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A preconditioner based on sine transform for two-dimensional semi-linear Riesz space fractional diffusion equations in convex domains
Huang, Xin; Sun, Hai Wei
2021-11-01
Source PublicationApplied Numerical Mathematics
ISSN0168-9274
Volume169Pages:289-302
Abstract

In this paper, we develop a fast numerical method for solving the time-dependent Riesz space fractional diffusion equations with a nonlinear source term in the convex domain. An implicit finite difference method is employed to discretize the Riesz space fractional diffusion equations with a penalty term in a rectangular region by the volume-penalization approach. The stability and the convergence of the proposed method are studied. As the coefficient matrix is with the Toeplitz-like structure, the generalized minimum residual method with a preconditioner based on the sine transform is exploited to solve the discretized linear system, where the preconditioner is constructed in view of the combination of two approximate inverse τ matrices, which can be diagonalized by the sine transform. The spectrum of the preconditioned matrix is also investigated. Numerical experiments are carried out to demonstrate the efficiency of the proposed method.

KeywordGmres Method Penalization Riesz Fractional Derivative Sine Transform Based Preconditioner Toeplitz Matrix
DOI10.1016/j.apnum.2021.07.003
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000684227000017
Scopus ID2-s2.0-85110553032
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Cited Times [WOS]:3   [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,Sun, Hai Wei. A preconditioner based on sine transform for two-dimensional semi-linear Riesz space fractional diffusion equations in convex domains[J]. Applied Numerical Mathematics,2021,169:289-302.
APA Huang, Xin,&Sun, Hai Wei.(2021).A preconditioner based on sine transform for two-dimensional semi-linear Riesz space fractional diffusion equations in convex domains.Applied Numerical Mathematics,169,289-302.
MLA Huang, Xin,et al."A preconditioner based on sine transform for two-dimensional semi-linear Riesz space fractional diffusion equations in convex domains".Applied Numerical Mathematics 169(2021):289-302.
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