Multigrid methods for two- and three-dimensional Poisson-type equations on the sphere (Q750108)

The efficient solution of two- and three-dimensional Poisson-type equations on the sphere with multigrid techniques is considered. The strong anisotropic behavior of the Laplacian in spherical coordinates is efficiently smoothed by using a new technique, called ``combined relaxation''. For three-dimensional problems the use of semi-coarsening is investigated, which should be useful in order to avoid plane- relaxation. The efficiency of the presented method is demonstrated by a compare with a direct fast solver of FISHPAK. In contrast to this direct solver the multigrid method can be applied to more general problems (e.g., for Helmholtz-type equations and 3D problems in spherical coordinates).