A fast Fourier-Galerkin method for solving singular boundary integral equations | |
Cai, Haotao2,3; Xu, Yuesheng1,2 | |
刊名 | SIAM JOURNAL ON NUMERICAL ANALYSIS
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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. |
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