A COMPARISON OF PRECONDITIONED NONSYMMETRIC KRYLOV METHODS ON A LARGE-SCALE MIMD MACHINE

Many complex physical processes are modeled by coupled systems of part ial differential equations (PDEs). Often, the numerical approximation of these PDEs requires the solution of large sparse nonsymmetric syste ms of equations. In this paper the authors compare the parallel perfor mance of a number of preconditioned Krylov subspace methods on a large -scale multiple instruction multiple data (MIMD) machine. These method s are among the most robust and efficient iterative algorithms tor the solution of large sparse linear systems. In this comparison, the focu s is on parallel issues associated with preconditioners within the gen eralized minimum residual (GMRES). conjugate gradient squared (CGS), b iconjugate gradient stabilized (Bi-CGSTAB), and quasi-minimal residual CGS (QMRCGS) methods. Conclusions are drawn on the effectiveness of t he different schemes based on results obtained from a 1024 processor n CUBE 2 hypercube.