T. Führer, J. Melenk, D. Praetorius, A. Rieder:
"Optimal additive Schwarz methods for the hp-BEM: the hypersingular integral operator in 3D on locally refined meshes";
Computers and Mathematics with Applications, 70 (2015), S. 1583 - 1605.

Kurzfassung englisch:
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. We prove a bound for the condition number that is independent of the mesh size h and polynomial order p. Additionally,we provide an extension to adaptive meshes based on a local multilevel preconditioner for the lowest order space. Numerical experiments on different geometries support our theoretical findings.

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