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

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

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Article ID: iaor201527802
Volume: 70
Issue: 7
Start Page Number: 1583
End Page Number: 1605
Publication Date: Oct 2015
Journal: Computers and Mathematics with Applications
Authors: , , ,
Keywords: numerical analysis
Abstract:

We propose and analyze an overlapping Schwarz preconditioner for the p equ1 and h p equ2 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 equ3 and the polynomial order p equ4. 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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