Fast Fourier-Galerkin methods for first-kind logarithmic-kernel integral equations on open arcs

doi:10.1007/s11425-010-0014-x

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	Fast Fourier-Galerkin methods for first-kind logarithmic-kernel integral equations on open arcs
	Wang Bo 4; Wang Rui 3; Xu YueSheng 1,2
	2010
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	53 期号:1 页码:1-22
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.
关键词	Dirichlet problem open arc singular boundary integral equations Fourier-Galerkin methods logarithmic potentials
DOI	10.1007/s11425-010-0014-x
语种	英语
资助项目	GUCAS ; US National Science Foundation[CCR-0407476] ; US National Science Foundation[DMS-0712827] ; National Natural Science Foundation of China[10371122] ; National Natural Science Foundation of China[10631080]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000276546200001
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/9982
专题	中国科学院数学与系统科学研究院
通讯作者	Xu YueSheng
作者单位	1.Syracuse Univ, Dept Math, Syracuse, NY 13244 USA 2.Sun Yat Sen Univ, Dept Sci Comp & Comp Applicat, Guangzhou 510275, Guangdong, Peoples R China 3.Chinese Acad Sci, Grad Univ, Sch Informat Sci & Engn, Beijing 100190, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wang Bo,Wang Rui,Xu YueSheng. Fast Fourier-Galerkin methods for first-kind logarithmic-kernel integral equations on open arcs[J]. SCIENCE CHINA-MATHEMATICS,2010,53(1):1-22.
APA	Wang Bo,Wang Rui,&Xu YueSheng.(2010).Fast Fourier-Galerkin methods for first-kind logarithmic-kernel integral equations on open arcs.SCIENCE CHINA-MATHEMATICS,53(1),1-22.
MLA	Wang Bo,et al."Fast Fourier-Galerkin methods for first-kind logarithmic-kernel integral equations on open arcs".SCIENCE CHINA-MATHEMATICS 53.1(2010):1-22.