On circulant and skew-circulant preconditioned Krylov methods for steady-state Riesz spatial fractional diffusion equations

The finite volume discretization of spatial fractional diffusion equations gives discretized linear systems whose coefficient matrices have a Toeplitz-like structure. By exploiting such a special structure, a class of efficient preconditioners based on the circulant and skew-circulant approximations is proposed to accelerate the convergence of Krylov subspace methods. Numerical experiments are carried out to illustrate the fact that the new preconditioners can significantly accelerate the convergence of CGNR and BiCGSTAB. Moreover, the numerical results indicate that there is little difference between the acceleration effect of the preconditioners based on the circulant and skew-circulant approximations for the proposed problems.

Automated summary

The paper presents efficient preconditioners based on circulant and skew-circulant approximations to accelerate the convergence of Krylov subspace methods for discretized linear systems of spatial fractional diffusion equations. Numerical experiments show that the new preconditioners can significantly speed up the convergence of CGNR and BiCGSTAB. Results also indicate that there is minimal difference in acceleration effects between the circulant and skew-circulant approximation-based preconditioners for the problems considered.