Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations | |
Jin X.-Q.2; Lin F.-R.1; Zhao Z.2 | |
2015 | |
Source Publication | Communications in Computational Physics |
ISSN | 19917120 18152406 |
Volume | 18Issue:2Pages:469-488 |
Abstract | In 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. |
Keyword | CN-WSGD scheme fast Fourier transform Fractional diffusion equation preconditioned CGNR method preconditioned GMRES method Toeplitz matrix |
DOI | 10.4208/cicp.120314.230115a |
URL | View the original |
Language | 英語English |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | DEPARTMENT OF MATHEMATICS |
Affiliation | 1.Shantou University 2.Universidade de Macau |
First Author Affilication | University of 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. |
Files in This Item: | ||||||
There are no files associated with this item. |
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment