Scientific Computing

Ron Elber

Keshav Pingali

Charlie Van Loan

Steve Vavasis

Time Scale Problems in the Popular Molecular Dynamics Approach

910 610 310 1

seconds

Mol. Dyn. ProteinActivation

Channel Gating. Fast folding

Slowfolding

Action optimization generates approximate trajectories

Initial value solution versus optimization of an action

• Interpolate to next coordinate based on previous coordinate and velocity vectors

• Optimize a current guess for the whole trajectory starting from an initial guess

2

1

1 1

2

2

i i i i

i i i i

tX X V t F

Mt

V V F FM

1,...,

S0 =0 2,..., 1

N

i

S X l S X X

Si N

X X

iX 1iX

Cytochrome c folding: a millisecond (10-3 seconds) process with the Stochastic

Difference Equation (SDE)Straightforward molecular dynamics can do 10-7 seconds

Mobile Computational Grid Programs

-Programs run for many hours on large machines with hundreds of processors.-Mobile programs can adapt to changing resource availability by migrating to new sites on grid. -New site may have different number and type of processors.-Goal: programs mobile programs in a semi-automatic way.

Programs Mobile Programs

• Solution: program transformation– Insert code for saving/restoring application state (done by

C3 compiler)

– Use type information to reconstruct state at remote site

– Applications become “self-checkpointing” and “self-restarting”

– Application-level checkpointing (ALC)

(cf. system-level checkpointing)– Efficient

• 5% overhead or less for sequential codes• About 10% for MPI codes (homogeneous platforms)

Ongoing Work

• Program analysis to reduce the amount of saved state– Joint work with Radu Rugina

• Heterogeneous platforms– Different architectures– Different number of processors

• Self-optimization• Other applications:

– Speculative computation– Backward differentiation

Real-Time Matrix-based Signal Processing

Maximize trace of U1T A1U1 + … + Uk

TAk Uk

where A1 ,…, Ak are symmetric matrices and U = [ U1 | … | Uk ] isorthogonal.

Repeat in real time:-Sense atmosphere-Solve matrix problem-Refocus deformable mirror

Mesh Generation & Guaranteed-Quality Triangulation

• Problem: Given a description of a 2D or 3D geometric set, produce a subdivision into triangles or tetrahedra

• First guaranteed solution to 2D problem uses constrained Delaunay triangulation (Chew, 1989)

• Shewchuk’s high-quality implementation of these ideas won 2003 Wilkinson prize.

2D Delaunay Mesh

• Each triangle has the empty circle property

3D Delaunay Mesh

• Empty sphere property holds but does not imply a quality mesh

• Some fixes in the literature, but it seems like a new idea is needed

• Alternative: hierarchical space decomposition– QMG (Mitchell & Vavasis 2000)– New algorithm based on longest edge

bisection