An efficient multigrid method with preconditioned smoother for two-dimensional anisotropic space-fractional diffusion equations

被引:4
|
作者
Xu, Yuan [1 ]
Lei, Siu-Long [1 ]
Sun, Hai-Wei [1 ]
机构
[1] Univ Macau, Dept Math, Macau, Peoples R China
关键词
Fractional diffusion equations; Multigrid method; Preconditioner; Anisotropy; FINITE-DIFFERENCE APPROXIMATIONS; SPECTRAL-ANALYSIS; LINEAR-SYSTEMS; SCHEME; REMOVAL;
D O I
10.1016/j.camwa.2022.08.030
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The anisotropic space-fractional diffusion equations in two dimensions are discretized by the Crank-Nicolson difference scheme with the weighted and shifted Grunwald formula, which is unconditionally stable and second -order convergence. The coefficient matrix of the discretized linear system possesses a two-level Toeplitz-like structure. Due to the anisotropy, the standard multigrid method converges slowly. By utilizing the GMRES method with a newly proposed tridiagonal preconditioner as a smoother, the convergence rate of the multigrid method can be accelerated significantly. The proposed tridiagonal preconditioner is shown to be invertible and a numerical experiment is given to demonstrate the efficiency of the proposed multigrid method with preconditioned smoother.
引用
收藏
页码:218 / 226
页数:9
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