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arXiv · 1412.2024

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

Thomas Führer·Jens Markus Melenk·Dirk Praetorius·Alexander Rieder
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Abstract

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.

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Thomas Führer, Jens Markus Melenk, Dirk Praetorius, Alexander Rieder. 2014-12-05. Optimal additive Schwarz methods for the $hp$-BEM: the hypersingular integral operator in 3D on locally refined meshes. https://doi.org/10.1016/j.camwa.2015.06.025

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