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 - <p style="text-align: justify;">&nbsp;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. &nbsp;</p>