An efficient matrix splitting preconditioning technique for two-dimensional unsteady space-fractional diffusion equations

We utilize the matrix splitting iteration method based on the structure of the coefficient matrix to construct the preconditioner for the finite difference discretization of two-dimensional time-dependent space-fractional diffusion equation with variable diffusivity coefficients. The spectral radius of the preconditioned matrix is shown to be clustered around one as we prove that it can be bounded by the Euclidean norm of a sum of three matrices where either the eigenvalues of the component matrices are clustered around one or their Euclidean norms decrease as we refine the spatial mesh size. Numerical comparisons are presented to demonstrate the effectiveness and efficiency of the proposed preconditioner. (C) 2019 Elsevier B.V. All rights reserved.