Applied Mathematics and Mechanics (English Edition) ›› 1988, Vol. 9 ›› Issue (10): 959-967.

• 论文 • 上一篇    下一篇

POLAR COORDINATE TRANSFORMATION APPROACH FOR TREATMENT OF SINGULAR INTEGRALS IN BOUNDARY ELEMENT METHODS

刘勇辉, 陆鑫森   

  1. Shanghai Jiaotong University, Shanghai
  • 收稿日期:1987-09-07 出版日期:1988-10-18 发布日期:1988-10-18

POLAR COORDINATE TRANSFORMATION APPROACH FOR TREATMENT OF SINGULAR INTEGRALS IN BOUNDARY ELEMENT METHODS

Liu Yong-hui, Lu Xin-sen   

  1. Shanghai Jiaotong University, Shanghai
  • Received:1987-09-07 Online:1988-10-18 Published:1988-10-18

摘要: In boundary element methods the treatment of singular integrals, as one of the main numerical problems has been noticed seriously. In this paper, by using polar coordinate transformation for elements a new approach is proposed to remove the singularities in the integrals explicitly. The formulations for treatment of the singularities in quadrilateral boundary elements with four nodes, eight nodes and nine nodes are derived and it can be extended easily to other higher order boundary elements. Numerical examples are given. The results show the present approach is effective and efficient.

Abstract: In boundary element methods the treatment of singular integrals, as one of the main numerical problems has been noticed seriously. In this paper, by using polar coordinate transformation for elements a new approach is proposed to remove the singularities in the integrals explicitly. The formulations for treatment of the singularities in quadrilateral boundary elements with four nodes, eight nodes and nine nodes are derived and it can be extended easily to other higher order boundary elements. Numerical examples are given. The results show the present approach is effective and efficient.

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