Iterative Methods for Nonsymmetric Systems on MIMD Machines

John N. Shadid, Ray S. Tuminaro

Sandia National Laboratories
Albuquerque, New Mexico 87185

Abstract
The parallelization of sophisticated applications has dramatically increased in recent years. Many of these applications require solutions to large sparse matrix equations which approximate systems of partial differential equations (PDEs). In this paper we present a comparison of parallel iterative solvers for large sparse nonsymmetric systems. These methods are based on preconditioned Krylov subspace and multigrid techniques. Algorithmic and implementation issues specific to the parallel environment are discussed. Based on numerical experiments, on a 1024 processor nCUBE 2 hypercube, conclusions are drawn about the relative merits of the different methods and preconditioners.