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

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 the authors compare the parallel performance of a number of preconditioned Krylov subspace methods on a large-scale multiple instruction multiple data (MIMD) machine. These methods are among the most robust and efficient iterative algorithms for the solution of large sparse linear systems. In this comparison, the focus is on parallel issues associated with preconditioners within the generalized minimum residual (GMRES), conjugate gradient squared (CGS), biconjugate gradient stabilized (Bi-CGSTAB), and quasi-minimal residual CGS (QMRCGS) methods. Conclusions are drawn on the effectiveness of the different schemes based on results obtained from a 1024 processor nCUBE 2 hypercube.