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Respectively scaled HSS iteration methods for solving discretized spatial fractional diffusion equations
Bai, Zhong-Zhi1,2
2018-10-01
Source PublicationNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
ISSN1070-5325
Volume25Issue:5Pages:18
AbstractFor 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.
Keywordconvergence property HSS iteration matrix splitting preconditioning respective scaling spatial fractional diffusion equation
DOI10.1002/nla.2157
Language英语
Funding ProjectNational Natural Science Foundation[11671393]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000448861300008
PublisherWILEY
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31635
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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