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Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations

Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations
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Year:    2015

Communications in Computational Physics, Vol. 18 (2015), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.120314.230115a

Communications in Computational Physics, Vol. 18 (2015), Iss. 2 : pp. 469–488

Published online:    2015-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    20

Keywords:   

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