Optimal additive Schwarz methods for the hp-BEM: The hypersingular integral operator in 3D on locally refined meshes. (October 2015) - Führer, T.; Melenk, J.M.; Praetorius, D.; Rieder, A.
Abstract We propose and analyze an overlapping Schwarz preconditioner for the <alternatives><inline-graphic xlink:href="ark:/27927/pgj2nc5m425" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />p</alternatives> and <alternatives><inline-graphic xlink:href="ark:/27927/pgj2nc5n123" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />hp</alternatives> 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 <alternatives><inline-graphic xlink:href="ark:/27927/pgj2nc5t445" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />h</alternatives> and the polynomial order <alternatives><inline-graphic xlink:href="ark:/27927/pgj2nc5m425" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />p</alternatives>. 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.