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A circulant preconditioner for fractional diffusion equations
Lei,Siu Long; Sun,Hai Wei
2013-04-09
Source PublicationJournal of Computational Physics
ISSN00219991 10902716
Volume242Pages:715-725
Abstract

The implicit finite difference scheme with the shifted Grünwald formula, which is unconditionally stable, is employed to discretize fractional diffusion equations. The resulting systems are Toeplitz-like and then the fast Fourier transform can be used to reduce the computational cost of the matrix-vector multiplication. The preconditioned conjugate gradient normal residual method with a circulant preconditioner is proposed to solve the discretized linear systems. The spectrum of the preconditioned matrix is proven to be clustered around 1 if diffusion coefficients are constant; hence the convergence rate of the proposed iterative algorithm is superlinear. Numerical experiments are carried out to demonstrate that our circulant preconditioner works very well, even though for cases of variable diffusion coefficients.

KeywordCgnr Method Circulant Preconditioner Fast Fourier Transform Fractional Diffusion Equations Shifted Grünwald Discretization Toeplitz
DOI10.1016/j.jcp.2013.02.025
URLView the original
Indexed BySCI
Language英语
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000319049800036
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Cited Times [WOS]:125   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
Personal research not belonging to the institution
AffiliationDepartment of MathematicsUniversity of Macau,China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Lei,Siu Long,Sun,Hai Wei. A circulant preconditioner for fractional diffusion equations[J]. Journal of Computational Physics,2013,242:715-725.
APA Lei,Siu Long,&Sun,Hai Wei.(2013).A circulant preconditioner for fractional diffusion equations.Journal of Computational Physics,242,715-725.
MLA Lei,Siu Long,et al."A circulant preconditioner for fractional diffusion equations".Journal of Computational Physics 242(2013):715-725.
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