Parallel Algorithm for 3D Elasticity Problems Based on an Overlapping DD Preconditioner

Abstract

In this paper we are mainly concerned with an additive overlapping domain decomposition (DD) algorithm and it implementation on parallel computers with shared and distributed memory including clusters of workstations. The problem under consideration is the numerical solution of 3D elasticity systems but the main ideas, algorithms and codes are applicable to 3D elliptic boundary value problems with discontinuous coefficients. The system of linear equations which has to be solved after a finite element method discretization is symmetric and positive definite and the Preconditioned Conjugate Gradient method with a preconditioner constructed via Domain Decomposition is used. The algorithm is highly parallelizable. The Message Passing Interface (MPI) standard is used on both shared and distributed memory parallel computer platforms. Results from numerical experiments on two symmetric multiprocessor systems and IBM SP parallel computer with distributed memory are discussed.