UM  > Faculty of Science and Technology
A circulant preconditioner for fractional diffusion equations
Lei,Siu Long; Sun,Hai Wei
Source PublicationJournal of Computational Physics
ISSN00219991 10902716

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
URLView the original
Indexed BySCIE
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000319049800036
Fulltext Access
Citation statistics
Cited Times [WOS]:162   [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.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Lei,Siu Long]'s Articles
[Sun,Hai Wei]'s Articles
Baidu academic
Similar articles in Baidu academic
[Lei,Siu Long]'s Articles
[Sun,Hai Wei]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Lei,Siu Long]'s Articles
[Sun,Hai Wei]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.