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A Robust Preconditioner for Two-dimensional Conservative Space-Fractional Diffusion Equations on Convex Domains
Chen,Xu; Deng,Si Wen; Lei,Siu Long
2019-08-15
Source PublicationJournal of Scientific Computing
ISSN0885-7474
Volume80Issue:2Pages:1033-1057
AbstractPreconditioners are popularly used for speeding up Krylov subspace iterative method for solving linear systems from discretization of fractional differential equations (FDEs) on rectangular domains. Though some recent works have been developed for FDEs in general convex domains, it still has room for improvement in the design of preconditioner. For this sake, in this paper, we theoretically study the preconditioner problem for two-dimensional conservative space-fractional diffusion equations with variable coefficients and propose a robust preconditioner with penalty term which can deal with any convex domains significantly. We further prove that the proposed preconditioner equals to the coefficient matrix plus a low rank matrix and a matrix with small norm under certain conditions. It implies that the new preconditioner can effectively accelerate the convergence rate of Krylov subspace method. Experimental results show the good performance of the robust preconditioner.
KeywordBlock-circulant-circulant-block matrix Convex domain Finite volume method Preconditioner Space-fractional diffusion equation
DOI10.1007/s10915-019-00966-7
URLView the original
Language英语
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Document TypeJournal article
CollectionUniversity of Macau
AffiliationDepartment of Mathematics,University of Macau,Macau,China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Chen,Xu,Deng,Si Wen,Lei,Siu Long. A Robust Preconditioner for Two-dimensional Conservative Space-Fractional Diffusion Equations on Convex Domains[J]. Journal of Scientific Computing,2019,80(2):1033-1057.
APA Chen,Xu,Deng,Si Wen,&Lei,Siu Long.(2019).A Robust Preconditioner for Two-dimensional Conservative Space-Fractional Diffusion Equations on Convex Domains.Journal of Scientific Computing,80(2),1033-1057.
MLA Chen,Xu,et al."A Robust Preconditioner for Two-dimensional Conservative Space-Fractional Diffusion Equations on Convex Domains".Journal of Scientific Computing 80.2(2019):1033-1057.
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