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The Sinh Transformation for Curved Elements Using the General Distance Function

J.H. Lv1, Y. Miao1,2, W.H. Gong1, H.P. Zhu1
School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China
Corresponding Author. Tel: 86 27 87540172; Fax: 86 27 87542231; Y. Miao Email:

Computer Modeling in Engineering & Sciences 2013, 93(2), 113-131.


Accurate numerical evaluation of the nearly singular boundary integrals is a major concerned issue in the implementation of boundary element method (BEM). In this paper, a general distance function independent on the nearly singular point is proposed. Combined with an iteration process, the position of the nearly singular point can be obtained more easily. Then, an extended form of the sinh transformation using the general distance function, which automatically takes into account the intrinsic coordinate of the nearly singular point and the minimum distance from source point to the element in the intrinsic parameter plane, is developed to deal with the nearly singular integrals. The iterated sinh transformation can also be achieved in a straightforward fashion. Results obtained by the one and two iterations of sinh transformation for various orders of singularities demonstrate the high efficiency and accuracy of presented method. Comparisons with other variable transformation methods are also carried out to show the superiority of the presented method.


Boundary element method, Nearly singular integrals, Sinh transformation, Distance transformation.

Cite This Article

Lv, J., Miao, Y., Gong, W., Zhu, H. (2013). The Sinh Transformation for Curved Elements Using the General Distance Function. CMES-Computer Modeling in Engineering & Sciences, 93(2), 113–131.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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