摘要
We propose a fully discrete fast Fourier-Galerkin method for solving an integral equation of the first kind with a logarithmic kernel on a smooth open arc,which is a reformulation of the Dirichlet problem of the Laplace equation in the plane.The optimal convergence order and quasi-linear complexity order of the proposed method are established.A precondition is introduced.Combining this method with an efficient numerical integration algorithm for computing the single-layer potential defined on an open arc,we obtain the solution of the Dirichlet problem on a smooth open arc in the plane.Numerical examples are presented to confirm the theoretical estimates and to demonstrate the efficiency and accuracy of the proposed method.
We propose a fully discrete fast Fourier-Galerkin method for solving an integral equation of the first kind with a logarithmic kernel on a smooth open arc,which is a reformulation of the Dirichlet problem of the Laplace equation in the plane.The optimal convergence order and quasi-linear complexity order of the proposed method are established.A precondition is introduced.Combining this method with an efficient numerical integration algorithm for computing the single-layer potential defined on an open arc,we obtain the solution of the Dirichlet problem on a smooth open arc in the plane.Numerical examples are presented to confirm the theoretical estimates and to demonstrate the efficiency and accuracy of the proposed method.
作者
WANG Bo1,WANG Rui2 & XU YueSheng3,4,1Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China
2School of Information Science and Engineering,Graduate University of the Chinese Academy of Sciences,Beijing 100190,China
3Department of Mathematics,Syracuse University,Syracuse,NY 13244,USA
4Department of Scientific Computing and Computer Applications,Sun Yat-sen University,Guangzhou 510275,China
基金
supported by the President Fund of GUCAS and the US National Science Foundation (Grant No.CCR-0407476,DMS-0712827)
National Natural Science Foundation of China(Grant No.10371122,10631080)
