物质点法模拟的大规模并行算法

Large Scale Parallel Algorithm for Material Point Method Simulation

【目的】物质点法是一种无网格法,常被用于求解碰撞、侵彻和大变形问题。一方面,为了获得更真实的模拟效果,实际应用场景涉及数亿的物质点和网格,这对存储资源和计算能力提出要求。另一方面,物质点和网格之间频繁的插值,需要综合考虑两者实现任务的划分,而物质点的分布相对于背景网格是不均匀的,设计灵活的划分方式实现任务负载均衡成为问题的关键。基于此,本文设计并实现了物质点法的大规模并行模拟算法。【方法】为了使得进程间的任务量相对均衡,对物质点实现自适应划分设计,然后对网格点上的数据依赖和进程间移动的物质点进行通信设计,最后实现了物质点和网格点耦合的并行。【结果】针对物质点法求解侵彻问题,强扩展性获得80%以上的并行效率。【局限】由于物质点不断在空间移动,对物质点进行动态负载均衡设计可能会获得更好地加速效果。【结论】本文实现了物质点法的三维自适应划分并行设计,获得了良好加速效果,相关的数据依赖分析为之后的动态负载平衡的设计和优化提供参考。

[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.