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

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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.

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
DDC:510 Mathematics
Uncontrolled Keywords:Boundary element method - numerical quadrature - collocation - panel method - cubature
Deposited On:29 Nov 2010 16:29
Last Modified:27 Nov 2013 16:34
Publisher DOI:10.1007/BF02238073
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0799.65028
Citations:Web of Science®. Times Cited: 26
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Scopus®. Citation Count: 27

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