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

By Barbara M. Johnston, Peter R. Johnston, David Elliott. 2007

116 citations recorded by the source corpus.

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 (00.01. For smaller values of b, the use of the L  1‐1/5 method is recommended for flux integrals. Copyright © 2006 John Wiley & Sons, Ltd.

Subfields: Mechanics of Materials, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/478c172e0b13154f1dffebaf080ffcf297a5d2f2

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In Mechanics of Materials

1. Yan Gu
2. Wen Chen
3. Chuanzeng Zhang
4. Zhuojia Fu
5. Wenzhen Qu
6. Jinyang Zhang
7. Hongwei Gao

In Statistics and Probability

1. Yan Gu
2. Wen Chen
3. Chuanzeng Zhang

Citations in the corpus

• The sinh transformation for evaluating nearly singular boundary element integrals over high-order geometry elements (2013, methodology): “[16,17,21] for further details.”