Studies On Parallel Algorithm Of Material Point Method

Material Point Method discretizes material domains by both regular gridand particles. Compared with Lagrangian FEM, MPM avoided numericaldifficulty induced by grid distortion which is common in FEM. And comparedwith Eulerian method, there is no numerical difficulty caused by nonlinearconvective term, and it’s easy for MPM to handle free surface and the materialinterface. As a result of these advantages, MPM is widely used in coupledfluid-solid problem and other dynamic problems that involve largedeformation. However, the computing capablity of common PCs greatlyrestrains the scale of problem that can be solved. When solving large scaleproblems, the bodies are often discretized with insufficient particles and theresults will definitely be very inaccurate. To enlarge the problem scale,parallelization of MPM is required. Meanwhile, load balance strategy alsoneeds to be raised to avoid wasting computing resources.Similar to all methods in which bodies are discretized by both grid andparticles, such as PIC method, the particles of MPM are free to moveanywhere within the grid. This feature will cause great difficulty in achievingload balance. This article addressed some issues in the parallel algorithm ofMPM using MPI or OpenMP and discussed how to furthur improve loadbalance.MPI provides a lot of funtions to pass messages between processes. It ispowerful, flexible but requires a lot of work to implement. In this article, the3D explicit material point method code, MPM3D, is parallelized employingstatic decomposition strategy and is named MPM3D_MPI. The article alsoverifies the correctness and stability of MPM3D_MPI. The parallel programgreatly increases the scale of problems that can be solved.OpenMP is a parallel model based on threads, which mainly uses directives to realize parallelism. We proposed an alternated grid updatingmethod to avoid data races when OpenMP is used in the stage of grid updating.This method can be widely used, easy to implement, easy to realize loadbalance and wastes no memory. Based on this method, MPM3D_OMP isdeveloped. Some examples show that the efficiency of MPM3D_OMP is verygood.