Respectively scaled HSS iteration methods for solving discretized spatial fractional diffusion equations

doi:10.1002/nla.2157

	Respectively scaled HSS iteration methods for solving discretized spatial fractional diffusion equations
	Bai, Zhong-Zhi1,2
	2018-10-01
发表期刊	NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
ISSN	1070-5325
卷号	25 期号:5 页码:18
摘要	For the discrete linear systems resulted from the discretization of the one-dimensional anisotropic spatial fractional diffusion equations of variable coefficients with the shifted finite-difference formulas of the Grunwald-Letnikov type, we propose a class of respectively scaled Hermitian and skew-Hermitian splitting iteration method and establish its asymptotic convergence theory. The corresponding induced matrix splitting preconditioner, through further replacements of the involved Toeplitz matrices with certain circulant matrices, leads to an economic variant that can be executed by fast Fourier transforms. Both theoretical analysis and numerical implementations show that this fast respectively scaled Hermitian and skew-Hermitian splitting preconditioner can significantly improve the computational efficiency of the Krylov subspace iteration methods employed as effective linear solvers for the target discrete linear systems.
关键词	convergence property HSS iteration matrix splitting preconditioning respective scaling spatial fractional diffusion equation
DOI	10.1002/nla.2157
语种	英语
资助项目	National Natural Science Foundation[11671393]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000448861300008
出版者	WILEY
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31635
专题	计算数学与科学工程计算研究所
通讯作者	Bai, Zhong-Zhi
作者单位	1.Chinese Acad Sci, State Key Lab Sci Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, 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. Respectively scaled HSS iteration methods for solving discretized spatial fractional diffusion equations[J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,2018,25(5):18.
APA	Bai, Zhong-Zhi.(2018).Respectively scaled HSS iteration methods for solving discretized spatial fractional diffusion equations.NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,25(5),18.
MLA	Bai, Zhong-Zhi."Respectively scaled HSS iteration methods for solving discretized spatial fractional diffusion equations".NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 25.5(2018):18.