An adaptive wavelet collocation method for the solution of partial differential equations on the sphere

A dynamic adaptive numerical method for solving partial differential equations on the sphere is developed. The method is based on second generation spherical wavelets on almost uniform nested spherical triangular grids, and is an extension of the adaptive wavelet collocation method to curved manifolds. Wavelet decomposition is used for grid adaption and interpolation. An O(N) hierarchical finite difference scheme based on the wavelet multilevel …