Optimal additive Schwarz methods for the hp-BEM: The hypersingular integral operator in 3D on locally refined meshes. (October 2015) - Führer, T.
Abstract We propose and analyze an overlapping Schwarz preconditioner for the p and hp boundary element method for the hypersingular integral equation in 3D. We consider surface triangulations consisting of triangles. The condition number is bounded uniformly in the mesh size h and the polynomial order p. The preconditioner handles adaptively refined meshes and is based on a local multilevel preconditioner for the lowest order space. Numerical experiments on different geometries illustrate its robustness.