SOR as a preconditioner
The paper contains numerical results concerning the use of successive overrelaxation (SOR) as a preconditioner for the nonsymmetric iterative solvers GMRES and BiCGSTAB. As a test example, the authors choose a 2D convection-diffusion equation on the unit square with Dirichlet boundary conditions discretized by standard five-point finite differences for the principal part and centered differences for the first-order derivatives. The numerical findings indicate that for both the lexicographic and the red-black ordering, multiple SOR preconditioning steps with a relaxation parameter \(\omega\) close to the optimal \(\omega_{\text{opt}}\) can reduce the number of iterations by at least a factor of 2. Moreover, the preconditioned nonsymmetric iterative solvers are robust with respect to \(\omega\) in the range \(\omega < \omega_{\text{opt}}\) but exhibit a very strong sensitivity for \(\omega > \omega_{\text{opt}}\).
scientific article; zbMATH DE number 826016