An efficient matrix splitting preconditioning technique for two-dimensional unsteady space-fractional diffusion equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:371

Article

Dai, Pingfei^1,2  Wu, Qingbiao¹  Wang, Hong²  Zheng, Xiangcheng² 

[1] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

[2] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

关键词: Fractional diffusion equations;    Matrix splitting;    Preconditioner;    Spectral analysis;    Krylov subspace iteration methods;   

DOI  :  10.1016/j.cam.2019.112673

来源: Elsevier

【 摘 要 】

We utilize the matrix splitting iteration method based on the structure of the coefficient matrix to construct the preconditioner for the finite difference discretization of two-dimensional time-dependent space-fractional diffusion equation with variable diffusivity coefficients. The spectral radius of the preconditioned matrix is shown to be clustered around one as we prove that it can be bounded by the Euclidean norm of a sum of three matrices where either the eigenvalues of the component matrices are clustered around one or their Euclidean norms decrease as we refine the spatial mesh size. Numerical comparisons are presented to demonstrate the effectiveness and efficiency of the proposed preconditioner. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free