Parallel Finite Element Domain Decomposition for Structural/Acoustic Analysis

Abstract

A domain decomposition (DD) formulation for solving sparse linear systems of equations resulting from finite element analysis is presented. The formulation incorporates mixed direct and iterative equation solving strategies and other novel algorithmic ideas that are optimized to take advantage of sparsity and exploit modern computer architecture, such as memory and parallel computing. The most time consuming part of the formulation is identified and the critical roles of direct sparse and iterative solvers within the framework of the formulation are discussed. Experiments on several computer platforms using real and complex test matrices are conducted using software based on the formulation. Small-scale structural examples are used to validate the steps in the formulation and large-scale (1,000,000+ unknowns) duct acoustic examples are used to evaluate the parallel performance of the formulation. Results are presented using 64 SUN 10000, 8 SGI ORIGIN 2000 processors, and a cluster of 6 PCs (running under the Windows environment). Statistics show that the formulation is efficient in both sequential and parallel computing environments and that the formulation is significantly faster and consumes less memory than that based on one of the best available commercialized parallel sparse solvers.