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A fast finite volume method for spatial fractional diffusion equations on nonuniform meshes[Formula presented]
Fang, Zhi Wei1; Zhang, Jia Li2; Sun, Hai Wei2
2022-02-15
Source PublicationComputers and Mathematics with Applications
ISSN0898-1221
Volume108Pages:175-184
Abstract

In this paper, a fast finite volume method is proposed for the initial and boundary value problems of spatial fractional diffusion equations on nonuniform meshes. The discretizations of the Riemann-Liouville fractional derivatives lead to unstructured dense coefficient matrices, differing from the Toeplitz-like structure under the uniform mesh. The fast algorithm is proposed by using the sum-of-exponentials (SOE) technique to the spatial kernel x,α∈(0,1). Then, the matrix-vector multiplications of the resulting coefficient matrices could be implemented in O(mlog⁡m) operations, where m denotes the size of matrices. Iterative solvers are preferably applied to obtain the numerical solution. The proposed fast scheme is proved to be unconditionally stable for sufficiently accurate SOE approximation. Meanwhile, a banded preconditioner is exploited to accelerate the Krylov subspace method. Numerical experiments are provided to demonstrate the efficiency of the proposed fast algorithm.

KeywordBanded Preconditioner Fast Algorithm Finite Volume Method Spatial Fractional Diffusion Equations Sum-of-exponentials Technique
DOI10.1016/j.camwa.2022.01.015
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000797889000012
Scopus ID2-s2.0-85123028986
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Citation statistics
Cited Times [WOS]:2   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorFang, Zhi Wei; Zhang, Jia Li; 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
Fang, Zhi Wei,Zhang, Jia Li,Sun, Hai Wei. A fast finite volume method for spatial fractional diffusion equations on nonuniform meshes[Formula presented][J]. Computers and Mathematics with Applications,2022,108:175-184.
APA Fang, Zhi Wei,Zhang, Jia Li,&Sun, Hai Wei.(2022).A fast finite volume method for spatial fractional diffusion equations on nonuniform meshes[Formula presented].Computers and Mathematics with Applications,108,175-184.
MLA Fang, Zhi Wei,et al."A fast finite volume method for spatial fractional diffusion equations on nonuniform meshes[Formula presented]".Computers and Mathematics with Applications 108(2022):175-184.
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