Fast matrix splitting preconditioners for higher dimensional spatial fractional diffusion equations

doi:10.1016/j.jcp.2019.109117

CSpace

	Fast matrix splitting preconditioners for higher dimensional spatial fractional diffusion equations
	Bai, Zhong-Zhi 1,2; Lu, Kang-Ya 1,2
	2020-03-01
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	404 页码:13
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.
关键词	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
收录类别	SCI
语种	英语
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
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000507854200015
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50577
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.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
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.