The distance sinh transformation for the numerical evaluation of nearly singular integrals over curved surface elements

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• 作者：Jiahe Lv (1)
  Yu Miao (1)
  Hongping Zhu (1)
  
• 关键词：Boundary element method ; Nearly singular integrals ; Numerical integration ; Distance function ; Sinh transformation
• 刊名：Computational Mechanics
• 出版年：2014
• 出版时间：February 2014
• 年：2014
• 卷：53
• 期：2
• 页码：359-367
• 全文大小：537 KB
• 作者单位：Jiahe Lv (1)
  Yu Miao (1)
  Hongping Zhu (1)
  
  1. School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan, 430074, China
  
• ISSN：1432-0924

文摘

This paper presents a new transformation termed as the distance sinh transformation for the numerical evaluation of nearly singular integrals arising in 3D BEM. The new transformation is an improvement of the previous sinh transformation. The original sinh transformation is only limited to planar elements. Moreover, when the nearly singular point is located outside the element, results obtained by the original sinh transformation combined with conventional subdivision method are not quite accurate. In the presented work, the sinh transformation combined with the distance function is proposed to overcome the drawbacks of the original sinh transformation. With the improved transformation, nearly singular integrals on the curved surface elements can be accurately calculated. Furthermore, an alternative subdivision method is proposed using an approximate nearly singular point, which is quite simple for programming and accurate results can be obtained. Numerical examples for both curved triangular and quadrangular elements are given to verify the accuracy and efficiency of the presented method.