Iterative methods for nonsymmetric systems on MIMD machines.

摘要

A wide variety of physical phenomena arising within many scientific disciplines can be described by systems of coupled partial differential equations (PDEs). The numerical approximation of these PDEs often involves the solution of a system of algebraic equations (possibly nonlinear) which are typically large, sparse and nonsymmetric. The increasing computational demands required by the solution of such complex scientific applications has motivated the current direction toward large-scale parallel computers. We, therefore, consider solution techniques of representative systems of equations on large scale MIMD machines. Our primary emphasis in this study is the evaluation of iterative methods for the solution of nonsymmetric systems. In particular, we discuss two Krylov subspace methods, the conjugate gradient squared algorithm (CGS) and the generalized minimum residual method (GMRES), along with the multigrid algorithm (MG) on massively parallel MIMD architectures. The focus of this evaluation considers the performance of various algorithm and implementation variations over a broad selection of problems using a parallel machine.