Overlapping additive Schwarz preconditioners for boundary element methods

Abstract

We study overlapping additive Schwarz preconditioners for the Galerkin boundary element method when used to solve Neumann problems for the Laplacian. Both the h and p versions of the Galerkin scheme are considered. We prove that the condition number of the additive Schwarz operator is bounded by O(1 + log2(H/δ)) for the h version, where H is the size of the coarse mesh and d is the size of the overlap, and bounded independently of the mesh size and the polynomial order for the p version.