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On numerical cubatures of nearly singular surface integrals arising in BEM collocation


Hackbusch, W; Sauter, S (1994). On numerical cubatures of nearly singular surface integrals arising in BEM collocation. Computing, 52(2):139-159.

Abstract

In this paper we present efficient methods to approximate nearly singular surface integrals arising massively when discretizing boundary integral equations via the collocation method. The idea is to introduce local polar coordinates centred at a corner of the triangle. Thus it is possible to perform the inner integration analytically, either using a numerically stable evaluation of the corresponding formulae or replacing them quite efficiently by simple (rational) approximations. We show how the outer integration can be performed by simple Gauss-Legendre quadrature and how to adapt the order of the Gauss formulae to a required order of consistency. Numerical tests highlight the efficiency of our method.

In this paper we present efficient methods to approximate nearly singular surface integrals arising massively when discretizing boundary integral equations via the collocation method. The idea is to introduce local polar coordinates centred at a corner of the triangle. Thus it is possible to perform the inner integration analytically, either using a numerically stable evaluation of the corresponding formulae or replacing them quite efficiently by simple (rational) approximations. We show how the outer integration can be performed by simple Gauss-Legendre quadrature and how to adapt the order of the Gauss formulae to a required order of consistency. Numerical tests highlight the efficiency of our method.

Citations

29 citations in Web of Science®
32 citations in Scopus®
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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 element method - numerical quadrature - collocation - panel method - cubature
Language:English
Date:1994
Deposited On:29 Nov 2010 16:29
Last Modified:05 Apr 2016 13:28
Publisher:Springer
ISSN:0010-485X
Publisher DOI:10.1007/BF02238073
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0799.65028

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