Meshless BEM and overlapping Schwarz preconditioners for exterior problems on spheroids

Abstract

We consider the exterior Neumann problem of the Laplacian with boundary condition on spheroids. We propose to use spherical radial basis functions in the solution of the boundary integral equation arising from the Dirichlet-to-Neumann map. Our meshless approach with radial basis functions is particularly suitable for handling scattered satellite data. We also propose a preconditioning technique based on an overlapping domain decomposition method to deal with ill-conditioned matrices arising from the approximation problem.