. In this presentation, we develop two time evolution

CS15 Abstracts 263

models combined with the ensemble Kalman filter to local-ize the electric source currents and capture the rapid neuralactivity in the brain. The utilization of the Bayesian frame-work allows sequential updating of the preceding estimatesof the activations. The effectiveness of the algorithms isdemonstrated with simulated data.

Lijun YuCase Western Reserve Universitylxy141@case.edu

Daniela CalvettiCase Western Reserve UnivDepartment of Mathematicsdxc57@case.edu

Erkki SomersaloCase Western Reserve Universityejs49@case.edu

PP13

Decomposition-Based Uncertainty Quantificationwith Application to Environmental Impacts of Avi-ation

We present a decomposition-based uncertainty quantifica-tion approach for feed-forward multicomponent systems.The aim is to decompose the uncertainty quantificationtask among the various components comprising a system,then synthesize these results to quantify uncertainty at thesystem level. We introduce concepts that extend our ap-proach to systems containing a large number of component-to-component interface variables. We apply the proposedmethod to quantify how uncertainty in aviation technologyaffects uncertainty in environmental impacts.

Sergio AmaralDepartment of Aeronautics & AstronauticsMassachusetts Institute of Technologysamaral@mit.edu

PP13

The Combined Block by Block - Monte CarloMethods for Numerical Treatment of the MixedNonlinear Stochastic Integral Equation

In this paper, we study the random effects, W(s), ona mixed nonlinear integral equation of the second kindwith time dependent. Two contributions are made: thefirst contribution discuses the existence and uniqueness ofthe solution of this equation and the second contributionpresents an algorithm in which we combine both Block-by-Block method and Monte-Carlo method, to accuratelyand efficiently solve a mixed nonlinear stochastic integralequation. Numerical examples are given to illustrate thepresented numerical method.

Abdallah A. BadrAlexandria UniversityDepartment of Mathematicsa.badr@ubt.edu.sa

PP13

Computational Investigation of Quasi-Random Se-quences for Error Estimation

Quasi-Monte Carlo methods has become a major vehi-cle for estimating high-dimensional integrations. However,

the asymptotic error convergence order depends on thesequences used in estimation integration. In this paper,we investigate a family of related quasi-random sequences,known low-discrepancy sequences, and study their effectsto convergence of error estimation. Our experimental re-sults show that some low-discrepancy sequences signifi-cantly improve the performance of error estimation.

Hongmei ChiComputer ScienceFlorida A&M Universityhchi@cis.famu.edu

PP13

Optimal Source Encoding in Medium ParameterReconstruction Problems

The computational cost of medium parameter reconstruc-tion scales linearly with the number of sources used. Toalleviate that bottleneck, several authors proposed to solveinstead for a few linear combinations of the sources. Inorder to preserve consistency with the original problem,those combinations must be chosen randomly. Instead wepropose to select the combinations that provide the mostconfidence in the reconstructed parameters, in the Bayesiansense. This leads us to minimize the nuclear norm of thevariance of the posterior distribution evaluated at the MAPpoint.

Benjamin CrestelUniversity of Texas at AustinInstitute for Computational Engineering and Sciencecrestel@ices.utexas.edu

Omar GhattasThe University of Texas at Austinomar@ices.utexas.edu

Georg StadlerCourant Institute for Mathematical SciencesNew York Universitystadler@cims.nyu.edu

PP13

Randomized Likelihood Method: A Scalable Ap-proach to Big Data in Large-Scale Pde-ConstrainedBayesian Inverse Problems

In this poster we present a scalable approach to tackle thebig-data challenge in large-scale PDE-constrained Bayesianinverse problems. In particular, we propose a MAP ap-proximation algorithm whose convergence is independentof the data dimension The idea is to randomize the likeli-hood to extract active/important/independent data whichis in general much less compared to the original big data.The active data is then used to obtain approximate MAPpoint. We rigorously analyze the convergence of the pro-posed randomized likelihood method for a large class ofinverse problems under mild conditions. One of the keyresults is that approximate MAPs converge to the big-dataMAP in probability, independent of the amount of data.Several numerical results for large-scale PDE-constrainedBayesian inverse problems are presented to show the effec-tiveness of the proposed method and to verify the theoret-ical results.

Aaron MyersUT Austin, ICESaaron@ices.utexas.edu

264 CS15 Abstracts

Tan Bui-ThanhThe University of Texas at Austintanbui@ices.utexas.edu

Ellen LeUniversity of Texas at Austin - ICESellen@ices.utexas.edu

PP13

MUQ (MIT Uncertainty Quantification): FlexibleSoftware for Connecting Algorithms and Applica-tions

It is difficult to interface uncertainty quantificationalgorithms—e.g., Bayesian inference, robust optimization,surrogate building, sensitivity analysis—with computa-tional models in a way that exposes model structure to thealgorithms while accommodating easy development of newmodels and new algorithms. The MIT Uncertainty Quan-tification (MUQ) library addresses these issues with a flex-ible software framework for constructing complex multi-component models and for developing new algorithms. Wediscuss our design goals and demonstrate MUQ by bothimplementing a new MCMC algorithm and constructing acoupled PDE model.

Matthew Parno, Patrick R. ConradMassachusetts Institute of Technologymparno@mit.edu, p.conrad@warwick.ac.uk

Andrew DavisMITdavisad@mit.edu

Youssef M. MarzoukMassachusetts Institute of Technologyymarz@mit.edu

PP13

A Stochastic Dynamic Programming Method forControlling a Combined Hydro/Wind Power Pro-ducer

We develop a computationally efficient nonlinear stochas-tic dynamic programming model to determine the optimalcontrol of a combined hydro and wind power producer. Thealgorithm efficiency is improved through use of a radial ba-sis function approximation within a corridor.

Kyle PerlineCornell Universitykrp73@cornell.edu

PP13

Efficient Error Estimation for Elliptic PDEs withRandom Data

When PDE models have uncertain inputs, efficient numer-ical methods for the forward problem are needed for un-certainty quantification. Stochastic Galerkin finite elementmethods have attractive approximation properties but aretoo expensive to implement on standard computers whenthe dimension of the random input space is high. To im-prove efficiency, we look to adaptive Galerkin schemes. Weintroduce a cheap a posteriori error estimator for ellipticproblems that can be implemented in a non-intrusive way.

Catherine PowellSchool of MathematicsUniversity of Manchesterc.powell@manchester.ac.uk

Alex BespalovUniversity of Birmingham, United Kingdoma.bespalov@bham.ac.uk

David SilvesterSchool of MathematicsUniversity of Manchesterdavid.silvester@manchester.ac.uk

PP13

Inference of Constitutive Parameters in a Nonlin-ear Stokes Mantle Flow Model

Motivated by inverse problems in mantle flow modelswith plate tectonics, we estimate constitutive parame-ters in a nonlinear Stokes system using a Bayesian in-ference approach. We compute the maximum a posteri-ori (MAP) point of the posterior parameter distribution,which amounts to the solution of a PDE-constrained op-timization problem. To quantify the uncertainty in theparameters, we compare a local Gaussian approximationof the posterior distribution at the MAP point with resultsobtained using MCMC sampling.

Vishagan RatnaswamyCalifornia Institute of TechnologySeismological Laboratoryvratnasw@caltech.edu

Georg StadlerCourant Institute for Mathematical SciencesNew York Universitystadler@cims.nyu.edu

Michael GurnisCalifornia Institute of Technologygurnis@gps.caltech.edu

Omar GhattasThe University of Texas at Austinomar@ices.utexas.edu

PP13

Uncertainty Quantification for Thermally DrivenFlow

The uncertainty in a scalar quantity of interest is quanti-fied for a natural convective flow in a cavity with randomboundary data. The performance of sparse grid stochasticcollocation is compared to quasi Monte Carlo, dependingon the variance of the random perturbation. The methodsare accelerated by making use of simulation results frompreviously visited sampling points. In particular, improvedstarting conditions for the iterative non-linear solver andPOD-Galerkin reduced-order modeling are considered.

Sebastian Ullmann, Lang JensTU Darmstadtullmann@gsc.tu-darmstadt.de, lang@mathematik.tu-

CS15 Abstracts 265

darmstadt.de

PP13

Computational and Statistical Tradeoffs: a Frame-work

The recent explosion in the quantity and dimension of datahas brought up many new computational and statisticalchallenges that must be addressed simultaneously such thatinference is both tractable and meaningful. We propose aframework that provides an explicit opportunity for thepractitioner to specify how much statistical risk they arewilling to accept for a given computational cost. We illus-trate this with an example of estimation from a stream ofiid normal variables.

Alexander VolfovskyStatistics Department, Harvard UniversityHarvard Universityvolfovsky@fas.harvard.edu

Edoardo Airoldi, Daniel SussmanHarvard Universityairoldi@fas.harvard.edu, daniellsussman@fas.harvard.edu

PP13

Efficiency of the Girsanov Transformation Ap-proach for Parametric Sensitivity Analysis ofStochastic Chemical Kinetics

Monte Carlo methods for sensitivity analysis of stochasticreaction networks can be classified into three categories,the pathwise derivative (PD) method, the finite differ-ence (FD) method and the Girsanov transformation (GT)method. It has been numerically observed that when ap-plicable, the PD method and FD method tend to be moreefficient than the GT method. We provide a theoreticaljustification for this observation in terms of system sizeasymptotic analysis.

Ting WangDepartment of Mathematics and StatisticsUniversity of Maryland Baltimore Countyting1@umbc.edu

Muruhan RathinamUniversity of Maryland, Baltimore Countymuruhan@umbc.edu

PP13

Convergence of the Robbins-Monro Algorithm inInfinite Dimensional Hilbert Spaces

Good proposal distributions can significantly improve theperformance of random walk Metropolis algorithms. Re-cent work has suggested that finding the best Gaussian,fit with respect to the relative entropy metric against thetarget distribution, can provide such speedup. Minimizingrelative entropy may be non-trivial, particularly in the caseof distributions on infinite dimensional spaces. We demon-strate that the Robbins-Monro algorithm can be used tofind the optimal Gaussian proposal distribution in infinitedimensional Hilbert spaces.

Daniel WatkinsDrexel Universitydanielmwatkins@gmail.com

Gideon SimpsonDepartment of MathematicsDrexel Universitysimpson@math.drexel.edu

PP13

Utilizing Adjoint-Based Techniques to EffectivelyPerform Uq on Discontinuous Responses

Uncertainty is ubiquitous in predictive modeling and sim-ulation due to unknown model parameters, initial condi-tions, etc. A number of recently developed methods for un-certainty quantification have focused on constructing sur-rogates of high-fidelity models using only a limited numberof model evaluations. Unfortunately, many of these tech-niques perform poorly when the response surface is discon-tinuous. In this poster, we show how adjoint-based tech-niques can be used to efficiently construct discontinuoussurrogate approximations.

Tim WildeyOptimization and Uncertainty Quantification Dept.Sandia National Laboratoriestmwilde@sandia.gov

Eric C. CyrScalable Algorithms DepartmentSandia National Laboratotorieseccyr@sandia.gov

John ShadidSandia National LaboratoriesAlbuquerque, NMjnshadi@sandia.gov

PP13

Optimization of Modeled Land Surface Fluxes byBayesian Parameter Calibration

The integration of observations and advanced modelingtools is critical for resolving issues of uncertainty in cli-mate models. We present results from an isotopically-enabled land surface model, including experiments parti-tioning evapotranspiration into contributions from planttranspiration and surface evaporation. We demonstrate amodel calibration approach in a Bayesian estimation frame-work, requiring Markov chain Monte Carlo sampling of theposterior distribution, which is shown to constrain uncer-tain parameters and inform relevant values for operationaluse.

Tony E. WongUniversity of Colorado at BoulderDepartment of Applied Mathematicsanthony.e.wong@colorado.edu

David NooneUniversity of Colorado at BoulderCooperative Institute for Research in EnvironmentalSciencesdcn@colorado.edu

William KleiberUniversity of Colorado at BoulderDepartment of Applied Mathematics

266 CS15 Abstracts

william.kleiber@colorado.edu

PP13

Efficient Monte Carlo Scheme for the Simulation ofthe Association of Lattice-model Proteins

A lattic Monte Carlo model with implicit membrane andwater is used to model certain types of protein aggregationin biological membranes. We describe a sampling schemethat attempts to combine the merits of parallel temper-ing and multicanonical sampling. The key to this schemeis deriving best estimates for the log density of statesfrom the MBAR estimator [Shirts, Michael R., and JohnD. Chodera. ”Statistically optimal analysis of samplesfrom multiple equilibrium states.” The Journal of chem-ical physics 129.12 (2008): 124105.]

Yuanwei Xu, Mark RodgerUniversity of WarwickYuanwei.Xu@warwick.ac.uk, p.m.rodger@warwick.ac.uk

PP14

Visualising Protein Sequence Alignment

In bioinformatics, protein sequence alignment used stringsof contiguous letters of amino acids, arranged in verticalregister in order to highlight regions of similarity and dif-ference. When sequences have different lengths, gap char-acters are inserted to denote insertions or deletions; how-ever, gaps have no meaning in 3D structures. This projectaims to revisit the protein sequence alignment problem byexploring possible ways to visualise the relationships be-tween sequences in 3D space wile eliminating gap charac-ters. In our work, an N -body Hamiltonian system in con-tact with a heat bath is built and it’s configuration in 3Dspace forms the basis of our visualisation. The novel 3D vi-sualisation method opens the possibility of analysing muchlarger alignments that wouldn’t be possible with conven-tional visualisations produced by current alignment toolsand editors.

Shaimaa M. AljuhaniPhD studentThe University of Manchestersmjuhani@gmail.com

Prof. Teresa AttwoodThe University of ManchesterFaculty of Life Sciencesteresa.k.attwood@manchester.ac.uk

Dr. Tony ShardlowUniversity of BathDepartment of Mathematical Sciencest.shardlow@bath.ac.uk

PP14

Reconstructing Physically Realistic Flow Fieldsfrom Sparse Experimental Data

Flow measurements from wind-tunnel experiments sufferfrom noise and low spatio-temporal resolution. To recon-struct complete flow fields we use physics-based interpola-tion, enforcing a vorticity formulation of momentum con-servation using a vortex-based solver. Its mesh-free natureand desirable stability characteristics enable a flexible andefficient framework. We formulate the data-assimilationprocedure as an adjoint-based optimization for efficiency.

We apply the methodology to particle tracking velocimetryexperiments and demonstrate reconstruction of smooth,physically-correct fields from limited data.

Iliass Azijli, Richard Dwight, Jan SchneidersDelft University of Technologyi.azijli@tudelft.nl, r.p.dwight@tudelft.nl,j.f.g.schneiders@tudelft.nl

Hester BijlFaculty Aerospace EngineeringDelft University of Technology, NLh.bijl@tudelft.nl

PP14

Parallel-in-Time Integration with Pfasst++

Iterative parallel-in-time integration methods like the re-cently developed “parallel full approximation scheme inspace and time’ (PFASST) provide parallelism along thetemporal axis by integrating multiple time-steps simul-taneously. We present PFASST++, a new performance-oriented library enabling time-parallelization for existingcodes. PFASST++ provides flexibility and ease of usewhile maintaining portability across many HPC architec-tures. We present preliminary results using a high-orderBoris integrator for charged particle dynamics in externalmagnetic fields.

Torbjorn KlattJuelich Supercomputing Centret.klatt@fz-juelich.de

Robert SpeckJuelich Supercomputing CentreForschungszentrum Juelichr.speck@fz-juelich.de

Mathias Winkel, Daniel RuprechtInstitute of Computational ScienceUniversita della Svizzera italianamathias.winkel@usi.ch, daniel.ruprecht@usi.ch

Matthew EmmettLawrence Berkeley National LaboratoryCenter for Computational Sciences and Engineeringmwemmett@lbl.gov

PP14

An Optimization-Based Approach Toward Elasto-plasticity: Introducing a Projected Newton Algo-rithm

In this study, we explore an alternative treatment of clas-sical plasticity by casting the theory into a mathemati-cal program. We propose a precise development and im-plicit implementation of a projected Newton algorithm todirectly solve the dual optimization problem of incrementalstate update in nonlinear models. In particular, implemen-tation of multi-surface plasticity models turns out to be nodifferent from that of single surface models.

Zahra S. Lotfian, Mettupalayam SivaselvanSUNY at Buffalozahrasad@buffalo.edu, mvs@buffalo.edu

PP14

Redesigning Laser-Plasma Simulations to Optimize

CS15 Abstracts 267

the Use of Limited Memory Bandwidth

Memory bandwidth limitations are a growing problem af-fecting pf3D, a large-scale multi-physics code simulatinglaser-plasma interactions. Implementing lossy hardwarecompression between DRAM and cache could improveavailable bandwidth use in the future. pf3D is resilient toerrors from lossy compression at each time step. We pre-dict pf3Ds hardware compression requirements, describestrategies to optimize data movement to utilize hardwarecompression for a variety of physics kernels, and presentsoftware experiments on several existing architectures.

Eileen R. MartinStanford Universityermartin@stanford.edu

Steve LangerLawrence Livermore National Laboratorylanger1@llnl.gov

PP14

Parallel Numerics for Partitioned MultiphysicsCoupling

Massively parallel multi-physics simulations require effi-cient parallel coupling schemes. This holds in particularfor partitioned simulations where singlephysics componentsare combined in a flexible and extensible way. Parallelismand more than two coupled fields pose new to a couplingscheme. Not all established coupling schemes can copewith these challenges. We propose a set of new implicitcoupling schemes that meet all requirements by replacingthe usual fixed-point equation by a different one. To acho-eve fast convergence, the resulting fixed-point equation iscombined with efficient quasi-Newton methods suitable forblack-box solvers.

Miriam MehlUniversitat Stuttgartmiriam.mehl@ipvs.uni-stuttgart.de

Benjamin UekermannTU Munichuekerman@in.tum.de

Florian LindnerUniversitat Stuttgartflorian.lindner@ipvs.uni-stuttgart.de

PP14

Applied Math and CS R&D on Doe LeadershipComputing Facilities

The DOE Leadership Computing Facilities at Argonne andOak Ridge national laboratories welcome applied mathe-maticians and computer scientists to carry out their re-search on our largest supercomputers. These systems,among the most powerful in the world, provide a unique en-vironment to explore algorithm scalability and implemen-tation at full scale. Examples of current projects and waysto gain access to our systems will be described.

Paul C. MessinaArgonne National Laboratory

messina@anl.gov

PP14

Simple Yet Fast Integration Method Using Qss forStiff Chemical Kinetic Odes

A simple yet robust and fast time integration method isproposed for efficiently solving stiff chemical kinetic ordi-nary differential equations. The proposed method is basedon a general formula which preserves the conservation lawsfor any integration operators constructed using the La-grange multiplier method. And a quasi-steady-state ap-proximation is used as the integrator. The time step size isautomatically controlled by keeping a Lagrange multipliersmall. The proposed method, named ERENA, providesthe good performances.

Youhi MoriiJapan Aerospace Exploration Agencymorii.yuuhi@jaxa.jp

Hiroshi TerashimaThe University of Tokyohtera@rocketlab.t.u-tokyo.ac.jp

Mitsuo KoshiYokohama National Universitykoshi@rocketlab.t.u-tokyo.ac.jp

Taro Shimizu, Eiji ShimaJapan Aerospace Exploration Agencyshimizu.taro@jaxa.jp, shima.eiji@jaxa.jp

PP14

PtychoLib: Parallel Ptychographic Reconstruction

Ptychography is a phase retrieval technique for recon-structing a specimen’s image from its diffraction patterns inlight, X-ray, and electron microscopes. Despite the poten-tial for ptychography there is a lack of tools for data onlineanalysis while it is being acquired. PtychoLib is a libraryfor real-time ptychographic phase retrieval. It uses a hy-brid parallel strategy to divide the computation betweenmultiple graphics processing units then merge partial re-constructions into one coherent phase contrast image.

Youssef NashedArgonne National Laboratoryynashed@anl.gov

David VineAdvanced Photon SourceArgonne National Laboratorydvine@anl.gov

Tom PeterkaMathematics and Computer Science DivisionArgonne National Laboratorytpeterka@mcs.anl.gov

Junjing DengApplied PhysicsNorthwestern Universityjunjingdeng2011@u.northwestern.edu

Rob RossArgonne National Laboratoryrross@mcs.anl.gov

268 CS15 Abstracts

Chris JacobsenAdvanced Photon SourceArgonne National Laboratorycjacobsen@aps.anl.gov

PP14

Efficient Numerical Algorithm for Virtual Designin Nanoplasmonics

Nanomaterials have given rise to many devices, from high-density data storage to optical bio-sensors capable of de-tecting specific biochemicals. The design of new nanode-vices relies increasingly on numerical simulations, driving aneed for efficient numerical methods. In this work, integralequations are used to efficiently solve the electromagnetictransmission problem at the interface of a dielectric and aperiodic metal nanostructure. Moreover, the same integralequations are used as the basis for an optimization method.

Alexandra OrtanUniversity of Minnesotaaortan@umn.edu

PP14

Model-Reduction for Closed-Loop Control of Un-steady Flows Using Plasma Actuators

Flow instabilities in aircraft aerodynamics increase noiseemissions and drag. Active closed-loop flow control usingplasma actuators is a promising way to reduce these effects.However, a rigorous model is required for the feedbackcontrol design. The spatially discretized actuator/flow dy-namics is high-dimensional, nonlinear and, thus, computa-tionally intractable for real-time applications. Therefore, asuitable control-oriented reduced-order model, which cap-tures the essential physics dominating the system dynamicresponse, while accounting for the closed-loop dynamics, isrequired.

Laura Pasquale, Paul Houston, Pericle ZanchettaUniversity of Nottinghamlaura.pasquale@nottingham.ac.uk,pmzph1@exmail.nottingham.ac.uk,eezpz@exmail.nottingham.ac.uk

PP14

Moving Pictures: Animating Still Images

We present a means of developing digital image transfor-mations that allow a still image to be turned into a shortand visually pleasing animation. Rather than manually al-tering successive frames to create the illusion of motion,the method presented here requires only the input of afew parameters for each transformation. We developed amathematical framework wherein we defined animations assequences of still images, and ’transformations’ as compos-able functions on such sequences.To implement this work, we have built a Matlab library ofcomposable functions that streamline the process of turn-ing still images into novel animations. Examples includemanipulation of contrast, intensity, and colors of pixels,as well as warps of contours, positions, and size of selectregions. The transformations allow for easy animation ofregions of interest, giving some semblance of life to stillimages by turning them into animated GIFs.

Michael PilosovUniversity of Colorado: Denver

michael.pilosov@ucdenver.edu

PP14

Bridging Multiple Structural Scales with a Gener-alized Finite Element Method

In thermo-mechanical problems subjected to intense heat-ing effects, locally high solution fidelity is required nearmaterial-scale interfaces to capture strong gradients whichmight not be resolved using, for example, traditional ho-mogenization approaches. Effective numerical methodsmust also bridge important localized, nonlinear behavior tothe structural scale. This poster introduces a generalizedfinite element method (GFEM) involving the solution of in-terdependent coarse- and fine-scale problems for resolvinglocalized material interfaces on the structural scale.

Julia A. PlewsDepartment of Civil and Environmental EngineeringUniversity of Illinois at Urbana-Champaignjplews2@illinois.edu

C. Armando DuarteUniversity of Illinois at Urbana-Champaigncaduarte@illinois.edu

PP14

A Parallelization Strategy for Large-Scale VibronicCoupling Calculations

The vibronic coupling model of Koppel, Domcke, andCederbaum is a powerful means to understand, predict,and analyze electronic spectra of molecules. We describea new distributed-memory parallel algorithm for carryingout such calculations, based on a stencil representation ofthe required computational steps. Our algorithm utilizescoarse-grained parallelism to achieve near-linear scaling.The algorithm is demonstrated by simulating the low en-ergy portion of the VUV spectrum of trans-1,3-butadiene.

Scott RabidouxInstitute for Computational Engineering and SciencesThe University of Texas at Austinscottrabidoux@gmail.com

Victor EijkhoutThe University of Texas at AustinTexas Advanced Computing Centereijkhout@tacc.utexas.edu

John StantonDepartment of ChemistryThe University of Texas at Austinjfstanton@gmail.com

PP14

Some Numerical Methods for Modified BesselFunctions

The high-quality numerical methods for the computationof modified Bessel functions of the second kind with imag-inary, complex order and real argument are elaborated. ATau method computational scheme is applied for the con-structive approximation of hypergeometric type differentialequations and their systems. The numerical solution ofsome mixed boundary value problems for the Helmholtz

CS15 Abstracts 269

equation in wedge domains is developed.

Juri M. RappoportRussian Academy of Sciencesjmrap@landau.ac.ru

PP14

Oof: An Object-Oriented Finite-Element Solver forMaterials Science

Materials scientists frequently have a requirement to buildfinite-element models of microstructural systems in orderto explore structure-property relationships. The OOF soft-ware provides researchers with a modeling tool which startsfrom familiar image data formats, speaks the language ofmaterials science, and provides push-button access to so-phisticated tools for image manipulation and mesh con-struction. The recently-released 3D version allows for morecomplex and realistic virtual experiments to be performed.

Andrew ReidCenter for Theoretical and Computational MaterialsScienceNational Institute of Standards and Technologyandrew.reid@nist.gov

Stephen LangerInformation Technology LaboratoryNational Institute of Standards and Technologystephen.langer@nist.gov

PP14

Analyzing and Classifying ”Two-Cycles” ofTrigonometric Functions in Newton’s Method

For this research we are analyzing trigonometric functions,specifically f(x) = sin(x), in order to find initial valuesthat when iterated upon, using Newton’s Method, will giveus a new value, which when iterated upon will give us theinitial value again, This process then repeats. So far wehave found reliable characterizing equations which give usthe exact roots that correspond to these special initial val-ues.

Morgan Rupard, Jennifer SwitkesCal Poly Pomonamorganrupard@gmail.com, jmswitkes@csupomona.edu

PP14

Orbital Localization in Madness

The Multiresolution ADaptive Numerical Environment forScientific Simulation (MADNESS) library provides a high-level environment for the solution of integral and dif-ferential equations in many dimensions using adaptive,fast methods with guaranteed precision based on multi-resolution analysis and novel separated representations.These features provide a backdrop in which linear scalingelectronic structure algorithms may be realized. Towardsthis goal, we will explore avenues such as fourth ordermolecular orbital localization to advance scalability withsystem size while maintaining accuracy and parallelism.

Bryan E. SundahlInstitute for Advanced Computational ScienceStony Brook Universitybryan.sundahl@stonybrook.edu

Robert HarrisonBrookhaven National Laboratory and Stony BrookUniversityrjharrison@gmail.com

Scott ThorntonInstitute for Advanced Computational Sciencewsttiger@gmail.com

PP14

Analysis of Anderson Acceleration for CoupledNeutronic and Thermal Hydraulic Calculations ina Light Water Reactor

In a coupling between Insilico (neutronics) and AMP (fuelperformance, subchannel flow), Picard iteration shows in-stability due to oscillatory error modes arising at highenough power. We consider Anderson acceleration as analternative solution method to Picard. We develop a sim-plified model which captures the relevant physics from thehigh fidelity simulation, and perform parametric studieswhich suggest that Anderson should be more robust andfaster converging than Picard for the Insilico/AMP cou-pling.

Alexander R. TothNorth Carolina State Universityartoth@ncsu.edu

C.T. KelleyNorth Carolina State UnivDepartment of Mathematicstim kelley@ncsu.edu

Stuart SlatteryComputer Science and Mathematics DivisionOak Ridge National Laboratoryslatterysr@ornl.gov

Steven HamiltonORNLhamiltonsp@ornl.gov

Kevin ClarnoOak Ridge National Laboratoryclarnokt@ornl.gov

Roger PawlowskiMultiphysics Simulation Technologies Dept.Sandia National Laboratoriesrppawlo@sandia.gov

PP14

The Rapid Optimization Library (rol) in Trilinos

The Rapid Optimization Library (ROL) in Trilinosprovides an object-oriented framework for large-scale,derivative-based optimization. The library is matrix-freeand linear-algebra agnostic permitting easy interface withapplication code. ROL implements a suite of unconstrainedand constrained optimization algorithms including: gradi-ent descent, quasi-Newton, and inexact-Newton with line-search and trust-region globalization. A stochastic opti-mization subpackage (SOL) supplies default implementa-tions of numerous risk measures and adaptive samplingcapabilities. Examples demonstrate solutions of large op-

270 CS15 Abstracts

timization problems with model uncertainties.

Bart G. Van Bloemen WaandersSandia National Laboratoriesbartv@sandia.gov

Drew P. KouriOptimization and Uncertainty QuantificationSandia National Laboratoriesdpkouri@sandia.gov

Denis RidzalSandia National Laboratoriesdridzal@sandia.gov

PP14

Integrating Software Tools to Parallel AdaptiveSimulations of Fusion Plasma in Tokamaks

Mesh-based methods are extensively applied in macro-scopic studies of fusion plasmas in the tokamak. Softwaretools that include the parallel unstructured mesh man-agement infrastructure (PUMI), the mesh adaption pro-cedure (meshAdapt), Simmetrix meshing tool and PETScequation solver are integrated to the physics simulationcodes under development at Princeton Plasma Physics Lab(PPPL) such as M3D-C1.

Fan ZhangRensselaer Polytechnic Institutefanzhangpku@gmail.com

Mark S. Shephard, E. Seegyoung SeolRensselaer Polytechnic InstituteScientific Computation Research Centershephard@rpi.edu, seols@rpi.edu

PP15

Using Radar Imagery Data to Invert for MaritimeEnvironments

Predicting in situ maritime conditions is of great impor-tance to radar detection in marine atmospheric bound-ary layers. To predict the maritime conditions, the radarwave propagation can be modeled using radar imagery datathrough proper orthogonal modes indexed on a specific en-vironment. These modes live on the compact Stiefel mani-fold, and by exploiting the Riemannian structure of it, in-terpolation between the modes is possible and can be usedto invert for the maritime environment.

Vasileios Fountoulakis, Christopher J. EarlsCornell Universityvf59@cornell.edu, cje23@cornell.edu

PP15

Thermal Imaging of Sub-Pixel Cracks ThroughMetal Plates

Active thermography has been studied as a non-destructiveevaluation technique for structural components, using thewell-understood theory of heat conduction to infer the pres-ence, location, and characteristics of flaws in a solid. Wehere use both theory and simulation to determine optimalranges of several operational parameters to be used in ther-mographic evaluation of thin metal plates, such as aircraftskins. We also implement a stochastic approach for char-

acterizing cracks smaller than the imaging resolution.

Andrew Loeb, Christopher EarlsCornell Universityael89@cornell.edu, earls@cornell.edu

PP15

Numerical Simulation of Ni Grain Growth in aThermal Gradient

The Potts model is well developed to simulate normal,curvature-driven grain growth and has been used exten-sively to study various aspects of grain growth. In thiswork, we use this model, implemented into the SPPARKScode to simulate grain growth of Ni turbine blades that areheat treated with temperature gradient intentionally intro-duced to vary the grain size for varied mechanical proper-ties across the extent of the blade. We will present themodel, demonstrate its application and estimate mechani-cal properties as a function of position.

John A. MitchellSandia National Laboratoryjamitch@sandia.gov

Veena TikareSandia National Laboratoriesvtikare@sandia.gov

PP15

Supply Chain Disruptions

Forecasting supply chain disruptions provides buyers witha tool to mitigate risk, avoid liability and increase revenue.A diffusion type algorithm is presented that can be used bya wholesale buyer to predict supply chain disruptions frommultiple distributors. A client use case is presented with adiscussion of the success of this algorithm via comparisonto a logistic regression model designed for the same usecase and comparison to chance.

Thomas MorriseyInfosysthomas morrisey@infosys.com

Ravi PrasadInfosys Limitedravi prasad02@infosys.com

PP15

Computational and Experimental Analysis of Den-tal Implants under Different Loading Conditionsand Locations

The use of dental implants to solve different problems indentistry has been growing rapidly. The success rates ofdental implants are also very important for patients. Thisstudy investigates the stability of dental implants underdifferent loading locations and conditions with the use ofFinite Element Analysis. The CAD model is obtained fromCT images. Designed dental implants were fabricated andexperimentally tested (ISO 14801) to compare with com-putational(FEA) results.

Emre OzyilmazHitit University Engineering Faculty, Dep. of MechanicalEngemre.hitit@gmail.com

CS15 Abstracts 271

Eda Ozyilmaz, Halil AykulHitit University Engineering Faculty,Dept. of Mechanical Eng.edaozyilmaz88@gmail.com, halilaykul@hitit.edu.tr

Mehmet DalkizMustafa Kemal University Dentistry Facultymdalkiz@yahoo.com

Ahmet CiniHitit University Engineering Faculty,Dept. of Mechanical Eng.ahmetcini@gmail.com

PP15

Math Projects with Tracker Video Analysis

Using Tracker freeware, students analyze own-recordedvideo clips and construct mathematical models in explor-ing real-world mathematical applications of concepts fromalgebra through calculus and differential equations.

Euguenia PetersonRichard J. Daley Collegeepeterson@ccc.edu

PP15

Investigation of Numerical Models for New HighTemperature Superconductors

Chad Sockwell, Florida State University

Dr. Janet Peterson and Dr. Max Gunzburger, FloridaState University

Recent discoveries of new high temperature super-conductors initiated investigations to harness these newmaterial’s properties. Unfortunately, many new hightemperature superconductors come with odd propertiessuch as multiband interactions and anisotropic behav-ior, as is the case for Magnesium Diboride. In thisresearch Ginzburg Landau model variants are modifiedand simulated to try and simulate these materials morerealistically. This extends to three dimensional domains,anisotropy, and microscopic corrections such as theExtended Ginzburg Landau model.

Chad SockwellFlorida State UniversityDepartment of Scientific Computingkcs12j@my.fsu.edu

PP15

Characterization of Ternary Eutectic SolidificationPatterns from Phase-Field Simulations and Exper-imental Micrographs

Large scale three-dimensional phase-field simulations basedon the grand potential are used to model the microstruc-ture evolution from directional solidification of ternary eu-tectics. To compare the computational cross-sections andexperimental micrographs, principal component analysis isapplied. With this, the influence of single parameters fromthe different reported data sets on the evolving patternscan be quantified. This allows to determine both, the con-vergence of microstructure simulations and the necessary

domain size for statistical reliable results.

Philipp Steinmetz, Johannes Hotzer, Marcus Jainta,Britta NestlerKarlsruhe Institute of Technology (KIT)Institute of Applied Materials (IAM-ZBS)philipp.steinmetz@kit.edu, johannes.hoetzer@kit.edu,marcus.jainta@kit.edu, britta.nestler@kit.edu

Yuksel Yabansu, Surya KalidindiGeorgia Institute of TechnologyMaterials Informatics for Engineering Designyabansu@gatech.edu, surya.kalidindi@me.gatech.edu

PP15

Multidisciplinary Development of An AutonomousUnderwater Vehicle: Cooperative Fleet for Surveil-lance Mission

A fleet of cooperative autonomous underwater vehicles(AUV) called Eco-Dolphin was designed to collect coastalscience data under saltwater condition. One AUVequipped both long-range wireless and Wireless sonar com-munication and the others equipped short-range acousticand wireless sonar communication. The fleet position canbe tracked via GPS and Wi-Fi and individual positions canbe calculated. Successful achieved wireless sonar commu-nication on prototype one this summer.

Ci Wen, Stacey Joseph-Ellison, Junzhen Shao, Qi Zhou,Jonathan Jaworski, Zakaria DaudEmbry-Riddle Aeronautical Universitywenc1@my.erau.edu, ellisos1@my.erau.edu,shaoj@my.erau.edu, zhouq@my.erau.edu, ja-worskj@my.erau.edu, daudz@my.erau.edu

PP15

Towards Real-Time Blob-Filaments Detection inFusion Plasma

Magnetic fusion is a viable energy source for the future.The success of magnetically confined fusion reactors de-mand steady-state plasma confinement which is challengedby the edge turbulence such as the blob-filaments. Wepresent a real-time outlier detection algorithm to effi-ciently find blob-filaments in fusion simulations and ex-periments. We have implemented this algorithm with hy-brid MPI/OpenMP and demonstrated the accuracy andefficiency with a set of data from the XGC1 fusion simula-tions.

Lingfei WuDepartment of Computer ScienceCollege of William & Marylfwu@cs.wm.edu

Kesheng WuNERSC, Lawrence Berkeley National Labkwu@lbl.gov

Alex SimLawrence Berkeley National Labasim@lbl.gov

Andreas StathopoulosCollege of William & MaryDepartment of Computer Science

272 CS15 Abstracts

andreas@cs.wm.edu

PP101

Bet: Algorithmic and Error Analyses

We review the basic theory behind the non-intrusivemeasure-theoretic algorithm for solving stochastic inverseproblems for deterministic models. We define sigma-algebra constraints on sampling methods to achieve cer-tain approximation properties of events. We provide con-vergence results and a priori and a posteriori error anal-yses producing fully computable a posteriori error esti-mates. The fully computable a posteriori error estimatesprovide lower and upper bounds for computed probabili-ties of events. We demonstrate the use of this analysis onnumerical results utilizing a posteriori error estimates toimprove the accuracy of computed probability measures.

Troy ButlerUniversity of Colorado Denvertroy.butler@ucdenver.edu

PP101

BET: Applications for an Open Source InverseProblems Package

We present example applications of the BET Python Pack-age to solve the stochastic inverse problem within a mea-sure theoretic framework. We demonstrate various featuresof the BET package for approximating inverse probabilitymeasures including goal-oriented adaptive sampling algo-rithms, parallel capabilities, differing approximation op-tions, and visualization capabilities. BET can interfacewith a variety of physics-based computational models.

Lindley C. GrahamUniversity of Austin at TexasInstitute for Computational Engineering and Sciences(ICES)lgraham@ices.utexas.edu

Steven MattisUniversity of Texas at Austinsteve.a.mattis@gmail.com

Troy ButlerUniversity of Colorado Denvertroy.butler@ucdenver.edu

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu

PP101

Bet: Modifications and Analysis for Model Dis-crepancies

We consider the selection of a model as an uncertain inputparameter and we quantify this uncertainty in the measure-theoretic framework using the BET Python Package. Forexample, in multi-scale models, optimal mesoscale modelsthat upscale fine-scale parameters for use in the macro-scale model are often uncertain. We describe and analyzemodifications to the BET package to optimize load balanc-ing taking into account the widely different computational

demands of different models with different resolutions

Nishant PandaColorado State Universitynishant.panda@gmail.com

PP102

Tsunami Modeling In North Africa Using Geo-claw Software: a Tool for the Tsunami ScenarioDatabase in the West Mediterranean

North Africa exhibits an active plate boundary with Eu-rope, highlighted by a moderate seismicity.The triggeringof regional tsunamis is due to (1) earthquakes generated inNorth Algeria and (2) landslides. Modeling carried out us-ing tsunami sources located along the Algerian coast is pre-sented hereby. Computing scenarios using the Riemannsalgorithm implemented within the GEOCLAW software tosolve the non linear shallow water equations provides ac-curate results in comparison with other tsunami software.

Lubna AmirUSTHB Universitylamir@usthb.dz

Walter DudleyUniversity of Hawaii at Hilo200 W. Kawili Street, Hilo, Hawaii, USAdudley@hawaii.edu

Jean RogerG-Mer Etudes MarinesAv. de l’Europe - Saint Francois Guadeloupe, Francejeanrog@hotmail.fr

PP102

ForestClaw : Parallel, Adaptive, Multiblock Simu-lations for Clawpack

We describe our recent progress in developing ForestClaw,an adaptive mesh refinement code based on the dynamicoctree library p4est (C. Burstedde, Univ. of Bonn) andfinite volume solvers, including ClawPack (R. J. LeVeque).One particular feature of ForestClaw is the ease with whichit can handle multi-block domains such as the cubed-sphere, or other geometries not easily described by a sin-gle logically rectangular domain. ForestClaw preserves allof the scalability and performance of the underlying gridmanagement library p4est.

Donna CalhounBoise State Universitydonnacalhoun@boisestate.edu

PP102

Adjoint Methods for Guiding Adaptive Mesh Re-finement in Wave Propagation Problems

AMRClaw and GeoClaw software uses block-structuredadaptive mesh refinement to selectively refine around prop-agating waves. The refinement criterion is often based onlocal estimates of error via Richardson extrapolation, orsome measure of solution smoothness such as the gradient.For problems where a small region of the solution is of pri-mary interest, solving the time-dependent adjoint equationand using a suitable inner product with the forward solu-

CS15 Abstracts 273

tion allows more precise refinement of the relevant waves.

Brisa DavisUniversity of Washingtonbndavis@uw.edu

Randall LeVequeUniversity of WashingtonApplied Mathrjl@uw.edu

PP102

A Community-Driven Collection of ApproximateRiemann Solvers for Hyperbolic Problems

The key ingredient in modern numerical methods for hy-perbolic problems is the Riemann solver. The same algo-rithms can then be used to solve a wide range of hyperbolicproblems – water waves, fluid dynamics, elasticity, electro-magnetics, etc. We present an effort to make available alarge library of Riemann solvers for general use, and thedevelopment of a set of IPython notebooks that describeand interactively explain the solvers for important systems.

Mauricio J. Del RazoUniversity of Washingtonmauricio delrazo@yahoo.com

David I. KetchesonCEMSE DivisionKing Abdullah University of Science & Technologydavid.ketcheson@kaust.edu.sa

Randall LeVequeUniversity of WashingtonApplied Mathrjl@uw.edu

PP102

High Resolution Tsunami Modeling at theMediterranean Coast of Israel Towards An EarlyWarning Tsunami Scenarios Data Bank

A tsunami modelling investigation using the state of theart, open source tsunami model (GeoClaw a subset of thesoftware package Clawpack), its adaptation to investigatethe impact of tsunami wave generation, propagation andinundation at the Mediterranean coast of Israel using highresolution bathymetric and topographic grid, aided by ad-ditional tsunami generation modelling tools simulating theinitial stages of tsunami generation by earthquake inducedtectonic plates rupture and movement or by landslide onthe coastal shelf.

Barak GalantiInter-University Computational CenterTel Aviv Universitygalanti@mail.iucc.ac.il

PP102

PyClaw: Accurate, Scalable Solution of HyperbolicPDEs in Python

PyClaw is a Python-based interface to fast and accurateGodunov-type numerical algorithms for modeling nonlin-ear waves. It is massively scalable and includes both 2nd-order TVD and higher-order WENO discretizations. It is

built on existing codes, including Clawpack, SharpClaw,and PETSc. We describe PyClaw’s design, development,and some applications.

David I. KetchesonCEMSE DivisionKing Abdullah University of Science & Technologydavid.ketcheson@kaust.edu.sa

Aron AhmadiaUS Army Engineer Research and Development Centeraron@ahmadia.net

Kyle T. MandliUniversity of Texas at AustinICESktm2132@columbia.edu

PP102

Practical Applications of GeoClaw to TsunamiHazard Assessment

The GeoClaw software has recently been used for severaltsunami hazard assessment projects and two examples willbe presented in this poster. The first is the analysis of anelementary school site in Ocosta, WA that has since beenselected for the first ”vertical evacuation structure” to bebuilt in the United States. The second is the developmentof improved probabilistic tsunami hazard assessment tech-niques.

Randall LeVequeUniversity of WashingtonApplied Mathrjl@uw.edu

Loyce AdamsUniversity of Washingtonlma3@uw.edu

Frank I. GonzalezU. Washington, Dept. of Earth and Space Sciencesfigonzal@u.washington.edu

PP102

CUDACLAW: A GPU Framework for the Solutionof Hyperbolic Pdes

CUDACLAW is a data-parallel framework that allowsusers to take advantage of GPU accelerators to solve hyper-bolic PDEs, without being burdened by the need to writeCUDA code, worry about thread and block details, datalayout, and data movement between the different levels ofthe memory hierarchy. The user defines the set of PDEsvia a serial Riemann solver and the framework takes careof orchestrating the computations and data transfers tomaximize arithmetic throughput. A prototype implemen-tation shows that, on 2D and 3D acoustics wave equationsand shallow water equations, the framework can achieveperformance comparable to that of manually-tuned code.

George M. TurkiyyahAmerican University of Beirutgt02@aub.edu.lb

H. Gorune OhannessianUniversity of Wisconsingorune@cs.wisc.edu

274 CS15 Abstracts

Aron AhmadiaUS Army Engineer Research and Development Centeraron@ahmadia.net

David I. KetchesonCEMSE DivisionKing Abdullah University of Science & Technologydavid.ketcheson@kaust.edu.sa

PP103

An Overview of PETSc

The changing landscape of scientific application needs andhigh-performance architectures requires continued innova-tion in mathematical algorithms for the robust solution oflarge-scale numerical problems. This poster provides anoverview of the Portable, Extensible Toolkit for ScientificComputing (PETSc), a suite of data structures and rou-tines for the scalable (parallel) solution of scientific appli-cations modeled by partial differential equations (PDEs).We also will provide demos of a variety of PDE-based ex-amples, including advances in composable linear, nonlin-ear, and timestepping solvers, which incorporate multiplelevels of nested algorithms and data models to exploit ar-chitectural features and/or problem-specific structure.

Satish BalayArgonne National Laboratorybalay@anl.gov

Jed BrownMathematics and Computer Science DivisionArgonne National Laboratory and CU Boulderjed@jedbrown.org

William D. GroppUniversity of Illinois at Urbana-ChampaignDept of Computer Sciencewgropp@illinois.edu

Matthew KnepleyUniversity of Chicagoknepley@gmail.com

Lois Curfman McInnesMathematics and Computer Science DivisionArgonne National Laboratorycurfman@mcs.anl.gov

Barry F. SmithArgonne National LabMCS Divisionbsmith@mcs.anl.gov

Hong ZhangMCS, Argonne National Laboratoryhzhang@mcs.anl.gov

PP103

Construction of Parallel Adaptive SimulationLoops

The automation of reliable large-scale simulations requiresthe integration of a number of operations that include meshgeneration, equation discretization, equation solution, er-ror estimation and discretization improvement within aloop that requires regular dynamic load balancing to main-tain scalability. This poster presents a set of components

to support adaptive unstructured simulations on massivelyparallel computers. The in-memory integration of thesecomponents with multiple unstructured mesh finite ele-ment and finite volume codes will be included.

Brian GranzowRensselaer Polytechnic Institutegranzb@rpi.edu

PP103

MueLu: Multigrid Framework for Advanced Ar-chitectures

MueLu multigrid library is a part of Sandia’s Trilinosproject. MueLu is designed to be flexible, easily exten-sible, and efficient on emerging architectures. MueLu al-lows users to specify preferred data (ordinal or scalar)and shared memory (”node”) types by leveraging Trilinos’sparse linear algebra libraries Kokkos and Tpetra. Cur-rent algorithms include smoothed aggregation (SA), non-symmetric SA, Maxwell solvers, and energy-minimization.In this poster, we highlight important design features andlarge-scale results on DOE supercomputers.

Jonathan J. HuSandia National LaboratoriesLivermore, CA 94551jhu@sandia.gov

Andrey ProkopenkoSandia National Laboratoriesaprokop@sandia.gov

PP103

Parallel Unstructured Mesh Infrastructure

The Parallel Unstructured Mesh Infrastructure (PUMI)supports the needs of parallel mesh-based analysis codesto develop complete simulation workflows. This poster willfocus on recent developments including array-based meshdata structures and field abstractions that provide sub-stantial reductions in memory usage. Component reorga-nization via dependency inversion provides a substantialdecrease in code size. The integration of PUMI with dy-namic load balancing and its use in simulation workflowswill be included.

Dan A. IbanezRensselaer Polytechnic InstituteSCORECdibanez@scorec.rpi.edu

E. Seegyoung SeolRensselaer Polytechnic InstituteScientific Computation Research Centerseols@rpi.edu

Gerrett DiamondRensselaer Polytechnic Institutediamog@rpi.edu

PP103

Massively Parallel Adaptive Simulations UsingPetsc for Turbulent Boundary Layer Flows

A set of tools and techniques are presented on adaptivemethods for boundary layer meshes. Such meshes are use-ful in wall-bounded turbulent flows. An adaptive approach

CS15 Abstracts 275

for such meshes must maintain highly anisotropic, graded,and layered elements near the walls. Parallel proceduresmust account for mixed elements, i.e., in mesh modifica-tions and load balancing. Additionally, we study the ef-ficiency and scalability of the linear solvers and precondi-tioners available via PETSc for this class of problems.

Michel RasquinUniversity of Colorado Bouldermichel.rasquin@colorado.edu

Dan A. IbanezRensselaer Polytechnic InstituteSCORECdibanez@scorec.rpi.edu

Benjamin MatthewsUniversity of Colorado Boulderbenjamin.a.matthews@colorado.edu

Cameron SmithScientific Computation Research CenterRensselaer Polytechnic Institutesmithc11@rpi.edu

Onkar SahniRensselaer Polytechnic Institutesahni@rpi.edu

Mark S. ShephardRensselaer Polytechnic InstituteScientific Computation Research Centershephard@rpi.edu

Kenneth JansenUniversity of Colorado at Boulderkenneth.jansen@colorado.edu

PP103

Sparse Direct Solvers and Preconditioners onManycore Systems

We develop scalable sparse direct linear solvers and effec-tive preconditioners for the most challenging linear systemson manycore parallel machines. Our focal efforts are thedevelopments of two types of solvers: The first is a pure di-rect solver, encapsulated in SuperLU software. The secondis the nearly-optimal preconditioners using the HSS low-rank approximate factorization of the dense submatrices,encapsulated in STRUMPACK software.

Xiaoye Sherry LiComputational Research DivisionLawrence Berkeley National Laboratoryxsli@lbl.gov

Pieter GhyselsLawrence Berkeley National LaboratoryComputational Research Divisionpghysels@lbl.gov

Francois-Henry RouetLawrence Berkeley National Laboratoryfhrouet@lbl.gov

Piyush Sao, Richard VuducGeorgia Institute of Technology

piyush3@gatech.edu, richie@cc.gatech.edu

PP103

Dynamic Partitioning Using Mesh Adjacencies

Parallel unstructured mesh-based applications running onthe latest petascale systems require partitions optimizingspecific balance metrics. Methods combining the mostpowerful graph based and geometric methods with diffu-sive methods directly operating on the unstructured meshare discussed. Implementation details will be provided forthe components comprising the direct unstructured meshbased methods as will initial results for applications withmeshes of several billion elements on over 500k parts.

Cameron SmithScientific Computation Research CenterRensselaer Polytechnic Institutesmithc11@rpi.edu

Dan A. IbanezRensselaer Polytechnic InstituteSCORECdibanez@scorec.rpi.edu

Gerrett DiamondRensselaer Polytechnic Institutediamog@rpi.edu

PP103

Fastmath Structured Mesh and Particle Technolo-gies

Scientific phenomenon happen over a wide range of lengthand time scales. Chombo and BoxLib are libraries that aredeveloping and deploying state-of-the-art structured adap-tive mesh and particle-in-cell technologies under the aegisof FASTMath. The evolving algorithms and computationalframeworks provided by these libraries allow scientific ap-plication codes to capture these scales efficiently and enablescientific discovery at scale currently, as well as prepare forthe future architectures.

Anshu Dubey, Phillip ColellaLawrence Berkeley National Laboratoryadubey@lbl.gov, PColella@lbl.gov

Mark AdamsLawrence Berkeley Laboratorymfadams@lbl.gov

Ann S. AlmgrenLawrence Berkeley National Laboratoryasalmgren@lbl.gov

Dan Graves, Terry J. LigockiLawrence Berkeley Laboratorydtgraves@lbl.gov, TJLigocki@lbl.gov

Brian Van StraalenLawrence Berkeley National LaboratoryCompuational Research Divisionbvstraalen@lbl.gov

Milo DorrCenter for Applied Scientific ComputingLawrence Livermore National Laboratory

276 CS15 Abstracts

dorr1@llnl.gov

PP103

Sundials: Suite of Nonlinear and Differen-tial/algebraic Solvers

In this poster we present the SUNDIALS library suite, con-sisting of the solver libraries CVODE, CVODES, ARKode,IDA, IDAS, and KINSOL. This DOE-funded solver libraryfocuses on robust and scalable solvers for systems of ordi-nary differential equations, systems of differential-algebraicequations and systems of nonlinear equations. Sharing acommon set of vector libraries and linear solvers (bothdirect and iterative), these solvers are designed for algo-rithmic flexibility, with interfaces in C, C++ and For-tran (some even in Matlab), and may be easily adaptedto application-specific and user-defined data structures.

Daniel R. ReynoldsSouthern Methodist UniversityMathematicsreynolds@smu.edu

Carol S. WoodwardLawrence Livermore Nat’l Labwoodward6@llnl.gov

PP103

Hypre: High Performance Preconditioners

The hypre software library provides high performance pre-conditioners and solvers for the solution of large sparselinear systems on massively parallel computers. One ofits attractive features is the provision of conceptual inter-faces, which include a structured, a semi-structured, and atraditional linear-algebra based interface. These interfacesgive application users a more natural means for describingtheir linear systems, and provide access to hypre’s solvers,which include structured and unstructured algebraic multi-grid solvers.

Robert Falgout, Tzanio V. KolevCenter for Applied Scientific ComputingLawrence Livermore National Laboratoryrfalgout@llnl.gov, tzanio@llnl.gov

Jacob B. Schroder, Ulrike M. YangLawrence Livermore National Laboratoryschroder2@llnl.gov, umyang@llnl.gov

PP104

Stochastic Methods in Mesoscopic Materials Mod-eling

For soft materials, a central challenge is to link bulk prop-erties with the behaviours of the material mesostructures.Such interactions/kinetics often involve a subtle interplayof enthalpic and entropic effects extending over a widerange of scales presenting well-known challenges for mod-elling and simulation. We present our recent progress ondynamic implicit-solvent coarse-grained approaches thatutilize a fluctuating hydrodynamics thermostat. We inves-tigate the properties of polymeric materials and biophysicalquestions for lipid bilayer membranes.

Paul J. AtzbergerUniversity of California-Santa Barbara

atzberg@math.ucsb.edu

PP104

Concurrent Coupling Methods in Mesoscopic Ma-terials Modeling

Mesoscopic methods with thermodynamic fluctuations,such as dissipative particle dynamics, are powerful toolsto study material properties at relevant spatial-temporalscales. Concurrently coupling a mesoscopic model with amicroscopic description, such as molecular dynamics, canbenefit further from microscopic description with great de-tails. Concurrently coupling a mesoscopic model with acontinuum discretization, such as smoothed particle hy-drodynamics, enables to simulate real applications at largescale with great computational efficiency.

Xin BianBrown UniversityXin Bian@brown.edu

PP104

Overview of Mathematics for Mesoscopic Modelingof Materials

The Collaboratory on Mathematics for Mesoscopic Mod-eling of Materials, or CM4, develops systematic mathe-matical foundations for understanding and controlling thefundamental mechanisms in mesoscale processes. CM4 fo-cuses on the development and integration of particle-based,continuum-based, and stochastic methods, as well as theconcurrent coupling between them. As science drivers, aset of demonstration problems will facilitate integration ofCM4 mathematical models and numerical approaches inthe context of important materials modeling challenges.

George E. KarniadakisBrown UniversityDivision of Applied Mathematicsgeorge karniadakis@brown.edu

PP104

Hierarchical Coarse-graining and ParallelizationMethods for Mesoscale material Models

We discuss information theory-based methods for the pa-rameterized coarse-graining of non-equilibrium extendedsystems, typically associated with coupled physicochemicalmechanisms or driven systems, and where steady states areunknown altogether, e.g. do not have a Gibbs structure.Our pathwise information theory tools provide reliablemolecular model parameterizations and rational model se-lection through suitable dynamics-based information crite-ria. We also discuss connections of the developed tools toforce-matching in a dynamics context and the transferabil-ity of coarse-graining maps.

Markos A. KatsoulakisUniversity of Massachusetts, AmherstDept of Mathematics and Statisticsmarkos@math.umass.edu

PP104

Particle-Based Methods in Mesoscopic MaterialsModeling

Coarse-grained particle-based method is capable of sim-ulating mesoscopic phenomena with a discrete or discon-

CS15 Abstracts 277

tinuous nature. Its governing equations can be obtainedby applying the Mori-Zwanzig projection on a microscopicdynamics. We present a bottom-up approach to quantifythe coarse-grained model via the Mori-Zwanzig formula-tion with microscopic data provided by molecular dynamics(MD) simulations. Results show that such MD-informedcoarse-grained model is able to accurately reproduce itsunderlying MD system.

Zhen LiBrown UniversityBrown UniversityZhen Li@brown.edu

PP104

Grid-Based Methods in Mesoscopic MaterialsModeling

Our focus is on developing continuum-level simulations todescribe the dynamics of colloidal systems, self-assemblyand flow transport in micro-channels. Generally the ap-proach is to use grid-based methods but we also work withLagrangian particle-based methods. Here we evaluate theelectrostatic or magnetostatic moments of particles in sus-pension, subject to an external field, and the resulting forceinteractions. We use both immersive methods (smoothedprofile method) and finite multipoles, and compare accu-racy and efficiency.

Martin MaxeyDivision of Applied Mathematics,Brown Universitymaxey@cfm.brown.edu

PP104

Fast Solvers for Mesoscopic Materials Modeling

The Collaboratory on Mathematics for Mesoscopic Model-ing of Materials is developing numerical solvers designed toefficiently solve systems modeling charge transport. Thesephenomena are commonly encountered in engineering ap-plications and are also of growing importance to biolog-ical contexts as well. We conduct a numerical analysisof our proposed schemes to understand important aspectsof our solvers, such as stability, consistency, and well-posedness. We consider fast solvers for the Poisson-Nernst-Planck (PNP) system using a finite element discretization.We leverage qualitative mathematical structures and phys-ical properties of this system to improve the quality andefficiency of computed solutions. Our proposed discretiza-tion scheme readily leads to an energy estimate for thecomputed solution that is characteristic of the continuousPNP system. Further analysis for the efficiency and robust-ness of the solvers is considered as a separate componentof the analysis.

Jinchao XuPennsylvania State Universityxu@math.psu.edu

Chun LiuDepartment of Mathematics, Penn State UniversityUniversity Park, PA 16802liu@math.psu.edu

Xiaozhe HuThe Pennsylvania State Universityxiaozhe.hu@tufts.edu

Maximilian S. MettiPenn State Universitymsm37@psu.edu

PP104

Applications in Mesoscopic Modeling of Materials

Recent applications in micro-/nano-technology, materialassembly and biological systems demand robust and ac-curate computational modeling of multiphysical processesat the mesoscale. In this poster we focus on mathe-matical models and numerical schemes that can effec-tively capture mesoscale multiphysics (hydrodynamics,transport, electrostatics and chemical reaction). Specifi-cally, we show simulation results on mixing and separa-tion processes in micro-/nano-channel, electrokinetic flowthrough semi-permeable membranes, and diffusive reactionon biomolecules.

Wenxiao PanPacific Northwest National Laboratorywenxiao.pan@pnnl.gov

Mauro PeregoCSRI Sandia National Laboratoriesmperego@fsu.edu

PP104

Coarse-Graining in Mesoscopic Materials Modeling

The mesoscopic modeling of materials is a flourishing sub-ject of research due to its importance for many techno-logical and societally relevant applications. By definition,mesoscopic models entail the process of coarse-grainingof microscopic (molecular) models. The resulting modelsmay exhibit space/time symmetry breaking. In our re-cent work as part of CM4 we have focused on the use ofrenormalization in order to construct coarse-grained mod-els which are adaptive, in the sense that the relevant co-efficients of the model are estimated on the fly as the sys-tem evolves. We believe that renormalization (perturbativeor non-perturbative) is a viable method for constructingcoarse-grained models of controlled accuracy for complexsystems. The purpose of the current poster is to presentour recent results on the subject as well as outline futuredirections and open problems.

Panos StinisUniversity of Minnesota, Twin Citiesstinis@umn.edu

PP105

Realizability Limiting in High-Order NumericalSolutions of Entropy-Based Moment Closures

Entropy moment closures for kinetic equations (colloqui-ally known as MN models) have attractive theoretical prop-erties (hyperbolicity, entropy dissipation, and positivity)but are only defined in the set of realizable moment vec-tors, that is those which are consistent with a positive dis-tribution. High-order numerical solutions do not alwaysstay in this set, so we investigate the use of a limiter tohandle nonrealizable moments in the implementation of ahigh-order discontinuous Galerkin method.

Graham AlldredgeRWTH AACHEN Universityalldredge@mathcces.rwth-aachen.de

278 CS15 Abstracts

Florian SchneiderTU Kaiserslauternfschneid@mathematik.uni-kl.de

PP105

Exploration and Validation of Full-Domain Mas-sively Parallel Transport Sweep Algorithms

Scaling of discrete-ordinates transport sweep-based algo-rithms is currently of great general interest. Recent re-search on volume-based spatial decomposition approachesshows great potential. Schedule conflict resolution and spa-tial domain overloading are essential algorithm characteris-tics for obtaining good scaling. We describe computationalexperiments performed on the IBM BG/Q machine (Se-quoia) at LLNL that indicate MPI based algorithms scaleto the full machine with good efficiencies predicted by par-allel performance models. We also present simple studies ofsingle node performance using task, thread and instructionlevel parallelism for these algorithms.

Teresa S. BaileyLLNLbailey42@llnl.gov

Peter Brown, Adam KunenLawrence Livermore National Laboratorypnbrown@llnl.gov, kunen1@llnl.gov

PP105

A New Moment Method in the Kinetic Theory ofGases Based on the L2 Function Space

Recently, a framework for hyperbolic model reduction inthe kinetic theory was proposed. Based on this framework,we reconsider the convergence of Grad’s expansion, andfind the function space may be insufficient in some cases.To make improvements, we replace the weighted L2 spaceused in the classic moment method by the plain L2 space,and special projections are used in the model recductionto maintain both hyperbolicity and conservation.

Zhenning CaiCenter for Computational Engineering ScienceRWTH Aachen Universitycai@mathcces.rwth-aachen.de

Manuel TorrilhonRWTH Aachen Universitymt@mathcces.rwth-aachen.de

PP105

Markov Chain Formalism for Radiative Transferin Planetary Atmospheres: Forward Modeling, In-cluding Linearization

The 1D vector radiative transfer problem is solved witha Markov chain approach. The matrix structure of thatmethod enables efficient numerical computation of polar-ized radiation fields throughout the atmosphere, as well asstraightforward linearization to derive Jacobian matrixesexactly. We applied this computational forward model-ing framework for remote sensing signals to aerosol/surfaceproperty retrievals from air- and spaceborne observationson Earth and to analyses of polarized imagery of Titanfrom the Cassini probe.

Anthony B. Davis, Feng Xu, Robert West, David Diner

Jet Propulsion LaboratoryCalifornia Institute of Technologyanthony.b.davis@jpl.nasa.gov, feng.xu@jpl.nasa.gov,robert.a.west@jpl.nasa.gov, david.j.diner@jpl.nasa.gov

PP105

On the Hyperbolicity of Grads 13 Moment System

In gas kinetic theory, lack of global hyperbolicity is a majorcritique for Grad’s moment method. For the well-knownGrad’s 13 moment system, I. Muller et. al.(1998) pointedout it is not globally hyperbolic for 1D flow. In this presen-tation, we will point out for 3D case, for each equilibriumstate, none of its neighbourhoods is contained in the hyper-bolicity region. And a globally hyperbolic regularizationfor it will be proposed.

Yuwei FanSchool of Mathematical SciencesPeking University, Beijing, P.R.Chinaywfan@pku.edu.cn

Zhenning CaiCenter for Computational Engineering ScienceRWTH Aachen Universitycai@mathcces.rwth-aachen.de

Ruo LiSchool of Mathematical SciencePeking Universityrli@math.pku.edu.cn

PP105

Convergence of Filtered Spherical Harmonic Equa-tions for Radiation Transport

We analyze the global convergence properties of the filteredspherical harmonic (FPN ) equations for radiation trans-port. The well-known spherical harmonic (PN ) equationsare a spectral method (in angle) for the radiation transportequation and are known to suffer from Gibbs phenomenaaround discontinuities. The filtered equations include ad-ditional terms to address this issue that are derived viaa spectral filtering procedure. We show explicitly how theglobal L2 convergence rate (in space and angle) of the spec-tral method to the solution of the transport equation de-pends on the smoothness of the solution (in angle only)and on the order of the filter. The results are confirmed bynumerical experiments. Numerical tests have been imple-mented in MATLAB and are available online.

Martin FrankRWTH Aachen UniversityCenter for Computational Engineering Sciencefrank@mathcces.rwth-aachen.de

Cory HauckOak Ridge National Laboratoryhauckc@ornl.gov

Kerstin KuepperRWTH Aachen UniversityCenter for Computational Engineering Sciencekuepper@mathcces.rwth-aachen.de

PP105

A High Order, Implicit, Hybrid Solver for Linear

CS15 Abstracts 279

Kinetic Equations

Recently, an implicit, hybrid solver for linear kinetic equa-tions has been investigated using a backward Euler solverin time. We present a high order time discretization basedon deferred corrections with respect to the backward Eulermethod. Also, several numerical results are given to showthe efficacy of the hybrid method for various orders of ac-curacy in time as well as streaming versus highly collisionalregimes.

Michael CrockatMichigan State Universitycrockat1@msu.edu

Charles K. Garrett, Cory HauckOak Ridge National Laboratorygarrettck@ornl.gov, hauckc@ornl.gov

PP105

A High Order Time Splitting Method Based onIntegral Deferred Correction for Semi-LagrangianVlasov Simulations

The dimensional splitting semi-Lagrangian methods withdifferent reconstruction/interpolation strategies have beenapplied to kinetic simulations in various settings. How-ever, the temporal error is dominated by the splitting er-ror. In order to have numerical algorithms that are highorder both in space and in time, we propose to use the in-tegral deferred correction (IDC) framework to reduce thesplitting error. The proposed algorithm is applied to theVlasov-Poisson system, the guiding center model and in-compressible flows.We show numerically that the IDC pro-cedure can automatically increase the order of accuracy intime.

Wei GuoMichigan State Universitywguo126@gmail.com

PP105

Analysis of Discontinuous Galerkin Algorithms forDiffusion and for Energy-Conserving HamiltonianDynamics

We present mixed continuous/discontinuous Galerkinschemes for solution of a class of kinetic Vlasov-Boltzmannproblems in Hamiltonian Poisson-bracket form (plus colli-sions). These schemes conserve energy, and optionally theL2 norm, exactly. Application to electromagnetic gyroki-netic problems requires novel extension to avoid the Am-pere cancellation problem and significant time step limita-tions. There are subtle properties of commonly used DGschemes for second order derivatives, such as from diffu-sion, which we compare with a recovery-based approach.

Greg HammettPrinceton Plasma Physics LaboratoryPrinceton Universityhammett@princeton.edu

Ammar HakimPrinceton Plasma Physics Laboratoryahakim@pppl.gov

Eric Shi, Ian Abel, Tim Stoltzfus-DueckPrinceton University

eshi@pppl.gov, iabel@princeton.edu,tstoltzf@princeton.edu

PP105

Massively Parallel Calculations of Neutronics Ex-periments Using Pdt

We demonstrate efficient parallel solution algorithms forhigh-fidelity neutron transport calculations and thermalradiative-transfer calculations. Calculations employ spa-tial grids that are structured at a coarse level but unstruc-tured at a fine level to accurately represent geometries ofsimulated experiments. Calculations employ optimal par-allel transport sweeps and physics-based preconditioners.

Marvin L. Adams, Aaron Holzaepfel, W. Daryl Hawkins,Michael Adams, Anthony Barbu, Timmie SmithTexas A&M Universitymladams@tamu.edu, aholzaepfel@neo.tamu.edu,dhawkins@tamu.edu, i.am.michael.adams@gmail.com,apbarbu@gmail.com, timmie@tamu.edu

PP105

Numerical Solution of the Boltzmann Equation Us-ing Quadrature-Based Projection Methods

The lack of hyperbolicity has posed many problems for ex-isting moment models based on the Boltzmann equation.We derive globally hyperbolic and rotationally invariantequations using the Quadrature-Based Moment Method.The method is explained by a newly developed frameworkof projection operators. In order to investigate the approxi-mation quality of the emerging non-conservative equations,we apply dedicated numerical methods on unstructuredtwo-dimensional quad grids and the results are comparedto reference solutions.

Julian Koellermeier, Manuel TorrilhonRWTH Aachen Universitykoellermeier@mathcces.rwth-aachen.de,mt@mathcces.rwth-aachen.de

PP105

Positive Filtered PN Closures for Linear KineticTransport Equations, with some Convergence Re-sults

We propose a modification to the standard spherical har-monic closure, known as PN closure, for kinetic equations.The modification produces smooth, nonnegative polyno-mial ansatzes by applying two-step filtering on the oscil-latory, partially negative PN solutions, and integrates theclosed moment system with filtered moments. We formu-late the filtering process as a quadratic program, proveconvergence of the proposed closure when the moment or-der goes to infinity, and report numerical results on theline source benchmark.

Ming Tse P. LaiuDepartment of Electrical and Computer EngineeringUniversity of Maryland - College Parkmtlaiu@umd.edu

Cory HauckOak Ridge National Laboratoryhauckc@ornl.gov

280 CS15 Abstracts

Dianne P. O’LearyUniversity of Maryland, College ParkDepartment of Computer Scienceoleary@cs.umd.edu

Andre TitsUniversity of Maryland at College Parkandre@umd.edu

PP105

Implicit, Filtered Pn Methods for Radiation Trans-port

The solution of thermal radiation transport as part ofradiation-hydrodynamics calculations is important in thesimulation of astrophysical phenomenon as well as high-energy density physics applications such as inertial confine-ment fusion. In this work we present an implicit methodfor solving the spherical harmonics (PN ) equations of ra-diation transport using filtered expansions. Since the in-troduction of such filtered PN methods by McClarren andHauck, these approaches have been successful in produc-ing high fidelity solutions to difficult transport problems.. In this poster we present results of implicit filtered PNradiation transport simulations and discuss precondition-ing strategies as well as the effect of implicit time inte-gration on the necessary filter strength. We compare theresults to reference Monte-Carlo calculations for severalstandard test problems, including radiation transport ina laser-driven shock tube experiment.

Ryan G. McClarrenTexas A & Mrmcclarren@ne.tamu.edu

Vincent LaboureTexas A&M Universityvincent.laboure@neo.tamu.edu

Cory HauckOak Ridge National Laboratoryhauckc@ornl.gov

PP105

Massively Parallel Nuclear Reactor Analysis UsingPdt

We demonstrate efficient parallel solution algorithms forhigh-fidelity neutron and gamma transport calculations innuclear reactors. Calculations employ spatial grids thatare structured at a coarse level but unstructured at a finelevel to accurately represent fuel and structural geometries.Calculations employ optimal parallel transport sweeps andsophisticated physics-based preconditioners.

Marvin L. Adams, Carolyn McGraw, W. Daryl Hawkins,Michael Adams, Timmie SmithTexas A&M Universitymladams@tamu.edu, car3262@tamu.edu,dhawkins@tamu.edu, i.am.michael.adams@gmail.com,timmie@tamu.edu

PP105

High Order Asymptotic Preserving Nodal Discon-tinuous Galerkin Imex Schemes for the Bgk Equa-tion

We develop high-order asymptotic preserving schemes for

the BGK equation in a hyperbolic scaling. Our approachesare based on the micro-macro formulation of the kineticequation which involves a natural decomposition of theproblem to the equilibrium and the non-equilibrium parts.The new ingredients for the proposed methods to achievehigh order accuracy are the following: we introduce dis-continuous Galerkin discretization of arbitrary order of ac-curacy with nodal Lagrangian basis functions in space;we employ a high order globally stiffly accurate implicit-explicit Runge-Kutta scheme as time discretization. Itis demonstrated that the proposed scheme becomes a lo-cal DG discretization with an explicit RK method forthe macroscopic compressible Navier-Stokes equations, amethod in a similar spirit to the ones in [Bassi & Rabey1997, Cockburn & Shu 1998]. Numerical results are pre-sented for a wide range of Knudsen number to illustratethe effectiveness and high order accuracy.

Jingmei QiuUniversity of Houstonjingqiu@math.uh.edu

Juhi JangMath departmentUC Riversidejuhi.jang@ucr.edu

Fengyan LiRensselaer Polytechnic Institutelif@rpi.edu

Tao XiongMath DepartmentUniversity of Houstontxiong@math.uh.edu

PP105

Towards Hyperbolic Moment Approximations ofMulticomponent Plasmas

Travelling shock waves through initially neutral gases caninitiate ionisation reactions leading to a multicomponentplasma. The description of such shock waves poses a greatmodelling challenge since not only collisional processes in-cluding reactive collisions, but also the interactions of thegas with the macroscopic force fields have to be takeninto account. In the most general case a kinetic descrip-tion of the plasma would require the numerical solutionof the Boltzmann equation for each species coupled to theMaxwell equations. We consider hyperbolic moment ap-proximations of the Boltzmann equation, which promise anefficient description of the plasma components for Knudsennumbers in the continuum and transition regime.

Roman P. Scharer, Manuel TorrilhonRWTH Aachen Universityschaerer@mathcces.rwth-aachen.de, mt@mathcces.rwth-aachen.de

PP105

Ifp: An Optimal, Fully Conservative, Fully Im-plicit, Vlasov-Fokker-Planck Solver: Poster

We introduce a new, exactly conservative (mass, momen-tum, and energy), and fully nonlinearly implicit solver fora multi-species 1D-2V Vlasov-Rosenbluth-Fokker-Plancksystem. The new solver optimizes mesh resolution require-ments by 1) adapting the velocity-space mesh based on thespecies’ local thermal-velocity, and 2) treating the cross-

CS15 Abstracts 281

species collisions exhibiting disparate thermal velocities byan asymptotic formulation. We demonstrate the efficiencyand accuracy properties of the approach with challengingnumerical examples.

William T. TaitanoLos Alamos National Laboratorytaitano@lanl.gov

PP105

Residual Monte Carlo Methods Within theMoment-Based Acceleration Framework

Over the past several years, Moment-Based Acceleration,or High-Order/Low-Order methods, have been used tosolve kinetic equations efficiently and accurately. Recentwork has adapted these methods to include Monte Carlotransport solvers. These Monte Carlo simulations oftencontain a significant level of stochastic noise which can cor-rupt the low-order solver, resulting in a breakdown of themethod or inaccurate results. In this poster we demon-strate that a residual form of the Monte Carlo method canbe used, producing significantly more accurate results. Wedisplay results for both thermal radiation transport andneutronics applications.

Jeffrey A. WillertLos Alamos National Laboratoryjaw@lanl.gov

PP105

Asymptotic Preserving Discontinuous GalerkinMethod for the Radiative Transfer Equation

Many kinetic equations converge to macroscopic models,known as the asymptotic limit of the kinetic equations,when ε (the ratio of mean free path over macroscopicsize) → 0. Asymptotic preserving (AP) methods aredesigned to preserve the asymptotic limits from micro-scopic to macroscopic models in the discrete setting. Inthis poster, we consider the radiative transfer equationwhich models isotropic particle scattering in a medium.Discontinuous Galerkin (DG) (with upwind flux and atleast piecewise linear polynomial) methods are known tohave such property, but require much more degree of free-dom, especially in high dimensional applications. We willpresent an AP mixed DG-FV method which has com-parable computational cost and memory as FV method.Rigorous analysis will be provided to show that the pro-posed methods are consistent with the limit equation inthe asymptotic regimes. Some numerical examples are pre-sented to demonstrate the performance of our methods.

Yulong XingDepartment of MathematicsUniveristy of Tennessee / Oak Ridge National Labxingy@math.utk.edu

Cory HauckOak Ridge National Laboratoryhauckc@ornl.gov

PP106

Architecture Portable Assembly for Maxwell’sEquations

This poster presents an architecture portable implemen-tation of Maxwell’s equations. To achieve portability the

Kokkos library is employed to handle memory layout andparallelization over a large number of threads in the as-sembly kernel. The PDE is discretized using edge-basisfunctions for the eletric field and face-basis functions formagnetics. We also explore the memory to computationtradeoffs of using these vector basis functions. Results il-lustrating the thread scalability of our approach will bepresented.

Eric C. CyrScalable Algorithms DepartmentSandia National Laboratotorieseccyr@sandia.gov

Irina DemeshkoSandia National Laboratoriesipdemes@sandia.gov

Roger PawlowskiMultiphysics Simulation Technologies Dept.Sandia National Laboratoriesrppawlo@sandia.gov

Matthew BettencourtSandia National Laboratoriesmbetten@sandia.gov

PP106

Towards Exascale Implementation of the Finite El-ement Based Application Development Environ-ment

It is not clear today which architecture Exascale supercom-puters will have, but we believe that multicore-CPUs andmanycore-accelerator devices, that promise improvementsin both runtime performance and energy consumption, aremajor candidates to be used in the future HPC systems.Nowadays, the Finite Element Method is actively used indiverse variety of scientific and industry simulations, thatrequire High Performance Computing (HPC) technology.In this poster we present our strategy for adapting FiniteElement-based codes for future architecture, based on us-ing a new Phalanx-Kokkoslocal field evaluation kernel fromTrilinos, specifically designed for general partial differen-tial equation solvers and portable acrossdiverse multicore/manycore architectures.We present performance evaluationresults for our strategy on the example of Finite ElementAssembly in Greenland Ice-Sheet simulations code.

Irina Demeshko, H. Carter Edwards, Michael Heroux,ROGER P. PawkowskiSandia National Laboratoriesipdemes@sandia.gov, hcedwar@sandia.gov,maherou@sandia.gov, rppawlo@sandia.gov

Eric PhippsSandia National LaboratoriesOptimization and Uncertainty Quantification Departmentetphipp@sandia.gov

Andrew SalingerCSRISandia National Labs

282 CS15 Abstracts

agsalin@sandia.gov

PP106

Multicore Finite Element Assembly Via Scans

Minisymposterium placeholder abstract to follow

Robert C. KirbyBaylor UniversityRobert Kirby@baylor.edu

PP106

Operator Transformation and Code Generation forScientific Computing

The present poster discusses three software components forscientific computing. ‘Pymbolic’ is an expression tree withtraversal and rewriting capabilities. Both its mathemati-cal vocabulary and its traversal operations are easily ex-tended for use in mathematical abstractions. ‘PyOpenCL’is a toolkit to facilitate code generation, access to massivelyparallel hardware, and basic parallel algorithms. ‘Loopy’ isa code generator targeting shared-memory, massively par-allel machines, that cleanly separates task specification andtransformation-based optimization.

Andreas KloecknerDepartment of Computer ScienceUniversity of Illinois at Urbana-Champaignandreask@illinois.edu

PP106

occa: A Unified Approach to Multi-ThreadingLanguages

The inability to predict lasting languages and architec-tures led us to develop occa, a library focused on host-device interactions. Using run-time compilation and macroexpansions, the result is a novel single kernel languagethat expands to multiple threading languages. Currently,occa supports device kernel expansions for the Pthreads,OpenMP, OpenCL, CUDA and COI platforms. OCCAcan be used through the front-ends provided for C++, C,Matlab, Python, Julia and C#.

David MedinaRice Universitydmedina@rice.edu

Tim WarburtonRice UniversityDepartment of Computational and Appliedtimwar@rice.edu

Amik St-CyrComputation and Modeling,Shell International E&P, Inc.amik.st-cyr@shell.com

PP106

Assembly Algorithms for Pdes with Uncertain In-put Data on Emerging Multicore Architectures

In this work we explore assembly algorithms for PDEs dis-cretized with stochastic Galerkin and sampling-based un-certainty quantification algorithms. We demonstrate thatrearrangements of these classical uncertainty propagation

algorithms lead to improved PDE assembly performance byamortizing communication latency, improving memory ac-cess patterns, and exposing new dimensions of fine-grainedparallelism. We also describe simple approaches for incor-porating these ideas in complex simulation codes.

Eric PhippsSandia National LaboratoriesOptimization and Uncertainty Quantification Departmentetphipp@sandia.gov

H. Carter EdwardsSandia National Laboratorieshcedwar@sandia.gov

PP106

Using Multicore Parallelism for Common Finite El-ement Operations

Whereas finite element assembly with MPI is well under-stood, assembly using a multithreading model has been lessexplored. This later model becomes more important as thenumber of cores on a chip, and thus in a node, increases.Using graph coloring and MapReduce on cells or sets ofcells, not only good scalability but bitwise reproducibilitycan be achieved for matrix assembly and other common op-erations such as post-processing, estimating discretizationerrors, etc.

Bruno TurcksinTexas A&M Universityturcksin@math.tamu.edu

Martin KronbichlerTechnische Universitat Munchenkronbichler@lnm.mw.tum.de

Wolfgang BangerthTexas A&M Universitybangerth@math.tamu.edu

PP201

Forward Backward Doubly Stochastic DifferentialEquations and Applications to The Optimal Filter-ing Problem

We consider the filtering problem where a signal processis modeled by an SDE and the observation is perturbedby a white noise. The goal is to find the best estimationof the signal process based on the observation. KalmanFilter, Particle Filter, Zakai Filter are some well-knownapproaches to solve optimal filter problems. In this effort,we shall show the optimal filter problem can also be solvedusing forward backward doubly stochastic differential equa-tions.

Feng BaoOak Ridge National Laboratorybaof@ornlgov

Yanzhao CaoDepartment of Mathematics & StatisticsAuburn Universityyzc0009@auburn.edu

Clayton G. Webster, Guannan ZhangOak Ridge National Laboratory

CS15 Abstracts 283

webstercg@ornl.gov, zhangg@ornl.gov

PP201

Embedded Sampling-Based Uncertainty Quantifi-cation Approaches for Emerging Computer Archi-tectures

In this work we explore embedded sampling-based uncer-tainty quantification approaches geared towards emergingcomputer architectures. These approaches improve perfor-mance by leveraging reuse of simulation information be-tween samples, improve memory access patterns, and ex-pose new dimensions of fine-grained parallelism. We in-vestigate the applicability of these ideas to relevant partialdifferential equations with uncertain input data.

Eric PhippsSandia National LaboratoriesOptimization and Uncertainty Quantification Departmentetphipp@sandia.gov

Marta D’Elia, H. Carter EdwardsSandia National Laboratoriesmdelia@sandia.gov, hcedwar@sandia.gov

Jonathan J. HuSandia National LaboratoriesLivermore, CA 94551jhu@sandia.gov

Siva RajamanickamSandia National Laboratoriessrajama@sandia.gov

PP201

A Unified Framework for Uncertainty and Sensitiv-ity Analysis of Computational Models with ManyInput Parameters

Computational models have found wide applications insimulating physical systems. Uncertainties in input pa-rameters of the system can greatly influence the outputs,which are studied by Uncertainty Analysis (UA) and Sensi-tivity Analysis (SA). As the system becomes more complex,the number of input parameters can be large and existingmethods for UA and SA are computationally intensive orprohibitive. We propose a unified framework by using a hi-erarchical variable selection approach to connect UA andSA with one design. By incorporating the effect hierarchyprinciple and the effect heredity principle, the approachworks well especially when the number of input parame-ters is large. Since the whole procedure requires only onedesign, it is economical in run size and computationallyefficient.

Li Gu, C. F. Jeff WuGeorgia Institute of Technologylgu@gatech.edu, jeffwu@isye.gatech.edu

PP201

Florida State University Efforts Withing theEquinox Project

We present the results of projects funded by the EQUINOXgrant from the Department of Energy Advanced SimulationComputing Research program of the US Department of En-ergy. Included in the presentation are extensions of 1/fα

noise to multi-dimensions, the construction of total degree

interpolation points that minimize the Lebesgue constant,and the treatment of uncertainty quantification for nonlo-cal diffusion equations, including fractional Laplacian mod-els.

Max GunzburgerFlorida State UniversitySchool for Computational Sciencesmgunzburger@fsu.edu

PP201

A Mathematical Environment for Quantifying Un-certainty: Integrated and Optimized at the EX-treme Scale (equinox)

This poster describes a modern mathematical and sta-tistical foundation that will enable next-generation, com-plex, stochastic predictive simulations. This is a collab-orative effort funded by the Advanced Scientific Com-puting Research at the US Department of Energy, fo-cused on combing novel paradigms in applied mathemat-ics, statistics and computational science into a unifiedframework, which we call an Environment for QuantifyingUncertainty: Integrated aNd Optimized at the eXtreme-scale (EQUINOX). This rigorous UQmethodology includesadaptive and quasi-optimal approximations, hierarchicaland multilevel methods, architecture aware UQ paradigms,and robust experimental design strategies.

Clayton G. WebsterOak Ridge National Laboratorywebstercg@ornl.gov

PP201

Hierarchical Acceleration of Multilevel Methodsfor Pdes with Random Input Data

Multilevel methods seek to decrease computational com-plexity by balancing spatial and stochastic discretizationerrors. As a form of variance reduction, multilevel MonteCarlo (MLMC) and multilevel stochastic collocation havebeen developed. We present an approach to adaptivelyaccelerate a sequence of hierarchical interpolants requiredby a multilevel method. Taking advantage of the hierar-chical structure, we build new iterates and improved pre-conditioners, at each level, by using the interpolant fromthe previous level. We provide rigorous complexity analysisof the fully discrete problem and demonstrate the increasedcomputational efficiency.

Guannan ZhangOak Ridge National Laboratoryzhangg@ornl.gov

PP202

Compatible Discrete Operator Schemes forAdvection-Diffusion Equations

Compatible Discrete Operator (CDO) schemes belong tothe class of mimetic (or structure-preserving) schemes andcan be deployed on polyhedral meshes. We extend theanalysis of CDO schemes, introduced by J. Bonelle and A.Ern for elliptic and Stokes equations, to advection-diffusionequations. The novelties are a discrete contraction op-erator for the advective derivative designed using ideasfrom Friedrichs’ systems and boundary Hodge operatorsto weakly enforce Dirichlet conditions. We prove stabilityand error bounds for the discrete problems. Two salient as-pects are Peclet-robust error estimates and the treatment

284 CS15 Abstracts

of divergence-free advection fields in the absence of reac-tive dissipation. Finally, we present numerical results onthree-dimensional polyhedral meshes.

Pierre CantinUniversite Paris-Est, Ecole des Ponts, Paris Tech,CERMICS,77455 Marne La Vallee, Cedex 2, Francepircantin@gmail.com

Alexandre ErnUniversite Paris-EstCERMICS, Ecole des Pontsern@cermics.enpc.fr

Jerome BonelleEDF R&Djerome.bonelle@edf.fr

PP202

Upwinding in the Mimetic Finite DifferenceMethod for Richards’ Equation

In porous media applications, harmonic averaging of ma-terial properties is the intrinsic property of FV, mimeticFD, and mixed FE methods reflecting continuity of theDarcy flux. In some cases, as as infiltration in a dry soil,it may lead to a strong nonlinear stability condition. Torelax this condition, upwinding of a relative permeabilityis often used. To preserve fundamental properties of themimetic methods such as symmetry and positive definite-ness of discrete operators, a special upwind technique isrequired that we present and analyze in this poster.

Konstantin LipnikovLos Alamos National Laboratorylipnikov@lanl.gov

PP202

The Virtual Element Method

We present a generalization of the finite element methodsto unstructured polygonal and polyhedral meshes. Thedevelopment is based on a new paradigm, dubbed virtualelement method, or VEM. In this new framework only apart of the approximation space is constructed explicitly,while the remaining (virtual) part of the space is given onlyin terms of some algebraic conditions. This new family ofnumerical methods is suitable to polygonal and polyhe-dral unstructured meshes and is applied to the numericalresolution of diffusion, reaction-diffusion and convection-diffusion problems, the Stokes equations and compressibleand incompressible elasticity equations.

Gianmarco ManziniLos Alamos National Laboratorygm.manzini@gmail.com

PP203

Optimal Control for Mass Conservative Level SetMethods

We present a conservative level set method for numericalsimulation of evolving interfaces. A PDE-constrained op-timization problem is formulated and solved in an itera-tive fashion. The proposed optimal control procedure con-strains the level set function to satisfy a conservation lawfor the corresponding Heaviside function. The control cor-

rects the convective flux in the nonlinear state equationso as to enforce mass conservation while minimizing devia-tions from the target state. The methodology is evaluatednumerically.

Christopher Basting, Dmitri KuzminDortmund University of Technologychristopher.basting@math.tu-dortmund.de,kuzmin@math.uni-dortmund.de

PP203

A New Partitioned Algorithm for Explicit Elasto-dynamics Based on Variational Flux Recovery

We present a new partitioned algorithm for explicit elasto-dynamics, based on variational flux recovery. This methodworks by the exchange of tractions which depend on boththe known state and the unknown state at the future timestep. The exchange of recovered tractions between thebodies formally involves modification of both the forcingterm and the mass matrix on each subdomain. Reliance onthe future time step distinguishes our approach from tra-ditional partitioned solution algorithms, which use inter-face conditions between subdomains and the current timestep solution to define boundary conditions for the models.Our approach offers some distinct numerical and theoreti-cal advantages. It passes a linear patch test and is secondorder accurate in space. Furthermore, if interface gridsmatch, our new partitioned method recovers the solutionof a monolithic coupling scheme for the solid-solid interac-tion problem.

Pavel BochevSandia National LaboratoriesComputational Math and Algorithmspbboche@sandia.gov

Paul KuberrySandia National Laboratoriespakuber@sandia.gov

PP203

Analysis of a Fluid-Structure Interaction ProblemDecoupled by Optimal Control

A new method is presented which allows fluid-structure in-teraction problems to be stably decoupled. This methodpermits the use of existing solvers for the fluid and struc-ture subsystems. With existence of an optimal solutionand Lagrange multipliers proven, the optimization problemconstrained by PDEs can be written unconstrained usingthe Lagrange multiplier rule. The first order optimalitysystem is derived and and a gradient based algorithm isgiven along with numerical results.

Paul A. KuberryClemson Universitypkuberr@clemson.edu

Hyesuk LeeClemson UniversityDep. of Mathematical Scienceshklee@clemson.edu

PP203

Feature-Preserving Finite Element Transport

CS15 Abstracts 285

Across Interfaces: Part 2, Direct Flux Recovery

We present an optimization-driven approach for couplingtransport codes across non-coincident interfaces. Ourapproach relies on the recently introduced methods foroptimization-based finite element transport (see Part 1).It uses constrained interpolation to recover and exchangeflux variables on the interfaces, and maintains key physicalproperties, such as mass conservation and monotonicity.

Kara PetersonSandia Natl. Labskjpeter@sandia.gov

Pavel BochevSandia National LaboratoriesComputational Math and Algorithmspbboche@sandia.gov

Denis RidzalSandia National Laboratoriesdridzal@sandia.gov

PP203

Feature-Preserving Finite Element TransportAcross Interfaces: Part 1, Optimization-BasedTransport

We discuss an optimization framework for the design ofrobust feature-preserving schemes for finite element trans-port. Our optimization models and algorithms preservekey physical features such as monotonicity and mass con-servation, and can be used to efficiently couple simulationcodes for transport across non-coincident interfaces (seePart 2).

Denis RidzalSandia National Laboratoriesdridzal@sandia.gov

Kara PetersonSandia Natl. Labskjpeter@sandia.gov

Pavel BochevSandia National LaboratoriesComputational Math and Algorithmspbboche@sandia.gov

PP203

Higher Order Finite ElementMethods for InterfaceProblems

We present a higher-order finite element method for solv-ing a class of interface problems in two dimensions. Themethod is based on correction terms added to the right-hand side of the natural method. We prove optimal errorestimates of the method on general quasi-uniform meshesin the maximum norms. In addition, we apply the methodto a Stokes interface problem obtaining optimal result.

Manuel A. Sanchez-UribeBrown Universitymanuel sanchez uribe@brown.edu

PP203

Extended and Conformal Decomposition Finite El-

ements for 3D Compatible Discretizations

Current tends to concentrate near material interfaces, ergoaccurate simulation of electromagnetics requires the reso-lution of said interfaces. Large deformations make body-fit meshes impractical, but the continuity requirements ofphysics-compatible discretizations are not satisfied with-out body-fitting. We propose using the existing non-conforming node and edge element bases to dynamicallyconstruct an interface-conforming basis in 3D. We also de-velop a conformal decomposition finite element method foredges and demonstrate their equivalence for tetrahedral el-ements.

Christopher Siefert, Richard KramerSandia National Laboratoriescsiefer@sandia.gov, rmkrame@sandia.gov

Pavel BochevSandia National LaboratoriesComputational Math and Algorithmspbboche@sandia.gov

Thomas VothSandia National Laboratorytevoth@sandia.gov

PP204

Chebfun

Chebfun is an open-source MATLAB package for comput-ing with functions instead of numbers. By overloadingcommon MATLAB commands to operate on function ob-jects called chebfuns, the package provides a computingexperience which feels symbolic but is actually driven bythe numerical tools of Chebyshev polynomial approxima-tion technology. Users can do things like plot and evaluatefunctions, compute roots and extrema, and solve differen-tial equations using a simple syntax intuitive to anyonefamiliar with MATLAB. This poster will provide a tour ofsome of Chebfun’s major features. A member of the Cheb-fun development team will be on site to present demos anddiscuss the software with anyone interested.

Anthony AustinUniversity of Oxfordaustin@maths.ox.ac.uk

PP204

Feel++: A Versatile High Performance Finite Ele-ment Embedded Library into C++

Feel++ (Finite Element method Embedded Language inC++) offers a domain specific language to partial differ-ential equations embedded in C++. It allows to use avery wide range of possibly, high order, Galerkin methods,and advanced numerical methods such as domain decom-position methods including h-p mortar methods, levelsetmethods, fictitious domain methods or certified reducedbasis. We illustrate on some applications the numericalbehavor up to millions and even billions of unknowns.

Vincent ChabannesLaboratoire Jean KuntzmannUniversite de Grenoble

286 CS15 Abstracts

vincent.chabannes@feelpp.org

PP204

Dolfin-Adjoint

dolfin-adjoint automatically derives parallel, efficient ad-joint and tangent linear models from finite-element mod-els written in the FEniCS environment. It also provideshigh-level tools to solve PDE-constrained optimisation andgeneralised stability problems. This poster presents anoverview of dolfin-adjoint, including examples and recentdevelopments. The dolfin-adjoint developers will live-demothe software and answer questions.

Simon W. FunkeCenter for Biomedical ComputingSimula Research Laboratorysimon@simula.no

Marie E. RognesSimula Research Laboratorymeg@simula.no

Patrick E. FarrellDepartment of MathematicsUniversity of Oxfordpatrick.farrell@maths.ox.ac.uk

David HamImperial College Londondavid.ham@imperial.ac.uk

PP204

Building Performance Transportable Codes for Ex-treme Scale

The goal of the Center for Exascale Simulation of Plasma-Coupled Combustion is to explore and understand a newapproach to controlling combustion though the use of plas-mas. The computation is multiscale and multiphysics, andis a challenge even with extreme scale computers. Thisposter highlights the approach to transportable perfor-mance being being taken by the center, including the use ofa golden copy for development and source transformationsfor data structure and loop optimization.

William D. GroppUniversity of Illinois at Urbana-ChampaignDept of Computer Sciencewgropp@illinois.edu

PP204

Firedrake: Automating Finite Element by Com-posing Abstractions

Firedrake automates the portable solution of partial dif-ferential equations using the finite element method. Fire-drake takes separation of concerns in automated FEM to anew level. In addition to the Unified Form Language fromthe FEniCS project, and PETSc’s linear algebra abstrac-tion, Firedrake introduces the PyOP2 abstraction for meshiteration and the COFFEE abstraction for kernel vectori-sation and optimisation. The result is faster, more flexibleand more capable automated simulation.

David Ham, Florian RathgeberImperial College Londondavid.ham@imperial.ac.uk, f.rathgeber10@imperial.ac.uk

Lawrence MitchellDepartment of ComputingImperial College Londonlawrence.mitchell@imperial.ac.uk

Michael LangeDepartment of Earth Science and EngineeringImperial College Londonmichael.lange@imperial.ac.uk

Andrew McRaeDepartment of MathematicsImperial College Londona.mcrae12@imperial.ac.uk

Gheorghe-Teodor Bercea, Fabio LuporiniDepartment of ComputingImperial College Londongheorghe-teodor.bercea08@imperial.ac.uk,f.luporini12@imperial.ac.uk

Paul KellyImperial College Londonp.kelly@imperial.ac.uk

PP204

The DEAL.II Finite Element Library

deal.II is a C++ software library supporting the creation offinite element codes and an open community of users anddevelopers. In this poster session, we present an overviewof deal.II, highlight some applications, and present futureplans.

Timo HeisterClemson UniversityMathematical Sciencesheister@clemson.edu

Wolfgang BangerthTexas A&M Universitybangerth@math.tamu.edu

Guido Kanschat, Matthias MaierUniversitat Heidelberg, Germanykanschat@uni-heidelberg.de, matthias.maier@iwr.uni-heidelberg.de

PP204

An Overview of the Trilinos Project

Trilinos is a large collection of interoperable packages forformulation, solution and analysis of large scale modelingand simulation problems. Trilinos provides libraries for(i) portable architecture-aware data containers and algo-rithms; (ii) geometry, meshing, discretization, load balanc-ing and scalable solution of linear, nonlinear and transientproblems; (iii) optimization, uncertainty quantification andanalysis and (iv) scalable IO. Trilinos also provides soft-ware tools and processes for developing scientific softwarefrom inception to post-delivery maintenance, supportingcomponents-based application development strategies in-tended to improve software quality, and reduce time tocompletion and cost.

Michael HerouxSandia National Laboratories

CS15 Abstracts 287

maherou@sandia.gov

PP204

FEniCS High Performance Computing with Appli-cations in Aerodynamics, Environmental Scienceand Biomedicine

Adaptive finite element methods (AFEM) using unstruc-tured meshes pose serious challenges for the development ofefficient algorithms and software implementations for mas-sively parallel architectures. We describe the open sourcesoftware DOLFIN-- HPC/Unicorn that implements AFEMfor a general class of problems in computational mechanics,as part of the software project FEniCS [1,2]. DOLFIN--HPC is based on a hybrid MPI+OpenMP/MPI+PGASprogramming model, and shows near optimal scaling up totens of thousands of processing elements for applications incomputational fluid dynamics (CFD) [3]. The method isbased on the computation of an adjoint (or dual) problemto derive a posteriori estimates of the error in a certain out-put of interest, such as the drag or lift of an airplane, whichguides the mesh refinement algorithms. Since the problemis nonlinear, the primal solution appears as data in the ad-joint problem, and since the adjoint problem is solved back-wards in time, the time series of the primal problem mustbe stored which is a challenge for large problems. In addi-tion, algorithms for local mesh refinement pose challengesin terms of dynamic load balancing and efficient commu-nication over the unstructured mesh data. In this posterpresentation we describe the methods and software imple-mentation, and highlight application projects based on thecomputational technology, including simulation of the aero-dynamics of airplanes, blood flow in the human heart, andhuman phonation.

Johan HoffmanRoyal Institute of Technology KTHjhoffman@kth.se

PP204

EMatter: A Materials Simulation Framework As aService

eMatter is a fledging new computational service that aimsto simplify life for computational materials scientists. Builton top of a stack of scalable high-performance libraries, in-cluding PETSc, libMesh and MOOSE, eMatter presentstheir capabilities as a service, or as a platform. Librarymaintenance, configuration and building, as well as jobsubmission, data handling and basic visualization capabil-ities are taken care of by the framework. eMatter demoswill be provided and developers will be available on site forquestions and hands-on exercises.

Dmitry A. KarpeyevUniversity of Chicagokarpeev@uchicago.edu

PP204

Composability in Petsc

Composability of lower-level abstractions is crucial forbuilding large software systems while controlling complex-ity. This fact is often overlooked in computational sciencesince it is not emphasized in the numerical analysis. Wepresent two examples of its role in PETSc. In the design ofnonlinear solvers, we allow preconditioning of one solve byanother, in analogy with the linear case, giving us much

richer and more robust alternatives for nonlinear solves.Likewise, for small scale parallelism, we propose a systemthat allows different threading models to interact, avoidingresource contention and over-provisioning. We attempt tominimize assumptions about our environment so as to max-imize the ability to compose with other packages and usersthat chose other models.

Matthew G. KnepleyUniversity of Chicagoknepley@ci.uchicago.edu

Jed BrownMathematics and Computer Science DivisionArgonne National Laboratory and CU Boulderjed@jedbrown.org

PP204

Fenics

FEniCS is a high-level, high-performance software envi-ronment for automated, efficient, and intuitive solution ofpartial differential equations by the finite element method.In this poster session, an overview of FEniCS is presented,together with explained examples and a summary of re-cently added new features. Live demos will be presentedand FEniCS developers will be on spot to chat with users.

Anders LoggChalmers University of Technologylogg@chalmers.se

PP204

Sigma: Scalable Interface for Geometry and MeshBased Applications

SIGMA provides components to define/query geometricentities (CGM), and apply efficient mesh generation algo-rithms (MeshKit) based on relational definitions (Lasso) tocreate high quality unstructured mesh databases (MOAB),which serves as a data backplane for applications (Nuclear,CFD, Climate, FEA) running on desktop to petascalearchitectures. SIGMA tools handle several I/O formatswith interfaces for visualization, solvers (PETSc) and scal-able conservative solution transfers (enabling multi-physicssolvers). We will present interactive workflow demos to en-courage further discussions with audience.

Vijay Mahadevan, Iulian Grindeanu, Rajeev JainArgonne National Laboratorymahadevan@anl.gov, iulian@mcs.anl.gov,jain@mcs.anl.gov

Navamita RayArgonne National Labratorynray@mcs.anl.gov

Danqing WuArgonne National Laboratorywuda@mcs.anl.gov

Paul WilsonUniversity of Wisconsin - Madisonwilsonp@engr.wisc.edu

PP204

Dune - The Distributed and Unified Numerics En-

288 CS15 Abstracts

vironment

DUNE is a modular open-source framework for the solutionof partial differential equations using grid-based methods,written in modern C++. It offers clear abstractions atall levels of a PDE simulation, providing the user withhigh-level abstractions for productive development, whilealso allowing access to lower-level functionality, enablingscalability from notebooks to HPC applications. Due toits modularity, DUNE easily integrates with legacy codeslike existing grid managers and LA libraries.

Steffen MuthingHeidelberg Universitysteffen.muething@iwr.uni-heidelberg.de

PP204

Elemental

Elemental is a modern C++11 implementation ofdistributed-memory dense linear algebra that has been ex-tended to various sparse-direct solvers, preconditioners,optimization, and medical imaging applications. In thisposter session, an overview of Elemental is presented, witha focus on the idioms that the project has converged uponfor manipulating (distributed) matrices and exposing ab-stract interfaces without incurring performance penalties.

Jack L. PoulsonComputational Science and EngineeringGeorgia Institute of Technologyjack.poulson@gmail.com

PP204

Jupyter Widgets: Interactive Computing Throughthe Browser in Any Programming Language

The Jupyter project, evolved from IPython, providesa generic architecture for interactive computing with alanguage-independent protocol for controlling code execu-tion over the network. In particular, it can be used fromweb browsers to provide interactive graphical explorationof complex computations by combining Javascript widgetscoupled to computational kernels written in Python, Ju-lia, R or any other language. This facilitates both rapidexploration and illustration of computational concepts foreducation.

Min Ragan-KelleyUC Berkeley AS&TMinRK@Berkeley.edu

Fernando PerezHelen Wills Neuroscience InstituteUniversity of California, BerkeleyFernando.Perez@berkeley.edu

PP204

Camellia: A Software Framework for Discontinu-ous Petrov-Galerkin Methods

The discontinuous Petrov-Galerkin (DPG) methodologyof Demkowicz and Gopalakrishnan minimizes the solutionresidual in a user-determinable energy norm and offers abuilt-in mechanism for evaluating error in the energy norm,among other desirable features. However, the methodologybrings with it some additional complexity for researcherswho wish to experiment with DPG in their computations.

In this poster, we introduce Camellia, a software frame-work whose central design goal is to enable developers tocreate efficient hp-adaptive DPG solvers with minimal ef-fort.

Nathan RobertsArgonne National Laboratorynvroberts@alcf.anl.gov

PP204

ViennaCL - Fast Linear Algebra for Multi andMany-Core Architectures

An overview of the linear algebra functionality and solversavailable in the Vienna Computing Library (ViennaCL) formulti-core CPUs as well as GPUs and Intel’s MIC architec-ture is given. Compute backends using OpenMP, CUDA,and OpenCL allow for maximum flexibility and best perfor-mance on the underlying hardware from all major vendors.

Karl RuppInstitute for Analysis and Scientific Computing, TU WienInstitute for Microelectronics, TU Wienrupp@iue.tuwien.ac.at

Philippe Tillet, Toby St Clere Smithe, Namik Karovic,Josef Weinbub, Florian RudolfInstitute for MicroelectronicsVienna University of Technologyphil.tillet@gmail.com, mail@tsmithe.net,namik.karovic@gmail.com, weinbub@iue.tuwien.ac.at,rudolf@iue.tuwien.ac.at

PP205

Radical Optimization Techniques for AsynchronousIterative Algorithms on Gpus

Asynchronous algorithms, with their ability to toleratememory latency, form an important class of algorithms formodern computer architectures. For the recently proposedasynchronous iterative algorithm for computing incompletefactorizations we present non-traditional optimizations toleverage the computing power of GPUs. These include con-trolling the order in which variables are updated, takingadvantage of cache reuse between thread blocks, and op-timizing the trade-off between parallelism and algorithmconvergence for time-to-solution performance.

Hartwig AnztInnovate Computing LabUniversity of Tennesseehanzt@icl.utk.edu

Edmond ChowSchool of Computational Science and EngineeringGeorgia Institute of Technologyechow@cc.gatech.edu

Jack J. DongarraDepartment of Computer ScienceThe University of Tennesseedongarra@cs.utk.edu

PP205

Experiences in Autotuning Linear Algebra Opera-tions for Energy Minimization on Gpus

Approaching the Exascale computing era requires a

CS15 Abstracts 289

paradigm shift from pure runtime performance to metricsaccounting also for resource efficiency. In this line, wepresent experiences about using the BEAST autotuningframework for optimizing the energy efficiency of GPU im-plementations of basic linear algebra building blocks. Weanalyze the kernel metrics to correlate the pruning param-eters to performance and resource usage.

Hartwig AnztInnovate Computing LabUniversity of Tennesseehanzt@icl.utk.edu

Blake HaugenInnovative Computing LabUniversity of Tennesseebhaugen@utk.edu

Jakub KurzakUniversity of Tennessee, Knoxvillekurzak@icl.utk.edu

Jack J. DongarraDepartment of Computer ScienceThe University of Tennesseedongarra@cs.utk.edu

PP205

CUSP: A Parallel Sparse Matrix Package for Gpus

CUSP, an open-source C++ templated library for sparsematrix and graph operations, enables collection orientedparallel processing on modern architec- tures, such asGPUs. In this presentation we will discuss the Thrust-based ab- stract programming model to express highly ir-regular computations involving sparse matrices, such as ad-dition and multiplication, and the integration of GPU ori-ented programming systems, such as CUB, to implementhigh-performance routines to perform reordering, coloring,and maximum-ow computations on GPU architectures.

Steven DaltonUniversity of Illinois at Urbana-Champaigndalton6@illinois.edu

Luke OlsonDepartment of Computer ScienceUniversity of Illinois at Urbana-Champaignlukeo@illinois.edu

PP205

Sparse Matrix-Matrix Multiplication on High-Throughput Architectures

Many computations in the physical and data sciences relyon sparse matrix operations such as the sparse matrix-matrix multiplication (SpMM) operation. Yet an efficientSpMM on high-throughput architectures requires expos-ing fine-grained parallelism in the operation while limitingthe use of the off-chip memory bandwidth. In this posterwe highlight an approach that decomposes the SpMM intothree phases: expansion, sorting, and contraction, therebyallowing the use of optimized throughput-oriented kernels.The result is a SpMM algorithm that requires low a pri-ori analysis of the matrix structures, yet yields substantialsavings for general classes of unstructured matrices.

Luke OlsonDepartment of Computer Science

University of Illinois at Urbana-Champaignlukeo@illinois.edu

Steven DaltonUniversity of Illinois at Urbana-Champaigndalton6@illinois.edu

PP206

Parallel Petascale Modeling of Transportation Ac-cidents Involving High Explosives

Simulations of multiple explosive devices undergoing com-bustion requires algorithms and models capable of solv-ing fluid-structure interactions, compressible flow, and fastsolid-¿gas reactions. We have been developing these toolsin the Uintah:MPMICE, which is capable of scaling upto 512k. This research will give insight in to the phys-ical mechanism of Deflagration to Detonation Transition(DDT) for large-scale explosions and help determine safepackaging configurations to eliminate DDT in transporta-tion accidents.

Jacqueline BeckvermitDepartment of ChemsitryUniversity of Utahbeckvermit@gmail.com

Andrew BezdjianUniversity of Utahandrewbezdjian@gmail.com

Todd HarmanDepartment of Mechanical EngineeringUniversity of Utaht.harman@utah.edu

John A. SchmidtSCI InstituteUniversity of Utahjas@sci.utah.edu

Martin BerzinsScientific Computing and Imaging InstituteUniversity of Utahmb@sci.utah.edu

Chuck WightWeber State Universitycwight@weber.edu

PP206

Radiation Modeling Using Reverse Monte CarloRay Tracing Within the Uintah Framework

The Uintah ARCHES component has previously used theDiscrete Ordinates algorithm for solving the RadiativeTransport Equation (RTE). This approach is expensive dueto the linear solves involved. We are exploring the use ofthe Reverse Monte Carlo Ray Tracing (RMCRT) techniquefor solving the RTE on both CPUs and GPUs to reducethis computational cost. Here we we discuss the challengesinvolved in moving to an RMCRT approach for solving theRTE at scale.

Alan HumphreyScientific Computing and Imaging InstituteUniversity of Utah

290 CS15 Abstracts

ahumphrey@sci.utah.edu

PP206

Using Uintah:mpmice for High Resolution UrbanFlow Studies

Urban flow transport plays a critical role in investigationsof the impact of local and global climate on urban in-habitants. We introduce Uintah:MPMICE for the simu-lation of fluid-structure interactions in urban flows. Uin-tah:MPMICE has been developed in a massively paral-lel computational infrastructure, uses material points torepresent buildings, and LES technique to represent mo-mentum and scalar transport. Using Uintah:MPMICE forhighly turbulent flows in urban areas introduce challengeson the implementation of appropriate boundary conditions.

Arash Nemati Hayati, Rob StollDepartment of Mechanical Engineering University of Utaha.nematihayati@utah.edu, rstoll2@gmail.com

Todd HarmanDepartment of Mechanical EngineeringUniversity of Utaht.harman@utah.edu

Eric PardyjakDepartment of Mechanical Engineering University of Utahpardyjak@gmail.com

PP206

Wasatch: A CPU/GPU-Ready Multiphysics CodeUsing a Domain Specific Language

Hybrid computing poses a challenge for computational sci-ence. Legacy code is unable to leverage the benefits ofCPU/GPU platforms without significant refactor. Here,we present a promising approach to making computationalcodes architecture-proof. Our method consists of using aDomain Specific Language to separate implementation andusage. At the outset, one can write a single code that maybe executed on multiple backends. This is shown to workwith our flagship multiphysics code, Wasatch.

Tony SaadThe Institute for Clean and Secure EnergyDepartment of Chemical Engineering, University of Utahtony.saad@utah.edu

Abhishek BagusettyChemical EngineeringUniversity of Utahabhishek.bagusetty@utah.edu

James C. SutherlandDepartment of Chemical EngineeringThe University of Utahjames.sutherland@chemeng.utah.edu

PP206

Applied Large Eddy Simulation: Validation andUncertainty Quantification of Lab and Pilot-Scale,Oxy-Coal Boiler Simulations

This work seeks to advance simulation capabilitiesrelat-edto oxy-coal combustion. The approach combines ex-perimental and simulation data from lab and pilot-scale

oxy-coal systems with Large Eddy Simulation (LES) in arigorous validation and uncertainty quantification (V/UQ)Bayesian technique. The method identifies a subset ofparameters that control the heat flux, temperature, andspecies concentrations within the boilers. Given the uncer-tain ranges in these variables, the V/UQ method discov-ers a range of simultaneously consistent values constrainedby the experimental data with uncertainties. The exper-imental systems of interest are the 15MW Alstom BoilerSimulation Facility and the 150 KW Oxy-Fired Combus-tor located at the University of Utah. The simulation workwas performedusing Arches, a large-eddy simulation com-ponent with DQMOM multiphase capabilities in the Uin-tah framework, at large scale.

Jeremy ThornockThe University of Utahjeremy.thornock@utah.edu

Wu YuxinInstitute for Clean and Secure EnergyUniversity of Utahwuyx02@gmail.com

Ben IsaacUniversity of Utah & Universite Libre de Bruxellesbisaac2@gmail.com

Sean SmithThe University of Utahsean.t.smith@utah.edu

Philip J. SmithUniversity of UtahPhilip.Smith@utah.edu

PP207

The Periodic Table of the Finite Elements

Since the dawn of the finite element method half a cen-tury ago, increasingly sophisticated finite element spaceshave been developed and applied. Even to specialists, theresulting collection of finite elements can seem a disorga-nized zoo of possibilities. By taking the viewpoint of finiteelement exterior calculus these spaces can be arranged in asort of periodic table, which explains their shape functions,degrees of freedom, and interrelationships, and guides im-plementation in advanced software environments.

Douglas N. ArnoldSchool of MathematicsUniversity of Minnesotaarnold@umn.edu

Anders LoggChalmers University of Technologylogg@chalmers.se

PP207

Convolution-Translation and Bounded CochainProjections for the Elasticity Complex

Uniformly bounded projections in L2 which commute withthe exterior derivative play an essential role in the finiteelement exterior calculus. The extension part of the pro-cess limits the construction of bounded cochain projec-tions for the elasticity complex to star shaped domains.In this work, we avoid the extension operator by using

CS15 Abstracts 291

convolution-translation. The construction is revisited fromthat point of view and cochain projections without the re-striction of star-shaped domains are constructed for theelasticity complex.

Gerard AwanouChicagoawanou@uic.edu

PP207

What is a Good Linear Finite Element... On aGeneric Polytope?

The notion of what constitutes a ”good” linear finite el-ement on geometries other than simplices and cubes re-mains largely unexplored. We use harmonic coordinates asa means to investigate this question, arriving at a few keyconclusions. On convex polygons, harmonic coordinatesin general provide no improvement over standard interpo-lation on the constrained Delaunay triangulation of thepolygon. On non-convex polygons, however, harmonic co-ordinates can provide optimal interpolation estimates evenwhen all triangulations fail to do so. We also present theextension and implication of these results to finite elementson non-convex polyhedra in 3D.

Andrew GilletteUniversity of ArizonaDepartment of Mathematicsagillette@math.arizona.edu

Alexander RandCD-adapcoAustin, Texasalexander.rand@cd-adapco.com

PP207

Stokes Elements on Cubic Meshes YieldingDivergence-Free Approximations

Using a finite element exterior calculus framework, con-forming piecewise polynomial spaces with respect to cu-bic meshes are constructed for the Stokes problem in ar-bitrary dimensions yielding exactly divergence–free veloc-ity approximations. We first present the construction ofthe lowest order case, its implementation, and convergenceanalysis. We then introduce finite element spaces with con-tinuous pressure approximations leading to a system of lessunknowns. Finally, numerical experiments are shown veri-fying the theoretical results.

Michael J. NeilanUniversity of PittsburghDepartment of Mathematicsneilan@pitt.edu

Duygu SapUniversity of Pittsburghduygusap@googlemail.com

PP207

Weak Galerkin Finite Element Methods

Weak Galerkin finite element method (WG-FEM)is a newapproximating technique for partial differential equations.The main idea behind the WG method is the use of discreteweak differential operators in the conventional variationalformulations for the corresponding PDEs. This presen-

tation shall introduce the WG-FEM through some modelproblems: (1) mixed formulation for second order ellipticequations, (2) the Stokes equations, and (3) div-curl prob-lems or Maxwell equations.

Junping WangNational Science Foundationjwang@nsf.gov

Chunmei WangGeorgia Institute of Technologycwang462@math.gatech.edu

Xiu YeUniversity of Arkansas, Little Rockxxye@ualr.edu

PP208

Approximate Active Bayesian Inference of Nonlin-ear Dynamical Systems

This poster introduces a computationally efficient approx-imation method to design experiments for Bayesian modelselection of nonlinear dynamical systems. The methodsemploys surrogate functions to reconstruct the total or-dering of the candidate experiments induced by the mu-tual information between the data and the models. Undermild assumptions, it can be shown that such approxima-tion achieves almost indistinguishable design results witha significant computational speedup.

AlbertoGiovanni BusettoUCSBagb@ece.ucsb.edu

PP208

Variational Reformulation of Bayesian InverseProblems

Despite of its computational appeal, the classical approachto inverse problems suffers from many shortcomings. TheBayesian formalism to inverse problems avoids most ofthese difficulties, albeit at an increased computational cost.In this work, we use information theoretic arguments in or-der to cast the Bayesian inference problem in terms of anoptimization problem. The resulting scheme combines thetheoretical soundness of fully Bayesian inference with thecomputational efficiency of a simple optimization.

Ilias BilionisPurdue Universityebilionis@gmail.com

Panagiotis TsilifisUniversity of Southern Californiapantsili@gmail.com

Nicholas ZabarasCornell Universitynzabaras@gmail.com

PP208

Bayesian Model Selection for Exploring Mecha-nisms Contributing to Differential Signaling

An important phenomenon in cytokine signaling, termed“differential signaling,” is the ability of structurally simi-lar ligands with different binding affinities to elicit diverse

292 CS15 Abstracts

biological actions through the same receptor. We modelsignaling networks as linear steady state models for whichwe derive explicit signaling differentials for single cells andcell populations. We explore the capacity of candidate sig-naling mechanisms to reproduce observed differential sig-naling dose response data by employing Bayesian modelselection.

Pencho YordanovETH Zurichpencho.yordanov@bsse.ethz.ch

Joerg StellingDepartment of Biosystems Science and Engineering, ETHZurichjoerg.stelling@bsse.ethz.ch