This paper focuses on the practical applications of the multigrid residual scaling techniques and is the continuation of an earlier companion paper: Residual scaling techniques in multigrid, I: equivalence proof (to appear in Applied Mathematics and Computation). We discuss the computational issues of some residual scaling techniques which have been proved mathematically equivalent in the companion paper. A heuristic residual analysis technique, based on the geometry of the grid points and the relaxation pattern, is introduced to estimate the optimal residual scaling factor for a high-order multigrid method. We compare the performance of a typical pre-optimization (pre-acceleration) technique with a typical post-optimization (post-acceleration) technique and show that the pre-optimization is preferable in both convergence and efficiency. Our numerical results support the theoretical conclusions made in the companion paper and demonstrate the full advantage of the pre-optimization technique over the post-optimization technique.
Key words and phrases: Multigrid method, minimal residual smoothing, residual scaling techniques, heuristic residual analysis.