Fast modified scaled HSS preconditioner for steady-state space-fractional diffusion equations

For the discrete linear system resulted from the considered steady-state space-fractional diffusion equations, we construct a modified scaled HSS (MSHSS) iteration method, and then design a fast MSHSS (FMSHSS) preconditioner to accelerate the convergence rates of the Krylov subspace iteration methods. Theoretical analyses and numerical experiments show that the eigenvalues of the FMSHSS preconditioned matrix will be clustered around a complex disk centred at 1 with the radius being much less than 1, especially when one of the diffusion coefficients is sufficiently larger than the other. In addition, the constructed FMSHSS preconditioner outperforms the fast respectively scaled HSS (FRSHSS) preconditioner proposed recently by Bai (2018). (C) 2019 Elsevier Ltd. All rights reserved.