A fast Fourier-Galerkin method for solving singular boundary integral equations
文献类型：期刊论文
| 作者 | Cai, Haotao2,3; Xu, Yuesheng1,2 |
| 刊名 | SIAM JOURNAL ON NUMERICAL ANALYSIS
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000256453400014 |
| 出版者 | SIAM PUBLICATIONS |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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