Testing of multi-cores graphic processors by molecular dynamics algorithm

E. M. Pestryaev

Matematičeskoe modelirovanie, Tome 26 (2014) no. 1, pp. 69-82.

Résumé

The testing of multi-cores graphic processors was made by the most difficult off-lattice algorithm of molecular dynamics simulation, i.e. computation of inter-particle distances. Some video cards NVIDIA GeForce with number of cores from 64 to 512 operating on various frequencies and specialized computing processor Tesla C 2050 were used. All tested processors have the same architecture and are able to execute binary code made by CUDA C. The relative performance of the algorithm executed by any tested graphic processor essentially increases with computational effort due to the growth as the number of the system particles as the cut radius of inter-particle interaction. The top video card performance value reaches 90 in comparison with the algorithm execution by one core of 2.2 GHz CPU in spite of the CPU executable code was made by optimizing C++ compiler of MS Visual Studio 2008. The reduced to frequency relative performance as a function of the video card core number is well described by Amdahl’s law.

Détail

Keywords: molecular dynamics, graphic processor, parallel algorithm, Amdahl’s law, GPU, CUDA.

Bibliographie

[1] Polukhin V. A., Ukhov V. F., Dzugutov M. M., Kompyuternoe modelirovanie dinamiki i struktury zhidkikh metallov, Nauka, M., 1981, 324 pp.

[2] Allen M. P., Tildesley D. J., Computer Simulation of Liquids, Clarendon Press, Oxford, 1991, 385 pp.

[3] Kheerman D. V., Metody kompyuternogo eksperimenta v statisticheskoi fizike, Per. s angl. pod red. S. A. Akhmanova, Nauka, M., 1990, 176 pp.; Heerman D. W., Computer simulations methods in theoretical physics, Springer Verlag, Berlin–Tokyo, 1986, 176 pp.

[4] Tuckerman M. E., Martyna G. J., “Understanding Modern Molecular Dynamics: Techniques and Applications”, J. Phys. Chem. B, 104:2 (2000), 159–178 | DOI

[5] Frenkel D., Smit B., Understanding molecular simulation, 2$^{\mathrm{nd}}$ edition, Academic Press, San Diego–San Francisco–New York–Boston–London–Tokio, 2002, 638 pp.

[6] Tuckerman M. E., Berne B. J., “Molecular Dynamics Algorithm for multiple time scales: Systems with disparate masses”, J. Chem. Phys., 94:2 (1991), 1465–1469 | DOI

[7] Schulz M., Winkler R. G., Reineker P., “Reptation of polymer chains: A combined Monte Carlo and molecular-dynamics study”, Phys. Rev. B, 48:1 (1993), 581–584 | DOI

[8] Procacci P., Berne B. J., “Multiple time scale methods for constant pressure molecular dynamics simulations of molecular system”, Mol. Phys., 83:2 (1994), 255–272 | DOI | MR

[9] Zhou R., Berne B. J., “A new molecular dynamics method combining the reference system propagator algorithm with a fast multi-pole method for simulating proteins and other complex systems”, J. Chem. Phys., 103:21 (1995), 9444–9459 | DOI

[10] Maximova N., Keasar C., “A Novel Algorithm for Non-Bonded-List Updating in Molecular Simulations”, J. Comput. Biol., 13:5 (2006), 1041–1048 http://www.liebertonline.com/doi/pdf/10.1089/cmb.2006.13.1041 | DOI | MR

[11] Praprotnik M., Site L. D., Kremer K., “Adaptive resolution scheme for efficient hybrid atomistic-mesoscale molecular dynamics simulations of dense liquids”, Phys. Rev. Lett. E, 73:6 (2006), 066701(12) | DOI

[12] Praprotnik M., Site L. D., Kremer K., “A Macromolecule in a Solvent: Adaptive resolution Molecular Dynamics Simulation”, J. Chem. Phys., 126:13 (2007), 134902(9) | DOI

[13] Cuendet M. A., van Gunsteren W. F., “On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration algorithm”, J. Chem. Phys., 127:18 (2007), 184102(8) | DOI

[14] Hess B., “P-LINCS: A Parallel Linear Constraint Solver for Molecular Simulation”, J. Chem. Theory Comput., 4:1 (2008), 116–122 | DOI

[15] Eastman P., Pande V. S., “Constant Constraint Matrix Approximation: A Robust Parallelizable Constraint Method for Molecular Simulations”, J. Chem. Theory Comput., 6:2 (2010), 434–437 | DOI

[16] Norman G. E., Stegailov V. V., “Metod klassicheskoi molekulyarnoi dinamiki: zamysel i realnost”, Nanostruktury. Matematicheskaya fizika i modelirovanie, 4:1 (2011), 31–58

[17] Norman G. E., Stegailov V. V., “Stokhasticheskaya teoriya metoda klassicheskoi molekulyarnoi dinamiki”, Matematicheskoe modelirovanie, 24:6 (2012), 3–44 | MR | Zbl

[18] Binder K., Paul W., Suntos S., Suter U. W., “Coarse-Graining Techniques”, Simulation Methods for Polymers, Ch. 15, eds. M. Kotelyanskii, D. N. Theodorou, Marcel Decker, New York–Basel, 2004, 20 pp.

[19] Liu H., Li M., Lu Z.-Y., Zhang Z.-G., Sun C.-C., Cui T., “Multi-scale Simulation Study on the Curing Reaction and the Network Structure in a Typical Epoxy System”, Macromolecules, 44:21 (2011), 8650–8660 | DOI

[20] Rakshit A., Piku R. C., “Coarse grained model of entangled polymer melts”, J. Chem. Phys., 125:16 (2006), 164907(10) | DOI

[21] Pike D. Q., Detcheverry F. A., Muller M., de Pablo J. J., “Theoretically informed coarse grain simulations of polymeric systems”, J. Chem. Phys., 131:8 (2009), 084903(10) | DOI | MR

[22] Krishna V., Larini L., “A generalized mean field theory of coarse-graining”, J. Chem. Phys., 135:12 (2011), 124103(12) | DOI

[23] Guk M., Yurov V., Protsessory Pentium 4, Athlon i Duron, Piter, SPb., 2001, 512 pp.

[24] Pestryaev E. M., “SSE-algoritm molekulyarnoi dinamiki”, Matematicheskoe modelirovanie, 15:12 (2003), 118–128 | Zbl

[25] Baranovskii V., “Dvukh'yadernye nastupayut”, Kompyutery+programmy, 2005, no. 10, 20–25

[26] Pestryaev E. M., “Parallelno-vektornyi algoritm molekulyarnoi dinamiki”, Matematicheskoe modelir., 19:4 (2007), 62–70 | Zbl

[27] Fomin E. S., “Sravnenie metoda Verlet-tablitsy i metoda svyazannykh yacheek dlya posledovatelnoi, vektorizovannoi i mnogopotochnoi realizatsii”, Vych. Met. Progr., 11 (2010), 299–305

[28] http://developer.nvidia.com/cuda-gpus

[29] Nyland L., Harris M., Prince J., “Fast N-Body Simulation with CUDA”, GPU Gems 3, Ch. 31, ed. H. Nguen, NVIDIA Corp., Addison Wesley, 2008, 958 pp. http://www.nvidia.com/cuda

[30] Maksimov K., “Ukroschenie komand SSE”, Programmist, 2001, no. 12, 17–22

[31] Pirogov V. Yu., Assembler dlya Windows, 3-e izd., BKhV-Peterburg, SPb., 2005, 864 pp.

[32] Voevodin V. V., Voevodin Vl. V., Parallelnye vychisleniya, BKhV-Peterburg, SPb., 2002, 608 pp.

[33] NVIDIA CUDA C Programming Guide, version 4.1, NVIDIA Corp., Santa Clara, 2011, 158 pp. http://www.nvidia.com/cuda

[34] CUDA C Best Practices Guide, version 4.0, NVIDIA Corp., Santa Clara, 2011, 76 pp. http://www.nvidia.com/cuda

[35] Pestryaev E. M., “O periodicheskikh granichnykh usloviyakh dlya tsepnoi molekuly v nereshetochnoi molekulyarnoi dinamike”, Matematicheskoe modelirovanie, 16:2 (2004), 102–110 | Zbl

[36] Boyarchenkov A. S., Potashnikov S. I., “Ispolzovanie graficheskikh protsessorov i tekhnologii CUDA dlya zadach molekulyarnoi dinamiki”, Vychislitelnye metody i programmirovanie, 10 (2009), 9–23 http://num-meth.srcc.msu.ru

[37] Boyarchenkov A. S., Potashnikov S. I., “Parallelnaya molekulyarnaya dinamika s summirovaniem Evalda i integrirovaniem na graficheskikh protsessorakh”, Vychislitelnye metody i programmirovanie, 10 (2009), 158–175 http://num-meth.srcc.msu.ru

[38] Shkvar E., “Effektivnost kompilyatorov: sravnitelnyi test”, Kompyuternoe obozrenie, 2003, no. 49, 1–8 http://itc.ua/articles/jeffektivnost_kompilyatorov_sravnitelnyj_test_15800/

[39] Van Meel J. A., Arnold A., Frenkel D., Zwart S. F. P., Belleman R. G., “Harvesting graphics power for MD simulations”, Mol. Simulat., 34:3 (2008), 259–266 http://cacs.usc.edu/education/cs653/Meel-GPUMD-MolSim08.pdf | DOI

[40] Rapaport D. C., “Enhanced molecular dynamics performance with a programmable graphics processor”, Comp. Phys. Communic., 182:12 (2011), 926–934 http://www.ph.biu.ac.il/r̃apaport/papers/11a-cpc.pdf | DOI | Zbl

[41] Larsson P., Hess B., Lindahl E., “Algorithm improvements for molecular dynamics simulations”, WIREs Comput. Mol. Sci., 1 (2011), 93–108 http://onlinelibrary.wiley.com/doi/10.1002/wcms.v1.3/issuetoc | DOI

[42] Anderson J. A., Lorenz C. D., Travesset A., “General purpose molecular dynamics simulations fully implemented on graphics processing units”, J. Comput. Phys., 227 (2008), 5342–5359 http://codeblue.umich.edu/hoomdblue/downloads/publications/Anderson2008_hoomd_preprint.pdf | DOI | Zbl

[43] Liu W., Schmidt B., Voss G., Muller-Wittig W., “Accelerating molecular dynamics simulations using Graphics Processing Units with CUDA”, Comput. Phys. Communic., 179:5 (2008), 634–641 http://www-micrel.deis.unibo.it/b̃enini/files/MD/MDCuda08.pdf | DOI

[44] Harvey M. J., De Fabritii G., “An Implementation of the Smooth Particle Mesh Ewald Method on GPU Hardware”, J. Chem. Theory Comput., 5:9 (2009), 2371–2377 | DOI

[45] Hardy D. J., Stone J. E., Schuten K., Dufresne E. R., Stinchcombe R., “Multilevel summation of electrostatic potentials using GPUs”, Parallel Comput. E, 35 (2009), 164–177 | DOI

[46] Jha P. K., Sknepnek R., Guerrero-Garcia G. I., de la Cruz M. O., “A Graphics Processing Unit Implementation of Coulomb Interaction in Molecular Dynamics”, J. Chem. Theory Comput., 6:10 (2010), 3058–3065 | DOI

[47] Ruymgaart A. P., Cardenas A. E., Elber R., “MOIL-opt: Energy-Conserving Molecular Dynamics on GPU/CPU System”, J. Chem. Theory Comput., 7:8 (2011), 3072–3082 | DOI

[48] Gross J., Janke W., Bachmann M., Massively parallelized replica-exchange simulations of polymers on GPUs, 2011, 8 pp., arXiv: physics.comp-ph/1107.3490v1

[49] Colberg P. H., Hofling F., Highly accelerated simulations of glassy dynamics using GPUs: caveats on limited floating-point precision, 2011, 12 pp., arXiv: physics.comp-ph/09123824v2

[50] Walters J. P., Balu V., Chaundhary V., Kofke D., Schultz A., Accelerating Molecular Dynamics Simulations with GPUs, , 6 pp. http://www.cse.buffalo.edu/ṽipin/papers/2008/2008_10.pdf

[51] Levine B. G., Stoneb J. E., Kohlmeyera A., Fast Analysis of Molecular Dynamics Trajectories with Graphics Processing Units — Radial Distribution Function Histogramming, , 25 pp. http://www.ks.uiuc.edu/Research/gpu/files/rdfgpu/rdfgpu.pdf

[52] Pestryaev E. M., “Comparison of various correlation times in polymer melts by molecular dynamics simulation”, J. Phys. Conf. Ser., 1324:1 (2011), 012031 http://iopscience.iop.org/1742-6596/324/1/012031 | DOI

[53] http://www.silicontaiga.ru/home.asp?artId=11441

[54] http://www.thg.ru/technews/20110615_182800.html

[55] Morozov I. V., Kazennov A. M., Bystryi R. G., Norman G. E., Pisarev V. V., Stegailov V. V., “Molecular dynamics simulations of the relaxation processes in the condensed matter on GPUs”, Comput. Phys. Communic., 182:12 (2011), 1974–1978 | DOI

[56] Dickson N. G., Karimi K., Hamze F., Importance of Explicit Vectorization for CPU and GPU Software Performance, 17 pp., arXiv: 1004.0024 | MR

[57] Karimi K., Dickson N. G., Hamze F., High-Performance Physics Simulations Using Multi-Core CPUs and GPGPUs in a Volunteer Computing, 15 pp., arXiv: 1004.0023