A domain decomposition method based on BEM and FEM for linear exterior boundary value problems

We develop the finite dimensional analysis of a new domain decomposition method for linear exterior boundary value problems arising in potential theory and heat conductivity. Our approach uses a Dirichlet-to-Neumann mapping to transform the exterior problem into an equivalent boundary value problem on a bounded domain. Then the domain is decomposed into a finite number of annular subregions and the local Steklov-Poincare operators arc expressed conveniently either by BEM or FEM in order to obtain a symmetric interface problem. The global Steklov-Poincare problem is solved by using both a Richardson-type scheme and the preconditioned conjugate gradient method, which yield iteration-by-subdomain algorithms well suited for parallel processing. Finally, contractivity results and finite dimensional approximations are provided. (C) 2001 Academic Press.