A Domain Decomposition Method Based on BEM and FEM for Linear Exterior Boundary Value Problems1

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 Poincar´e operators are expressed conveniently either by BEM or FEM in order to obtain a symmetric interface problem. The global Steklov Poincar´e 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