Revenge of the Semicoarsening Frequency Decomposition Multigrid Method

The frequency decomposition multigrid method was previously considered and modified so as to obtain robustness for problems with discontinuous coefficients while retaining robustness for problems with anisotropic coefficients. The application of this modified method to a problem arising in global ocean modeling was also considered. For this problem it was shown that the discretization employed gives rise to an operator for which point relaxation is not robust. In fact, alternating line relaxation is required for robustness, negating the main advantage of the frequency decomposition method: robustness for anisotropic operators using only point relaxation. In this paper a semicoarsening variant, which requires line relaxation in one direction only, is considered, and it is shown that this variant works well for the global ocean modeling problem.