A fast Fourier-Galerkin method for solving singular boundary integral equations

doi:10.1137/070703478

	A fast Fourier-Galerkin method for solving singular boundary integral equations
	Cai, Haotao 2,3; Xu, Yuesheng 1,2
刊名	SIAM JOURNAL ON NUMERICAL ANALYSIS
	2008
卷号	46 期号:4 页码:1965-1984
关键词	singular boundary integral equations Fourier-Galerkin methods fast solutions
ISSN号	0036-1429
DOI	10.1137/070703478
英文摘要	We propose in this paper a convenient way to compress the dense matrix representation of a compact integral operator with a smooth kernel under the Fourier basis. The compression leads to a sparse matrix with only O(n log n) nonzero entries, where 2n or 2n + 1 denotes the order of the matrix. Based on this compression strategy, we develop a fast Fourier-Galerkin method for solving a class of singular boundary integral equations. We prove that the fast Fourier-Galerkin method gives the optimal convergence order O( n(-t)), where t denotes the degree of regularity of the exact solution. Moreover, we design a fast scheme for solving the corresponding truncated linear system. We show that solving this system requires only an O( n log(2) n) number of multiplications. We present numerical examples to confirm the theoretical estimates and to demonstrate the efficiency and accuracy of the proposed algorithm.
WOS研究方向	Mathematics
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000256453400014
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/6039]
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.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 3.Shandong Univ, Dept Math & Stat, Jinan 250002, Peoples R China
推荐引用方式 GB/T 7714	Cai, Haotao,Xu, Yuesheng. A fast Fourier-Galerkin method for solving singular boundary integral equations[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2008,46(4):1965-1984.
APA	Cai, Haotao,&Xu, Yuesheng.(2008).A fast Fourier-Galerkin method for solving singular boundary integral equations.SIAM JOURNAL ON NUMERICAL ANALYSIS,46(4),1965-1984.
MLA	Cai, Haotao,et al."A fast Fourier-Galerkin method for solving singular boundary integral equations".SIAM JOURNAL ON NUMERICAL ANALYSIS 46.4(2008):1965-1984.