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Numerical Algorithms

, Volume 74, Issue 1, pp 153–173 | Cite as

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

  • Jianyu Pan
  • Michael NgEmail author
  • Hong Wang
Original Paper

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.

Keywords

Iterative methods Preconditioning Space-fractional diffusion equations Finite volume methods 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsHong Kong Baptist UniversityKowloon TongHong Kong
  2. 2.Department of Mathematics, Shanghai Key Laboratory of PMMPEast China Normal UniversityShanghaiChina
  3. 3.Department of MathematicsUniversity of South CarolinaColumbiaUSA

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