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BEM with linear complexity for the classical boundary integral operators


Börm, S; Sauter, S (2005). BEM with linear complexity for the classical boundary integral operators. Mathematics of Computation, 74(251):1139-1177 (electronic).

Abstract

Alternative representations of boundary integral operators corresponding to elliptic boundary value problems are developed as a starting point for numerical approximations as, e.g., Galerkin boundary elements including numerical quadrature and panel-clustering. These representations have the advantage that the integrands of the integral operators have a reduced singular behaviour allowing one to choose the order of the numerical approximations much lower than for the classical formulations. Low-order discretisations for the single layer integral equations as well as for the classical double layer potential and the hypersingular integral equation are considered. We will present fully discrete Galerkin boundary element methods where the storage amount and the CPU time grow only linearly with respect to the number of unknowns.

Abstract

Alternative representations of boundary integral operators corresponding to elliptic boundary value problems are developed as a starting point for numerical approximations as, e.g., Galerkin boundary elements including numerical quadrature and panel-clustering. These representations have the advantage that the integrands of the integral operators have a reduced singular behaviour allowing one to choose the order of the numerical approximations much lower than for the classical formulations. Low-order discretisations for the single layer integral equations as well as for the classical double layer potential and the hypersingular integral equation are considered. We will present fully discrete Galerkin boundary element methods where the storage amount and the CPU time grow only linearly with respect to the number of unknowns.

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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
Language:English
Date:2005
Deposited On:03 Feb 2010 08:03
Last Modified:06 Dec 2017 20:46
Publisher:American Mathematical Society
ISSN:0025-5718
Additional Information:First published in [Math. Comp. 74 (2005), no. 251], published by the American Mathematical Society
Publisher DOI:https://doi.org/10.1090/S0025-5718-04-01733-8

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