Parallelization of FDM/FEM computation for PDEs on PARAM YUVA-II cluster of Xeon Phi coprocessors

Sonia Rani, V. C. V. Rao, Samrit Kumar Maity, Krishan Gopal Gupta
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引用次数: 4

Abstract

This paper discusses an efficient implementation of finite difference method (FDM) and finite element method (FEM) computations for Partial Differential Equation (Poisson Equation) on a message passing cluster with Intel Xeon Phi coprocessors[6,15]. We have performed computations on PARAM YUVA-II [9] which is a message passing cluster with compute nodes as Xeon multi-core processors and Xeon Phi coprocessors [6,15,17-19]. A combination of OpenMP [4] and MPI [5,19,20] is used for structured grid FDM computations. The unstructured triangular and hexahedral meshes and graph partitioning software METIS [10] are used in FEM computations. The Jacobi iterative method is used to solve resulting matrix system of linear equations. A detailed performance analysis of optimizations on Xeon Phi coprocessor using OpenMP and MPI framework are presented. Our experiments indicate that MPI-OpenMP codes on FDM computations achieve 2X to 3X speed-ups for large mesh sizes. The FEM implementation has shown marginal improvement in speed-up on Xeon Phi Cluster.
Xeon Phi协处理器PARAM YUVA-II集群上PDEs的FDM/FEM并行化
本文讨论了在使用Intel Xeon Phi协处理器的消息传递集群上对偏微分方程(泊松方程)进行有限差分法(FDM)和有限元法(FEM)计算的有效实现[6,15]。我们已经在PARAM YUVA-II上进行了计算[9],这是一个消息传递集群,计算节点作为Xeon多核处理器和Xeon Phi协处理器[6,15,17-19]。OpenMP[4]和MPI[5,19,20]的组合用于结构化网格FDM计算。有限元计算采用非结构化三角形和六面体网格及图形划分软件METIS[10]。采用雅可比迭代法求解线性方程组的矩阵系统。详细分析了基于OpenMP和MPI框架的Xeon Phi协处理器的性能优化。我们的实验表明,MPI-OpenMP代码在FDM计算上实现了2到3倍的大网格尺寸加速。FEM实现在Xeon Phi集群上的加速性能有了微小的提高。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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