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Volume 22, Issue 2
A Fast Numerical Method for Integral Equations of the First Kind with Logarithmic Kernel Using Mesh Grading

Qiyuan Chen, Tao Tang & Zhenhuan Teng

J. Comp. Math., 22 (2004), pp. 287-298.

Published online: 2004-04

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  • Abstract

 The aim of this paper is to develop a fast numerical method for two-dimensional boundary integral equations of the first kind with logarithm kernels when the boundary of the domain is smooth and closed. In this case, the use of the conventional boundary element methods gives linear systems with dense matrix. In this paper, we demonstrate that the dense matrix can be replaced by a sparse one if appropriate graded meshes are used in the quadrature rules. It will be demonstrated that this technique can increase the numerical efficiency significantly.  

  • Keywords

Integral equations, Mesh grading, Fast numerical method.

  • AMS Subject Headings

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-287, author = {Chen , QiyuanTang , Tao and Teng , Zhenhuan}, title = {A Fast Numerical Method for Integral Equations of the First Kind with Logarithmic Kernel Using Mesh Grading}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {2}, pages = {287--298}, abstract = {

 The aim of this paper is to develop a fast numerical method for two-dimensional boundary integral equations of the first kind with logarithm kernels when the boundary of the domain is smooth and closed. In this case, the use of the conventional boundary element methods gives linear systems with dense matrix. In this paper, we demonstrate that the dense matrix can be replaced by a sparse one if appropriate graded meshes are used in the quadrature rules. It will be demonstrated that this technique can increase the numerical efficiency significantly.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10329.html} }
TY - JOUR T1 - A Fast Numerical Method for Integral Equations of the First Kind with Logarithmic Kernel Using Mesh Grading AU - Chen , Qiyuan AU - Tang , Tao AU - Teng , Zhenhuan JO - Journal of Computational Mathematics VL - 2 SP - 287 EP - 298 PY - 2004 DA - 2004/04 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10329.html KW - Integral equations, Mesh grading, Fast numerical method. AB -

 The aim of this paper is to develop a fast numerical method for two-dimensional boundary integral equations of the first kind with logarithm kernels when the boundary of the domain is smooth and closed. In this case, the use of the conventional boundary element methods gives linear systems with dense matrix. In this paper, we demonstrate that the dense matrix can be replaced by a sparse one if appropriate graded meshes are used in the quadrature rules. It will be demonstrated that this technique can increase the numerical efficiency significantly.  

Chen , QiyuanTang , Tao and Teng , Zhenhuan. (2004). A Fast Numerical Method for Integral Equations of the First Kind with Logarithmic Kernel Using Mesh Grading. Journal of Computational Mathematics. 22 (2). 287-298. doi:
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