ab initio simulations for (the witch) penning traps using a graphics cards for faster coulomb...
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Ab initio simulations for (the WITCH) Penning traps using a graphics cards for faster coulomb
interaction calculations
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S. Van Gorp, M. Breitenfeldt , M. Tandecki, F. Wauters, E. Traykov, , N. Severijns (K.U.Leuven, Belgium),
M. Beck, P. Friedag, C. Weinheimer (Univ. Munster, Germany), A. Herlert (ISOLDE-CERN, Geneva, Switserland),V. Kozlov, F. Gluck (Univ. Karlsruhe, Germany),
D. Zakoucky (NPI-Rez, Prague, Czech)
Simon Van Gorp – TCP Saariselkä- 14.04.2010
WITCH introduction Simulation motivation Coulomb interactions
• Tree codes• Chamomile scheme: Coulomb on a GPU.• Performance GPU vs CPU
Simonion, a Penning Trap simulation program• Integrator• Buffer gas collisions
Conclusion and Outlook
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Overview
Simon Van Gorp – TCP Saariselkä- 14.04.2010
WITCH Introduction
H = gP
j =S;V;A ;T ;P (ÃpOj Ãn)(ÃeOj (Cj +C
0
j °5)Ãn) +h:c:H = g
X
j =S;V;A ;T ;P
(ÃpOj Ãn)(ÃeOj (Cj +C
0
j °5)Ãn) +h:c: (1)H = gX
j =S;V;A ;T ;P
(ÃpOj Ãn)(ÃeOj (Cj +C
0
j °5)Ãn) +h:c: (1)
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The WITCH experiment looks for scalar currents in nuclear beta decay.A scattering free source is needed because of the low recoil energy.
A retardation barrier is applied and the # ions reaching an MCP detector are counted.
Simulation Motivation
Simon Van Gorp – TCP Saariselkä- 14.04.2010
The retardation spectrometer is a combination of E and B fields. A particle tracking routine was developed to understand the behavior of the ions by F. Gluck. A good source of ions is needed to describe the process correctly.
Understand space charge effects in the Penning traps.
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WITCH: 106 ions per cycle -> Computer simulations which are
dominated by the Coulomb interaction calculation
Coulomb interactions
Simon Van Gorp – TCP Saariselkä- 14.04.2010
Coulomb force scales with O(N2) Tree methods (Barnes Hut, PM, P3M, FMM)
reduces this to O(N log N)
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2coulomb e
QqkF rr
Space is divided in nodes. Which are subdivided A node has the total charge and mass, and is located on the centre of mass. Approx. long range force by aggregating particles
into one particle and use the force of this one particle
Scaled Coulomb Force puts more weight to the charge of one ion to simulate more ions. Works well [1]
[1]: D. Beck et al, Hyp. Int. 132, 2001
Why a GPU?
Simon Van Gorp – TCP Saariselkä- 14.04.2010
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GPU CPU-high parallelism STILL TO DO-very fast floating point calculations-SIMD structure (pipelining!)
Geforce 8800 GTX
Chamomile scheme
Simon Van Gorp – TCP Saariselkä- 14.04.2010
Calculating gravitational interactions on a Graphics Card via the Chamomile scheme from Hamada and Iitaka (in 2007).
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Why a GPU?-parallelism!-only 20 float operations-CUDA programming
language for GPU’s
J-bagI-pot
force[2]: T. Hamada and T. Iitaka, arXiv.org:astro-ph/0703100, 2007
Chamomile scheme: practical usage
Simon Van Gorp – TCP Saariselkä- 14.04.2010
Function provided by Hamada and Iitaka:
Gravitational force ≈ Coulomb Force
Conversion coefficient:
Needed: -64 bit linux -NVIDIA Graphics Card that supports CUDA - CUDA environment v2.3
Not needed: -CUDA knowledge -…
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2 2 grav coulomb e
Mm QqG k F r F rr r
cunbody1_force(xj, mj, xi, eps, ai, nmax, nmax)
2
;eCoulomb
q ka ai
m
Simon Van Gorp – TCP Saariselkä- 14.04.2010
3000 35Ar+ ions No Buffergas
9/14
Movie
Simon Van Gorp – TCP Saariselkä- 14.04.2010
GPU vs CPU•GPU blows the CPU away. The effect becomes more visible with even more particles simulated.•Simulated is a quadrupole excitation for 100ms with buffer gas. This takes 3 days with a GPU compared to 3-4 years with a CPU!
GPU improvement factor CPU and GPU simulation time
Simon Van Gorp – TCP Saariselkä- 14.04.2010
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Simonion overview Simonion is a modular Penning Trap simulation package.
Reading external fieldmaps Trap excitations 3 different integrators 2 buffergas routines Possibility to include external fieldmaps Can run on CPU and GPU Compile with g++ or icpc A root analysis file is provided A Makefile is provided
http://sourceforge.net/projects/simonion/
Integrators and buffer gas models
Simon Van Gorp – TCP Saariselkä- 14.04.2010
•Integrators:•4th and 5th order Runga Kutta with adaptive stepsize and error control.•1st order (predictor corrector) Gear method.
• Buffer gas models:•Langevin or polarizability model (= for all mases)•Ion Mobility based model ( ≈ for all mases)
12/14
Simon Van Gorp – TCP Saariselkä- 14.04.2010
Other GPU bases libraries:• Kirin: + corrector and predictor integrator [3]
2 x faster• Sapporo: double precision, corrector on CPU [4]
2 x faster ?• N-Body from Nvidia [5]
2 x faster ? Tree codes Scaled Coulomb force
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Possible improvements
[3]: Belleman et al, New Astronomy, 13(2),103-112,2007[4]: Evghenii et al, New Astronomy, 14(7),630-637,2009[5]:Nyland et al, GPU Gems 3, Chapter 31, Addison-Wesley, 2007
Simon Van Gorp – TCP Saariselkä- 14.04.2010
A Penning Trap simulation package Simonion is presented that is stable and intuitive to use.
The first program that uses a GPU to calculate Coulomb interactions much faster!
GPU computing is a new field of which we barely scratched the surface.
Possible improvements like tree codes and scaled Coulomb force will push the limit to 106 particles
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Conclusion
Thank you for your attention
Simon Van Gorp – TCP Saariselkä- 14.04.2010
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