Large Scale Parallel Algorithm for Material Point Method Simulation

doi:10.11871/jfdc.issn.2096-742X.2024.05.014

Abstract

Abstract:

[Objective] As a meshless method, the material point method (MPM) is commonly used to solve collision, penetration, and large deformation problems. On the one hand, in order to accomplish more realistic simulation effects, actual application scenarios involve hundreds of millions of material points and grids. On the other hand, frequent interpolation occurs between the material points and grid nodes. Therefore, a comprehensive consideration of both is necessary to achieve task division. Moreover, since material points are inhomogeneous with relation to the background grid, a flexible division method needs to be designed to achieve workload balancing. Based on it, we design and implement the parallel algorithm to achieve large-scale simulation. [Methods] An adaptive partitioning design is used for MPM to achieve a relatively balanced workload between processes. Then, the communication design is carried out for data dependencies on grid points and material points moving between processes. Finally, the parallel coupling of material points and grid points is implemented. [Results] For solving the penetration problem, its parallel efficiency is more than 80% in the strong scalability testing. [Limitations] Due to the continuous movement of material points in space, dynamic load balancing of material points may get better acceleration effects. [Conclusions] We design a parallel algorithm of 3D adaptive partitioning for MPM, which achieves good acceleration effects. The data dependency analysis provides a reference for the design and optimization of dynamic load-balancing strategies in the future.

Key words: material point method, load balancing, 3D parallel, large scale

TIAN Shaobo, LI jialin, ZHANG Jian. Large Scale Parallel Algorithm for Material Point Method Simulation[J]. Frontiers of Data and Computing, 2024, 6(5): 148-158, https://cstr.cn/32002.14.jfdc.CN10-1649/TP.2024.05.014.

Figures/Tables 18

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Algorithm 1: Calculation of momentum and mass:
for each particle p in particle list for grid node n do $m I n ? ← ? m I n + ? m p S I p n$ $p i I n ? ? ← ? p i I n ? + m p v i p n S I p n$ end for

Fig.9

Table 1

Fig.10

Fig.11

Fig.12

Fig.13

Table 2

Fig.14

Table 3

References 23

[1]	HARLOW F H. The particle-in-cell computing method for fluid dynamics[J]. Methods in Computational Physics, 1964, 3(1): 319-343.
[2]	SULSKY D, CHEN Z, SCHREYER H L. A particle method for history-dependent materials[R]. Sandia National Laboratories, 1993.
[3]	GRIGORYEV Y N, VSHIVKOV V A, Fedoruk M P. Numerical "particle-in-cell" methods: theory and applications[M]. de Gruyter, 2002.
[4]	BRACKBILL J U, RUPPEL H M. FLIP: A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions[J]. Journal of Computational Physics, 1986, 65(2): 314-343.
[5]	BRACKBILL J U, KOTHE D B, RUPPEL H M. FLIP: a low-dissipation, particle-in-cell method for fluid flow[J]. Computer Physics Communications, 1988, 48(1): 25-38.
[6]	BRACKBILL J U. The ringing instability in particle-in-cell calculations of low-speed flow[J]. Journal of Computational Physics, 1988, 75(2): 469-492.
[7]	ZHU Y, BRIDSON R. Animating sand as a fluid[J]. ACM Transactions on Graphics, 2005, 24(3): 965-972.
[8]	HU W, CHEN Z. Model-based simulation of the synergistic effects of blast and fragmentation on a concrete wall using the MPM[J]. International Journal of Impact Engineering, 2006, 32(12): 2066-2096.
[9]	ZHANGE D Z, ZOU Q, VANDERHEYDEN W B, et al. Material point method applied to multiphase flows[J]. Journal of Computational Physics, 2008, 227(6): 3159-3173.
[10]	GAO M, PRADHANA A, HAN X, et al. Animating fluid sediment mixture in particle-laden flows[J]. ACM Transactions on Graphics, 2018, 37(4): 1-11.
[11]	GUO Y J, NAIRN J A. Three-dimensional dynamic fracture analysis using the material point method[J]. Computer Modeling in Engineering and Sciences, 2006, 16(3): 141-155.
[12]	WANG S, DING M, GAST T F, et al. Simulation and visualization of ductile fracture with the material point method[J]. Proceedings of the ACM on Computer Graphics and Interactive Techniques, 2019, 2(2): 1-20.
[13]	WOLPER J, FANG Y, LI M, et al. CD-MPM: continuum damage material point methods for dynamic fracture animation[J]. ACM Transactions on Graphics, 2019, 38(4): 1-15.
[14]	WRETBORN J, ARMIENTO R, MUSETHK. Animation of crack propagation by means of an extended multi-body solver for the material point method[J]. Computers & Graphics, 2017, 69(1): 131-139.
[15]	STOMAKHIN A, SCHROEDER C, CHAI L, et al. A material point method for snow simulation[J]. ACM Transactions on Graphics, 2013, 32(4): 1-10.
[16]	MONTAZERI Z, XIAO C, FEI Y, et al. Mechanics-aware modeling of cloth appearance[J]. IEEE Transactions on Visualization and Computer Graphics, 2019, 27(1): 137-150.
[17]	HUANG P, ZHANG X, MA S, et al. Shared memory OpenMP parallelization of explicit MPM and its application to hypervelocity impact[J]. Computer Modeling in Engineering & Sciences, 2008, 38(2): 119-148.
[18]	DONG Y, WANG D, RANDOLPH M F. A GPU parallel computing strategy for the material point method[J]. Computers and Geotechnics, 2015, 66(1): 31-38.
[19]	GAOM, WANG X, WU K, et al. GPU optimization of material point methods[J]. ACM Transactions on Graphics (TOG), 2018, 37(6): 1-12.
[20]	WANG X, QIU Y, SLATTERY S R, et al. A massively parallel and scalable multi-GPU material point method[J]. ACM Transactions on Graphics, 2020, 39(4): 30-45.
[21]	De VAUCORBEIL A, NGUYEN V P, NGUYEN-THANH C. Karamelo: an open source parallel C++ package for the material point method[J]. Computational Particle Mechanics, 2021, 8: 767-789.
[22]	RUGGIRELLO K P, SCHUMACHER S C. A comparison of parallelization strategies for the material point method[C]. 11th World Congress on Computational Mechanics, 2014: 20-25.
[23]	廉艳平, 张帆, 刘岩, 等. 物质点法的理论和应用[J]. 力学进展, 2013, 43(2): 237-264.

类型	软硬件配置
处理器	国产x86处理器
操作系统	Linux Centos
编程语言	C、C++和Fortran等
并行语言	MPI和OpenMP等
主要的依赖软件	Cmake-3.16.2
	Zlib-1.2.7
	Qt-4.8.7
	Vtk-5.10

进程数	最多质点数	时间（ms）	并行效率（%）
1	9,571,888	10731.6	100
4	2,518,780	2708.85	99.0
16	652,048	761.784	88.05
64	225,112	264.525	63.39
256	86,028	96.3567	43.51
1,024	37,750	41.4468	25.29

进程数	时间（ms）	并行效率（%）
64	4418.74	100
128	2211.01	99.93
256	1196.85	92.30
512	620.07	89.08
1,024	341.97	80.76