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

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.