Additive Schwarz Methods for Weakly Singular Integral Equations In R³ — The P-Version

Summary

We study additive Schwarz preconditioners with and without overlapping subspaces for the p-version of the boundary element method for solving weakly singular integral equations of the first kind in three dimensions. We prove that the condition numbers of both versions, with and without overlapping subspaces, of the additive Schwarz operator P grow not worse than p ^ε where ε is an arbitrary positive constant. Here p is the degree of the polynomials used in the Galerkin boundary element scheme. Numerical experiments underline these theoretical results and demonstrate the applicability of additive Schwarz methods for boundary element schemes in three dimensions.