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A circulant preconditioner for the Riesz distributed-order space-fractional diffusion equations
Huang,Xin; Fang,Zhi Wei; Sun,Hai Wei; Zhang,Chun Hua
2022-09
Source PublicationLinear and Multilinear Algebra
ISSN0308-1087
Abstract

In this paper, we study a fast algorithm for the numerical solution of the 1D distributed-order space-fractional diffusion equation. After discretization by the finite difference method, the resulting system is the symmetric positive definite Toeplitz matrix. The preconditioned conjugate gradient method with a circulant preconditioner is employed to solve the linear system. Theoretically, the spectrum of the preconditioned matrix is proved to be clustered around 1, which can guarantee the superlinear convergence rate of the proposed method. Numerical experiments are carried out to demonstrate the effectiveness of our proposed method.

KeywordCirculant Preconditioner Distributed-order Preconditioned Conjugated Gradient Method Space-fractional Diffusion Equations
DOI10.1080/03081087.2020.1823309
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000572232100001
PublisherTAYLOR & FRANCIS LTD2-4 PARK SQUARE, MILTON PARK, ABINGDON OR14 4RN, OXON, ENGLAND
Scopus ID2-s2.0-85091360573
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Cited Times [WOS]:5   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorSun,Hai Wei
AffiliationDepartment of Mathematics,University of Macau,Macao
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Huang,Xin,Fang,Zhi Wei,Sun,Hai Wei,et al. A circulant preconditioner for the Riesz distributed-order space-fractional diffusion equations[J]. Linear and Multilinear Algebra,2022.
APA Huang,Xin,Fang,Zhi Wei,Sun,Hai Wei,&Zhang,Chun Hua.(2022).A circulant preconditioner for the Riesz distributed-order space-fractional diffusion equations.Linear and Multilinear Algebra.
MLA Huang,Xin,et al."A circulant preconditioner for the Riesz distributed-order space-fractional diffusion equations".Linear and Multilinear Algebra (2022).
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