Fast iterative solvers for linear systems arising from time-dependent space-fractional diffusion equations

Jianyu Pan, Kwok Po NG*, Hong Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)

Abstract

In this paper, we study the linear systems arising from the discretization of timedependent space-fractional diffusion equations. By using a finite difference discretization scheme for the time derivative and a finite volume discretization scheme for the space-fractional derivative, Toeplitz-like linear systems are obtained. We propose using the approximate inverse-circulant preconditioner to deal with such Toeplitz-like matrices, and we show that the spectra of the corresponding preconditioned matrices are clustered around 1. Experimental results on time-dependent and space-fractional diffusion equations are presented to demonstrate that the preconditioned Krylov subspace methods converge very quickly.

Original languageEnglish
Pages (from-to)A2806-A2826
JournalSIAM Journal of Scientific Computing
Volume38
Issue number5
DOIs
Publication statusPublished - 2016

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Fractional diffusion equations
  • Iterative methods
  • Local mass conservative form
  • Preconditioners
  • Spectral analysis

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