Parallelization Strategies for Element-by-Element Preconditioned Conjugate Gradient Solver Using High-Performance Fortran for Unstructured Finite-Element Applications on Linux Clusters

Abstract

Parallel implementation of an unstructured finite-element solver using the preconditioned conjugate gradient (PCG) method is described here. High-performance Fortran has been used with the implementation based on a 32-node Pentium II 350MHz cluster running Linux. The PCG solver is set up for the element-by-element method. While this is a highly suitable method for the solution of very large problems, it is not inherently parallelizable in a distributed memory environment. The difficulties associated with the parallelization of this algorithm are presented here, as well as two ways to overcome them in this environment. Initial results have been presented for fairly large problems ranging from 500,000 to 1.6 million unknowns using an eight-noded isoparametric quadrilateral element.