Fast preconditioned iterative methods for finite volume discretization of steady-state space-fractional diffusion equations

Jianyu Pan, Kwok Po NG*, Hong Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)

Abstract

We consider the preconditioned Krylov subspace method for linear systems arising from the finite volume discretization method of steady-state variable-coefficient conservative space-fractional diffusion equations. We propose to use a scaled-circulant preconditioner to deal with such Toeplitz-like discretization matrices. We show that the difference between the scaled-circulant preconditioner and the coefficient matrix is equal to the sum of a small-norm matrix and a low-rank matrix. Numerical tests are conducted to show the effectiveness of the proposed method for one- and two-dimensional steady-state space-fractional diffusion equations and demonstrate that the preconditioned Krylov subspace method converges very quickly.

Original languageEnglish
Pages (from-to)153-173
Number of pages21
JournalNumerical Algorithms
Volume74
Issue number1
DOIs
Publication statusPublished - 1 Jan 2017

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

  • Finite volume methods
  • Iterative methods
  • Preconditioning
  • Space-fractional diffusion equations

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