A Comparison of Preconditioned Nonsymmetric Krylov Methods on a Large-Scale MIMD Machine

John N. Shadid, Ray S. Tuminaro

Sandia National Laboratories
Albuquerque, New Mexico 87185


Many complex physical processes are modeled by coupled systems of partial differential equations (PDEs). Often, the numerical approximation of these PDEs requires the solution of large sparse nonsymmetric systems of equations. In this paper we compare the parallel performance of a number of preconditioned Krylov subspace methods on a large-scale MIMD machine. These methods are among the most robust and efficient iterative algorithms for the solution of large sparse linear systems. In this comparison we focus on parallel issues associated with preconditioners within the GMRES, CGS, BiCGSTAB, and QMRCGS methods. Conclusions are drawn on the effectiveness of the different schemes based on results obtained from a 1024 processor nCUBE 2 hypercube.