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Accelerating solidification process simulation for large-sized system of liquid metal atoms using GPU with CUDA. (English) Zbl 1349.82093
Summary: Molecular dynamics simulation is a powerful tool to simulate and analyze complex physical processes and phenomena at atomic characteristic for predicting the natural time-evolution of a system of atoms. Precise simulation of physical processes has strong requirements both in the simulation size and computing timescale. Therefore, finding available computing resources is crucial to accelerate computation. However, a tremendous computational resource (GPGPU) are recently being utilized for general purpose computing due to its high performance of floating-point arithmetic operation, wide memory bandwidth and enhanced programmability. As for the most time-consuming component in MD simulation calculation during the case of studying liquid metal solidification processes, this paper presents a fine-grained spatial decomposition method to accelerate the computation of update of neighbor lists and interaction force calculation by take advantage of modern graphics processors units (GPU), enlarging the scale of the simulation system to a simulation system involving 10 000 000 atoms. In addition, a number of evaluations and tests, ranging from executions on different precision enabled-CUDA versions, over various types of GPU (NVIDIA 480GTX, 580GTX and M2050) to CPU clusters with different number of CPU cores are discussed. The experimental results demonstrate that GPU-based calculations are typically \(9\sim 11\) times faster than the corresponding sequential execution and approximately \(1.5\sim 2\) times faster than 16 CPU cores clusters implementations. On the basis of the simulated results, the comparisons between the theoretical results and the experimental ones are executed, and the good agreement between the two and more complete and larger cluster structures in the actual macroscopic materials are observed. Moreover, different nucleation and evolution mechanism of nano-clusters and nano-crystals formed in the processes of metal solidification is observed with large-sized system.

82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
82D35 Statistical mechanical studies of metals
Full Text: DOI
[1] Alder, B. J.; Wainwright, T. E., Phase transition for a hard sphere system, J. Chem. Phys., 1208-1209, (1957)
[2] Allen, M. P.; Tildesley, D. J., Computer simulation of liquids, (1987), Clarendon Oxford · Zbl 0703.68099
[3] Anderson, J. A.; Lorenz, C. D.; Travesset, A., General purpose molecular dynamics simulations fully implemented on graphics processing units, J. Comput. Phys., 227, 10, 5342-5359, (2008) · Zbl 1148.81301
[4] Friedrichs, M. S.; Eastman, P.; Vaidyanathan, V., Accelerating molecular dynamic simulation on graphics processing units, J. Comput. Chem., 30, 6, 864-872, (2009)
[5] Liu, Weiguo; Schmidt, Bertil; Voss, Gerrit; Muller-witting, Wolfgang, Accelerating molecular dynamics simulations using graphics processing units with CUDA, Comput. Phys. Commun., 179, 634-641, (2008)
[6] Preis, T.; Virnau, P.; Paul, W., GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model, J. Comput. Phys., 228, 12, 4468-4477, (2009) · Zbl 1167.82347
[7] Ren, N.; Liang, J.; Qu, X., GPU-based Monte Carlo simulation for light propagation in complex heterogeneous tissues, Opt. Express, 18, 7, 6811-6823, (2010)
[8] Komura, Y.; Okabe, Y., GPU-based swendsen-Wang multi-cluster algorithm for the simulation of two-dimensional classical spin systems, Comput. Phys. Commun., 183, 6, 1155-1161, (2012)
[9] Liu, R. S., Subqeaks of structure factors for rapidly quenched metals, Phys. Rev. B, 45, 1, 451-453, (1992)
[10] Liu, R. S., Anomalies in the structure factor for some rapidly quenched metals, Phys. Rev. B, 46, 18, 12001-12003, (1992)
[11] Liu, R. S., Formation and description of nano-clusters formed during rapid solidification processes in liquid metals, J. Non-Cryst. Solids, 351, 612-617, (2005)
[12] Liu, R. S., Formation and magic number characteristics of clusters formed during solidification processes, J. Phys. Condens. Matter, 19, 196103, (2007)
[13] Hou, Z. Y., Simulation study on the formation and evolution properties of nano-clusters in rapid solidification structures of sodium, Model. Simul. Mater. Sci. Eng., 15, 911-922, (2007)
[14] Hou, Z. Y., Short-range and medium-range order in ca_7mg_3 metallic Glass, J. Appl. Phys., 107, 083511, (2010)
[15] Dong, K. J., Parallel algorithm of solidification process simulation for large-sized system of liquid metal atoms, Trans. Nonferr. Met. Soc. China, 04, 0824-06, (2003)
[16] Bowers, Kevin J.; Chow, E.; Xu, Huafeng; Dror, Ron O.; Eastwood, Michael P., Scalable algorithms for molecular dynamics simulations on commodity clusters, (ACM/IEEE SCʼ, vol. 06, (2006)), 7695-7700
[17] Macedonia, M., The GPU enters computingʼs mainstream, IEEE Comput., 36, 106-108, (2003)
[18] NVIDIA CUDA Homepage
[19] nVIDIA, NVIDIA CUDA Computer Unified Device Architecture programming Guide Version 2.0, nVIDIA, 2008.
[20] Matinsen, P.; Blaschke, J.; Knnemeyer, R.; Jordan, R., Accelerating Monte Carlo simulations with an NVIDIA@/graphics processor, Comput. Phys. Commun., 180, 10, 1983-1989, (2009)
[21] Januszewski, M.; Kostur, M., Accelerating numerical solution of stochastic differential equations with CUDA, Comput. Phys. Commun., 181, 1, 183-188, (2010) · Zbl 1205.65024
[22] Stone, J. E., Accelerating molecular modeling applications with graphics processors, J. Comput. Chem., 28, 16, 2618-2640, (2007)
[23] Anderson, A. G.; Goddard, W. A.; Schroder, P., Quantum Monte Carlo on graphical processing units, Comput. Phys. Commun., 177, 298-306, (2007) · Zbl 1196.81044
[24] Collange, S.; Daumas, M.; Defour, D., Line-by-line spectroscopy simulations on graphics processing units, Comput. Phys. Commun., 178, 135-143, (2008)
[25] Belleman, R. G.; Bdorf, J.; Portegies Zwart, S. F., High performance direct gravitational N-body simulations on graphics processing units II: an implementation in CUDA, New Astron., 13, 103-112, (2008)
[26] Liu, W.; Schmidt, B.; Voss, G.; Mller-Wittig, W., Streaming algorithms for biological sequence alignment on gpus, IEEE Trans. Parallel Distrib. Syst., 18, 9, 1270-1281, (2007)
[27] Schatz, M. C.; Trapnell, C.; Delcher, A. L.; Varshney, A., High-throughput sequence alignment using graphics processing units, BMC Bioinform., 8, 474, (2007)
[28] Elsen, E.; Vishal, V.; Houston, M., N-body simulations on gpus, (2007)
[29] Wang, S.; Lai, S. K., Structure and electrical resistivities of liquid binary alloys, J. Phys. F, 102717, 2737, (1980)
[30] Li, D. H., Variational calculation of Helmholtz free energies with applications to the sp-type liquid metals, J. Phys. F, 18, 309-321, (1986)
[31] Lai, S. K.; Matsuura, M.; Wang, S., Variational thermodynamic calculation for simple liquid metals and alkali alloys, J. Phys. F, Met. Phys., 13, 10, 2033, (1983)
[32] Nakano, H.; Qi, D. W.; Wang, S., Variational calculations for metastable systems: thermodynamic properties of Glass transitions, J. Chem. Phys., 90, 1871, (1989)
[33] Jin, Z. H.; Lu, K.; Gong, Y. D., Glass transition and atomic structures in supercooled gaznmg metallic liquids: A constant pressure molecular dynamics study, J. Chem. Phys., 106, 8830, (1997)
[34] Allen, M. P., Introduction to molecular dynamics simulation, (Computational Soft Matter-From Synthetic Polymers to Proteins, NIC Series, vol. 23, (2004), John von Neumann Institute for Computing), 1-28
[35] Plimpton, S., Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys., 117, 1-19, (1995) · Zbl 0830.65120
[36] JiXu, Chaofeng Hou; Wang, Peng; Huang, Wenlai; Wang, Xiaowei; Ge, Wei; He, Xianfeng; Guo, Li; Li, Jinghai, Petascale molecular dynamics simulation of crystalline silicon on tianhe-1A, Int. J. High Perform. Comput. Appl., 1-11, (2012)
[37] NVIDIA CUDA compute unified device architecture programming guide (V1.1), (November 2007)
[38] Myung, H. J.; Sakamaki, R.; Oh, K. J., Accelerating molecular dynamics simulation using graphics processing unit, Bull. Korean Chem. Soc., 31, 12, 3639-3643, (2010)
[39] Trott, C. R.; Winterfeld, L.; Crozier, P. S., General-purpose molecular dynamics simulations on GPU-based clusters, (2010)
[40] Lipscomb, T. J.; Zou, A.; Cho, S. S., Parallel Verlet neighbor List algorithm for GPU-optimized MD simulations, (Proceedings of the ACM Conference on Bioinformatics, Computational Biology and Biomedicine, (2012), ACM), 321-328
[41] Shelley, J. C.; Shelley, M. Y.; Reeder, R. C., A coarse grain model for phospholipid simulations, J. Phys. Chem. B, 105, 19, 4464-4470, (2001)
[42] Oh, K. J.; Deng, Y., An efficient parallel implementation of the smooth particle mesh ewald method for molecular dynamics simulations, Comput. Phys. Commun., 177, 5, 426-431, (2007) · Zbl 1196.82059
[43] Oh, K. J.; Klein, M. L., A parallel molecular dynamics simulation scheme for a molecular system with bond constraints in NPT ensemble, Comput. Phys. Commun., 174, 4, 263-269, (2006)
[44] Xian, Wang; Takayuki, Aoki, Multi-GPU performance of incompressible flow computation by lattice Boltzmann method on GPU cluster, Parallel Comput., 37, 521-535, (2011)
[45] Waseda, Y., The structure of non-crystalline materials, vol. 270, (1980), McGraw-Hill New York
[46] Hirata, Akihiko; Guan, Pengfei; Fujita, Takeshi, Direct observation of local atomic order in a metallic Glass, Nat. Mater., 10, 28-33, (2011)
[47] Bhatele, Abhinav; Kumar, Sameer; Mei, Chao; Phillips, James C.; Zheng, Gengbin; Kale, Laxmikant V., Overcoming scaling challenges in biomolecular simulations across multiple platforms, Parallel Distrib. Proc., 1530-2075, (2008)
[48] Spafford, K.; Meredith, J. S.; Vetter, J. S., Quantifying numa and contention effects in multi-gpu systems, (Proceedings of the Fourth Workshop on General Purpose Processing on Graphics Processing Units, (2011), ACM), 11
[49] Chen, L.; Villa, O.; Krishnamoorthy, S., Dynamic load balancing on single-and multi-GPU systems, (IEEE International Symposium on Parallel and Distributed Processing (IPDPS), (2010), IEEE), 1-12
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