Combination of the finite and the boundary element methods for an externalboundary value problem of the Poisson equation

A numerical algorithm for an external Dirichlet problem of the Poisson equa tion is considered. The domain Omega extending to infinity is divided into a bounded subdomain Omega(0) and the unbounded subdomain Omega(1). The fini te and the boundary element methods are applied to the boundary value probl ems in the bounded and the unbounded subdomains, respectively. An iterative scheme using the Dirichlet-Neumann map on the interface partial derivative Omega(1) is presented. The convergence of the scheme is mathematically gua ranteed. A simple numerical example shows the effectiveness of our scheme.