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Fast Fourier-Galerkin methods for first-kind logarithmic-kernel integral equations on open arcs |
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| Authors: | WANG Bo WANG Rui & XU YueSheng Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China School of Information Science Engineering Graduate University of the Chinese Academy of Sciences |
| Institution: | WANG Bo1,WANG Rui2 & XU YueSheng3,4,1Academy of Mathematics , Systems Science,Chinese Academy of Sciences,Beijing 100190,China,2School of Information Science , Engineering,Graduate University of the Chinese Academy of Sciences,3Department of Mathematics,Syracuse University,Syracuse,NY 13244,USA,4Department of Scientific Computing , Computer Applications,Sun Yat-sen University,Guangzhou 510275 |
| Abstract: | 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... |
| Keywords: | Dirichlet problem open arc singular boundary integral equations Fourier-Galerkin methods logarithmic potentials |
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