65 Numerical analysis -- 65F Numerical linear algebra 65F10 Iterative methods for linear systems
65 Numerical analysis -- 65M Partial differential equations, initial value and time-dependent initial-boundary value problems 65M22 Solution of discretized equations
Summary: ``The finite-difference discretization of a class of spatial fractional diffusion equations gives the discrete linear system whose coefficient matrix is in the form of a sum of two diagonal-times-Toeplitz-like matrices. In this paper, for the discrete linear system of two- or three-dimensional discretized almost-istropic spatial fractional diffusion equation, we solve it by using the preconditioned Krylov subspace iteration methods, so we propose a block fast regularized Hermitian splitting preconditioner. From theoretical analysis, we prove that most of the eigenvalues of the corresponding preconditioned matrix are clustered around 1. Numerical experiments also demonstrate that the block fast regularized Hermitian splitting preconditioner can significantly accelerate the convergence rates of the Krylov subspace iteration methods such as generalized minimal residual (GMRES) and bi-conjugate gradient stabilized (BiCGSTAB) methods.''MRES