Performance and Scalability of Finite Element Analysis for Distributed Parallel Computation

Abstract

A two dimensional (h; p) finite element scheme for distributed parallel computation is developed. The approach is based on an element - by - element domain decomposition and is implemented on the NCUBE2 system. Example problems are used to demonstrate performance of the algorithm for a range of (h; p) and to validate a run-time model. The run-time model is then used to examine the scaling properties of conjugate gradients and the (h; p) FEM over a range of p. 1 Introduction Recently, considerable attention has been focused on the performance of iterative methods for solving standard finite difference and element discretizations on distributed memory multiprocessors. This includes both gradient type methods, such as conjugate gradients (CG), and multigrid methods (MG). Parallel schemes based on Domain Decomposition and block iteration have also been extensively investigated. Recent studies of such methods can be found in [4, 6, 9]. However, comparatively little has been done to date wi..