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- Title
Use of the sinh transformation for evaluating 2D nearly singular integrals in 3D BEM.
- Authors
Li, XiaoChao; Zhang, Yaoming; Gong, Yanpeng; Su, Yu; Gao, Xiaowei
- Abstract
This paper presents a new strategy for the numerical evaluation of 2D nearly singular integrals that arise in the solution of 3D BEM using eight-node second-order quadrilateral surface elements. The strategy is an extension of the previous sinh transformation techniques, which is used to evaluate the 1D or 2D nearly singular integrals on simple geometry elements, such as linear or planar elements. The novel feature of the proposed method is that a new distance formula is introduced here, and based on this an ingenious combination of the distance formula and the sinh transformation is developed, and hence, the rapid variation of the distance formula on the integration interval can been smoothed out. Several numerical examples involving boundary layer effect and thin-body problems in 3D potential theory are given to verify the accuracy and efficiency of the presented method.
- Subjects
SINGULAR integrals; BOUNDARY element methods; NUMERICAL analysis; MATHEMATICAL formulas; POTENTIAL theory (Mathematics); MATHEMATICAL transformations
- Publication
Acta Mechanica, 2015, Vol 226, Issue 9, p2873
- ISSN
0001-5970
- Publication type
Article
- DOI
10.1007/s00707-015-1361-z