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Transformations for evaluating singular boundary element integrals


Johnston, PR and Elliott, D, Transformations for evaluating singular boundary element integrals, Journal of Computational and Applied Mathematics, 146, (2) pp. 231-251. ISSN 0377-0427 (2002) [Refereed Article]

DOI: doi:10.1016/S0377-0427(02)00357-6


Accurate numerical integration of line integrals is of fundamental importance for the reliable implementation of the boundary element method. Usually, the regular integrals arising from a boundary element method implementation are evaluated using standard Gaussian quadrature. However, the singular integrals which arise are often evaluated in another way, sometimes using a different integration method with different nodes and weights. This paper presents a straightforward transformation to improve the accuracy of evaluating singular integrals. The transformation is, in a sense, a generalisation of the popular method of Telles with the underlying idea being to utilise the same Gaussian quadrature points as used for evaluating nonsingular integrals in a typical boundary element method implementation. The new transformation is also shown to be equivalent to other existing transformations in certain situations. Comparison of the new method with existing coordinate transformation techniques shows that a more accurate evaluation of weakly singular integrals can be obtained. The technique can also be extended to evaluate certain Hadamard finite-part integrals. Based on the observation of several integrals considered, guidelines are suggested for the best transformation order to use (i.e. the degree to which nodes should be clustered near the singular point). © 2002 Elsevier Science B.V. All rights reserved.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Numerical and computational mathematics
Research Field:Numerical analysis
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Elliott, D (Professor David Elliott)
ID Code:24295
Year Published:2002
Web of Science® Times Cited:19
Deposited By:Mathematics
Deposited On:2002-08-01
Last Modified:2011-08-02

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