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Record link: 
http://hdl.handle.net/20.500.12708/141183
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Title: 
Stable decompositions of hp-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D
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Citation: 
Karkulik, M., Melenk, J. M., & Rieder, A. (2020). Stable decompositions of hp-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D. ESAIM: Mathematical Modelling and Numerical Analysis, 54(1), 145–180. https://doi.org/10.1051/m2an/2019041
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Publisher DOI: 
10.1051/m2an/2019041
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Publication Type: 
Article - Original Research Article
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Authors: 
Karkulik, Michael 
Melenk, Jens Markus 
Rieder, Alexander 
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Organisational Unit: 
E101-02 - Forschungsbereich Numerik 
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Journal: 
ESAIM: Mathematical Modelling and Numerical Analysis 
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ISSN: 
0764-583X
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Date (published): 
2020
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Number of Pages: 
36
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Peer reviewed: 
Yes
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Keywords: 
Applied Mathematics; Modeling and Simulation; Analysis; Computational Mathematics; Numerical Analysis; hp-FEM; hp-BEM; preconditioning; stable decomposition
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Abstract: 
We consider fractional Sobolev spaces H^(\theta)(\Gamma), \theta \in [0, 1] on a 2D surface Γ. We show that functions in H^(\theta(\Gamma) 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.
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Research Areas: 
Mathematical and Algorithmic Foundations: 80%
Computer Science Foundations: 20%
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Science Branch: 
Mathematik
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