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A sinh transformation for evaluating two-dimensional nearly singular boundary element integrals


Johnston, BM and Johnston, PR and Elliott, D, A sinh transformation for evaluating two-dimensional nearly singular boundary element integrals, International Journal for Numerical Methods in Engineering, 69, (7) pp. 1460-1479. ISSN 0029-5981 (2007) [Refereed Article]

DOI: doi:10.1002/nme.1816


A new transformation technique is introduced for evaluating the two-dimensional nearly singular integrals, which arise in the solution of Laplace's equation in three dimensions, using the boundary element method, when the source point is very close to the element of integration. The integrals are evaluated using (in a product fashion) a transformation which has recently been used to evaluate one-dimensional near singular integrals. This sinh transformation method automatically takes into account the position of the projection of the source point onto the element and also the distance b between the source point and the element. The method is straightforward to implement and, when it is compared with a number of existing techniques for evaluating two-dimensional near singular integrals, it is found that the sinh method is superior to the existing methods considered, both for potential integrals across the full range of b values considered (0<b≤10), and for flux integrals where b>0.01. For smaller values of b, the use of the L1 -1/5 method is recommended for flux integrals. Copyright © 2006 John Wiley & Sons, Ltd.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure mathematics
Research Field:Ordinary differential equations, difference equations and dynamical systems
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:46415
Year Published:2007
Web of Science® Times Cited:82
Deposited By:Mathematics
Deposited On:2007-08-01
Last Modified:2008-06-14

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