Additive Schwarz preconditioners for a fully-discrete and symmetric boundary element method

Abstract

We discuss various additive Schwarz preconditioners for a fully-discrete and symmetric boundary element method when used to solve a Dirichlet problem in the plane. These preconditioners work in the same way as when they are used for the Galerkin boundary element method: the condition numbers of the preconditioned stiffness matrices grow at most logarithmically with the degree of freedom. Several numerical results are presented to support the theory.