KMS Of Academy of mathematics and systems sciences, CAS
| Fast matrix splitting preconditioners for higher dimensional spatial fractional diffusion equations | |
| Bai, Zhong-Zhi1,2; Lu, Kang-Ya1,2 | |
| 2020-03-01 | |
| Source Publication | JOURNAL OF COMPUTATIONAL PHYSICS
 |
| ISSN | 0021-9991 |
| Volume | 404Pages:13 |
| Abstract | 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. |
| Keyword | Spatial fractional diffusion equations Shifted finite-difference discretization Block Toeplitz-like matrix Block circulant-like matrix Preconditioning Eigenvalue distribution |
| DOI | 10.1016/j.jcp.2019.109117 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation, P.R. China[11671393] ; National Natural Science Foundation, P.R. China[11911530082] |
| WOS Research Area | Computer Science ; Physics |
| WOS Subject | Computer Science, Interdisciplinary Applications ; Physics, Mathematical |
| WOS ID | WOS:000507854200015 |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/50577 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Bai, Zhong-Zhi |
| Affiliation | 1.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 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| Recommended Citation 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. |
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