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

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Johnston, BM and Johnston, PR and Elliott, D (2007) 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

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Abstract

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<b10), and for flux integrals where b>0.01. For smaller values of b, the use of the L−1/5
1 method is
recommended for flux integrals.

Item Type: Article
Journal or Publication Title: International Journal for Numerical Methods in Engineering
Publisher: John Wiley & Sons Ltd
Page Range: pp. 1460-1479
ISSN: 0029-5981
Identification Number - DOI: 10.1002/nme.1816
Additional Information:

The original publication is available at
http://www.interscience.wiley.com/

Date Deposited: 07 Apr 2008 14:31
Last Modified: 20 Aug 2008 01:27
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