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

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.

References in corpus (1)

• Efficient additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations

Cited by in corpus (5)

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• Exponential meshes and $\mathcal{H}$-matrices
• Well-conditioned frames for high order finite element methods