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Splitting preconditioning based on sine transform for time-dependent Riesz space fractional diffusion equations
Lu,Xin1; Fang,Zhi Wei1; Sun,Hai Wei2
2021-06
Source PublicationJournal of Applied Mathematics and Computing
ISSN1598-5865
Volume66Issue:1-2Pages:673–700
Abstract

We study the sine-transform-based splitting preconditioning technique for the linear systems arising in the numerical discretization of time-dependent one dimensional and two dimensional Riesz space fractional diffusion equations. Those linear systems are Toeplitz-like. By making use of diagonal-plus-Toeplitz splitting iteration technique, a sine-transform-based splitting preconditioner is proposed to accelerate the convergence rate efficiently when the Krylov subspace method is implemented. Theoretically, we prove that the spectrum of the preconditioned matrix of the proposed method is clustering around 1. In practical computations, by the fast sine transform the computational complexity at each time level can be done in O(nlog n) operations where n is the matrix size. Numerical examples are presented to illustrate the effectiveness of the proposed algorithm.

KeywordGmres Method Riesz Space Fractional Diffusion Equations Shifted Grünwald Discretization Sine-transform-based Splitting Preconditioner Symmetric Positive Definite Toeplitz Matrix
DOI10.1007/s12190-020-01454-0
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000583120300002
PublisherSPRINGER HEIDELBERG, TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY
Scopus ID2-s2.0-85094831533
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorLu,Xin; Fang,Zhi Wei; Sun,Hai Wei
Affiliation1.School of Mathematics and Big Data,Foshan University,Foshan,528000,China
2.Department of Mathematics,University of Macau,Macao
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Lu,Xin,Fang,Zhi Wei,Sun,Hai Wei. Splitting preconditioning based on sine transform for time-dependent Riesz space fractional diffusion equations[J]. Journal of Applied Mathematics and Computing,2021,66(1-2):673–700.
APA Lu,Xin,Fang,Zhi Wei,&Sun,Hai Wei.(2021).Splitting preconditioning based on sine transform for time-dependent Riesz space fractional diffusion equations.Journal of Applied Mathematics and Computing,66(1-2),673–700.
MLA Lu,Xin,et al."Splitting preconditioning based on sine transform for time-dependent Riesz space fractional diffusion equations".Journal of Applied Mathematics and Computing 66.1-2(2021):673–700.
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