Stable decompositions of $hp$-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2018
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| _version_ | 1866907990054928384 |
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| author | Karkulik, Michael Melenk, Jens Markus Rieder, Alexander |
| author_facet | Karkulik, Michael Melenk, Jens Markus Rieder, Alexander |
| contents | We consider fractional Sobolev spaces $H^θ(Γ)$, $θ\in [0,1]$, on a 2D surface $Γ$. We show that functions in $H^θ(Γ)$ 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 $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_11097 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Stable decompositions of $hp$-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D Karkulik, Michael Melenk, Jens Markus Rieder, Alexander Numerical Analysis 65M38, 65M55, 65F08 We consider fractional Sobolev spaces $H^θ(Γ)$, $θ\in [0,1]$, on a 2D surface $Γ$. We show that functions in $H^θ(Γ)$ 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 $p$. |
| title | Stable decompositions of $hp$-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D |
| topic | Numerical Analysis 65M38, 65M55, 65F08 |
| url | https://arxiv.org/abs/1811.11097 |