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.
@article{arxiv.1412.2024,
title = {Optimal additive Schwarz methods for the $hp$-BEM: the hypersingular integral operator in 3D on locally refined meshes},
author = {Thomas Führer and Jens Markus Melenk and Dirk Praetorius and Alexander Rieder},
journal= {arXiv preprint arXiv:1412.2024},
year = {2015}
}