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

doi:10.1137/070703478

CSpace

	A fast Fourier-Galerkin method for solving singular boundary integral equations
	Cai, Haotao 2,3; Xu, Yuesheng 1,2
	2008
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	46 期号:4 页码:1965-1984
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.
关键词	singular boundary integral equations Fourier-Galerkin methods fast solutions
DOI	10.1137/070703478
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000256453400014
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6040
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.