SOR as a Preconditioner

Abstract

We show by experimental results on some convection-diffusion type equations that the SOR iteration may be a promising preconditioner in conjunction with the GMRES method. Our results indicate that it is critical to take several Gauss-Seidel or SOR iterations, rather than just one, and that at least a factor of two improvement over Gauss-Seidel can be expected with a reasonable approximation to the optimal omega. This approximation must be on the low side of the optimum, however, as an omega only slightly too large can lead to no convergence. We also show that the red/black ordering leads to no degradation and is usually slightly beneficial. Thus, we expect good parallel results although the current experiments are only on a serial machine. Limited experiments with BiCGSTAB do not show similar improvements for Gauss-Seidel preconditioning although a suitable omega can give a factor of two speedup.