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Fast cluster techniques for BEM


Krzebek, N; Sauter, S (2003). Fast cluster techniques for BEM. Engineering Analysis with Boundary Elements, 27(5):455-467.

Abstract

In this paper, we will present a new approach for solving boundary integral equations with panel clustering. In contrast to all former versions of panel clustering, the computational and storage complexity of the algorithm scales linearly with respect to the number of degrees of freedom without any additional logarithmic factors. The idea is to develop alternative formulations of all classical boundary integral operators for the Laplace problem where the kernel function has a reduced singular behaviour. It turns out that the application of the panel-clustering method with variable approximation order preserves the asymptotic convergence rate of the discretisation and has significantly reduced complexity.

Abstract

In this paper, we will present a new approach for solving boundary integral equations with panel clustering. In contrast to all former versions of panel clustering, the computational and storage complexity of the algorithm scales linearly with respect to the number of degrees of freedom without any additional logarithmic factors. The idea is to develop alternative formulations of all classical boundary integral operators for the Laplace problem where the kernel function has a reduced singular behaviour. It turns out that the application of the panel-clustering method with variable approximation order preserves the asymptotic convergence rate of the discretisation and has significantly reduced complexity.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Boundary integral equations; Panel-clustering method; Galerkin boundary element method; Alternative representations
Language:English
Date:2003
Deposited On:29 Nov 2010 16:26
Last Modified:19 Feb 2018 21:13
Publisher:Elsevier
ISSN:0955-7997
Additional Information:Copyright © 2003 Published by Elsevier Science Ltd.
OA Status:Green
Publisher DOI:https://doi.org/10.1016/S0955-7997(02)00155-8
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1035.65142

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