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Multilevel circulant preconditioner for high-dimensional fractional diffusion equations
Lei S.-L.; Chen X.; Zhang X.
2016-05-01
Source PublicationEast Asian Journal on Applied Mathematics
ISSN20797370 20797362
Volume6Issue:2Pages:109-130
Abstract

High-dimensional two-sided space fractional diffusion equations with variable diffusion coefficients are discussed. The problems can be solved by an implicit finite difference scheme that is proven to be uniquely solvable, unconditionally stable and first-order convergent in the infinity norm. A nonsingular multilevel circulant preconditoner is proposed to accelerate the convergence rate of the Krylov subspace linear system solver efficiently. The preconditoned matrix for fast convergence is a sum of the identity matrix, a matrix with small norm, and a matrix with low rank under certain conditions. Moreover, the preconditioner is practical, with an O(N logN) operation cost and O(N) memory requirement. Illustrative numerical examples are also presented.

KeywordGmres Method High-dimensional Two-sided Fractional Diffusion Equation Implicit Finite Difference Method Multilevel Circulant Preconditioner Unconditionally Stable
DOI10.4208/eajam.060815.180116a
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000376171200001
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Citation statistics
Cited Times [WOS]:18   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
AffiliationUniversidade de Macau
Recommended Citation
GB/T 7714
Lei S.-L.,Chen X.,Zhang X.. Multilevel circulant preconditioner for high-dimensional fractional diffusion equations[J]. East Asian Journal on Applied Mathematics,2016,6(2):109-130.
APA Lei S.-L.,Chen X.,&Zhang X..(2016).Multilevel circulant preconditioner for high-dimensional fractional diffusion equations.East Asian Journal on Applied Mathematics,6(2),109-130.
MLA Lei S.-L.,et al."Multilevel circulant preconditioner for high-dimensional fractional diffusion equations".East Asian Journal on Applied Mathematics 6.2(2016):109-130.
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