Volume 54, Number 1, January-February 2020
|Page(s)||145 - 180|
|Published online||27 January 2020|
Stable decompositions of hp-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D
Departamento de Matemática, Universidad Técnica Federico Santa María, Valparaíso, Chile
2 Institut für Analysis und Scientific Computing, Technische Universität Wien, Wien Austria
* Corresponding author: firstname.lastname@example.org
Accepted: 11 June 2019
We consider fractional Sobolev spaces Hθ(Γ), θ∈[0, 1] on a 2D surface Γ. We show that functions in Hθ(Γ) can be decomposed into contributions with local support in a stable way. Stability of the decomposition is inherited by piecewise polynomial subspaces. Applications include the analysis of additive Schwarz preconditioners for discretizations of the hypersingular integral operator by the p-version of the boundary element method with condition number bounds that are uniform in the polynomial degree p.
Mathematics Subject Classification: 65F08 / 65N38 / 41A35
Key words: Preconditioning high order BEM / stable localization / domain decomposition
© EDP Sciences, SMAI 2020
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