| Issue |
ESAIM: M2AN
Volume 54, Number 1, January-February 2020
|
|
|---|---|---|
| Page(s) | 145 - 180 | |
| DOI | https://doi.org/10.1051/m2an/2019041 | |
| Published online | 27 January 2020 | |
Stable decompositions of hp-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D
1
Departamento de Matemática, Universidad Técnica Federico Santa María, Valparaíso, Chile
2
Institut für Analysis und Scientific Computing, Technische Universität Wien, Wien Austria
* Corresponding author: alexander.rieder@tuwien.ac.at
Received:
27
November
2018
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.