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Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations
Jin X.-Q.2; Lin F.-R.1; Zhao Z.2
2015
Source PublicationCommunications in Computational Physics
ISSN19917120 18152406
Volume18Issue:2Pages:469-488
AbstractIn this paper, preconditioned iterative methods for solving two-dimensional space-fractional diffusion equations are considered. The fractional diffusion equation is discretized by a second-order finite difference scheme, namely, the Crank-Nicolson weighted and shifted Grünwald difference (CN-WSGD) scheme proposed in [W. Tian, H. Zhou and W. Deng, A class of second order difference approximation for solving space fractional diffusion equations, Math. Comp., 84 (2015) 1703-1727]. For the discretized linear systems, we first propose preconditioned iterative methods to solve them. Then we apply the D'Yakonov ADI scheme to split the linear systems and solve the obtained splitting systems by iterative methods. Two preconditioned iterative methods, the preconditioned generalized minimal residual (preconditioned GMRES) method and the preconditioned conjugate gradient normal residual (preconditioned CGNR) method, are proposed to solve relevant linear systems. By fully exploiting the structure of the coefficient matrix, we design two special kinds of preconditioners, which are easily constructed and are able to accelerate convergence of iterative solvers. Numerical results show the efficiency of our preconditioners.
KeywordCN-WSGD scheme fast Fourier transform Fractional diffusion equation preconditioned CGNR method preconditioned GMRES method Toeplitz matrix
DOI10.4208/cicp.120314.230115a
URLView the original
Language英語
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Cited Times [WOS]:30   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.Shantou University
2.Universidade de Macau
Recommended Citation
GB/T 7714
Jin X.-Q.,Lin F.-R.,Zhao Z.. Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations[J]. Communications in Computational Physics,2015,18(2):469-488.
APA Jin X.-Q.,Lin F.-R.,&Zhao Z..(2015).Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations.Communications in Computational Physics,18(2),469-488.
MLA Jin X.-Q.,et al."Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations".Communications in Computational Physics 18.2(2015):469-488.
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