The Method of Fundamental Solution for the Dirichlet Problem in with the Boundary of the two Spheres

Abstract

In this paper we deal with the method of fundamental solution for the three-dimensional Dirichlet problem, where the fundamental solution of Laplace operator is used. First we construct the arrangement of the collocation points on the spherical surface. We deal with the three problems: the problem of the concentric ring domain, the problem of the non-concentric ring domain, and the problem of the unbounded domain with the boundary of the two spheres. For these problems, we have developed some algorithms by rearranging the singular points. By our algorithms we can obtain the accurate approximation even if the distance of the two spheres is small.