Preconditioned iterative methods for space-time fractional advection-diffusion equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:319

Article

Zhao, Zhi¹  Jin, Xiao-Qing²  Lin, Matthew M.³ 

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

[2] Univ Macau, Dept Math, Macau, Peoples R China

[3] Natl Chung Cheng Univ, Dept Math, Chiayi 621, Taiwan

关键词: Fractional diffusion equations;    Toeplitz matrix;    Preconditioner;    Fast Fourier transform;    Conjugate gradient normal residual method;    Generalized minimal residual method;   

DOI  :  10.1016/j.jcp.2016.05.021

来源: Elsevier

【 摘 要 】

In this paper, we propose practical numerical methods for solving a class of initial-boundary value problems of space-time fractional advection-diffusion equations. First, we propose an implicit method based on two-sided Grunwald formulae and discuss its stability and consistency. Then, we develop the preconditioned generalized minimal residual (preconditioned GMRES) method and preconditioned conjugate gradient normal residual (preconditioned CGNR) method with easily constructed preconditioners. Importantly, because resulting systems are Toeplitz-like, fast Fourier transform can be applied to significantly reduce the computational cost. We perform numerical experiments to demonstrate the efficiency of our preconditioners, even in cases with variable coefficients. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free