Optimal additive Schwarz methods for the hphp-BEM: The hypersingular integral operator in 3D on locally refined meshes

We propose and analyze an overlapping Schwarz preconditioner for the pp and hphp 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 hh and the polynomial order pp. 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.