@Article{CiCP-18-469,
author = {Xiao-Qing Jin, Fu-Rong Lin and Zhi Zhao},
title = {Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations},
journal = {Communications in Computational Physics},
year = {2018},
volume = {18},
number = {2},
pages = {469--488},
abstract = {<p style="text-align: justify;">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, <em>A class of second order difference approximation for solving space
fractional diffusion equations</em>, 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&#39;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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.120314.230115a},
url = {http://global-sci.org/intro/article_detail/cicp/11036.html}
}