Fast matrix splitting preconditioners for higher dimensional spatial fractional diffusion equations
文献类型：期刊论文
| 作者 | Bai, Zhong-Zhi1,2; Lu, Kang-Ya1,2 |
| 刊名 | JOURNAL OF COMPUTATIONAL PHYSICS
 |
| 出版日期 | 2020-03-01 |
| 卷号 | 404页码:13 |
| 关键词 | Spatial fractional diffusion equations Shifted finite-difference discretization Block Toeplitz-like matrix Block circulant-like matrix Preconditioning Eigenvalue distribution |
| ISSN号 | 0021-9991 |
| DOI | 10.1016/j.jcp.2019.109117 |
| 英文摘要 | The discretizations of two- and three-dimensional spatial fractional diffusion equations with the shifted finite-difference formulas of the Grunwald-Letnikov type can result in discrete linear systems whose coefficient matrices are of the form D + T, where D is a nonnegative diagonal matrix and T is a block-Toeplitz with Toeplitz-block matrix or a block-Toeplitz with each block being block-Toeplitz with Toeplitz-block matrix. For these discrete spatial fractional diffusion matrices, we construct diagonal and block-circulant with circulant-block splitting preconditioner for the two-dimensional case, and diagonal and block-circulant with each block being block-circulant with circulant-block splitting preconditioner for the three-dimensional case, to further accelerate the convergence rates of Krylov subspace iteration methods, and we analyze the eigenvalue distributions for the corresponding preconditioned matrices. Theoretical results show that except for a small number of outliners the eigenvalues of the preconditioned matrices are located within a complex disk centered at 1 with the radius being exactly less than 1, and numerical experiments demonstrate that these structured preconditioners can significantly improve the convergence behavior of the Krylov subspace iteration methods. Moreover, this approach is superior to the geometric multigrid method and the preconditioned conjugate gradient methods incorporated with the approximate inverse circulant-plusdiagonal preconditioners in both iteration counts and computing times. (C) 2019 Elsevier Inc. All rights reserved. |
| 资助项目 | National Natural Science Foundation, P.R. China[11671393] ; National Natural Science Foundation, P.R. China[11911530082] |
| WOS研究方向 | Computer Science ; Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000507854200015 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/50576]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Bai, Zhong-Zhi |
| 作者单位 | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, POB 2719, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Bai, Zhong-Zhi,Lu, Kang-Ya. Fast matrix splitting preconditioners for higher dimensional spatial fractional diffusion equations[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2020,404:13. |
| APA | Bai, Zhong-Zhi,&Lu, Kang-Ya.(2020).Fast matrix splitting preconditioners for higher dimensional spatial fractional diffusion equations.JOURNAL OF COMPUTATIONAL PHYSICS,404,13. |
| MLA | Bai, Zhong-Zhi,et al."Fast matrix splitting preconditioners for higher dimensional spatial fractional diffusion equations".JOURNAL OF COMPUTATIONAL PHYSICS 404(2020):13. |
入库方式： OAI收割
来源：数学与系统科学研究院
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