Efficient spectral-galerkin methods IV. spherical geometries

摘要

Fast spectral-Galerkin algorithms are developed for elliptic equations on the sphere. The algorithms are based on a double Fourier expansion and have quasi-optimal (optimal up to a logarithmic term) computational complexity. Numerical experiments indicate that they are significantly more efficient and/or accurate when compared with the algorithms based on spherical harmonics and on finite difference. Extensions to problems in spherical layers and to vector equations are also discussed.