Optimal additive Schwarz methods for the $hp$-BEM: the hypersingular   integral operator in 3D on locally refined meshes
  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. 
Thomas F\"uhrer, Jens Markus Melenk, Dirk Praetorius, Alexander Rieder
math.NA