Two-parameter Splitting Circulant Preconditioner For Space Fractional Advection-diffusion Equations With Riesz Derivative

For the system of linear equations arising from the discretization of the space fractional advection–diffusion equations with Riesz derivative,we construct a twoparameter splitting(TPS)iterative method,and discuss its asymptotic convergence and the optimal parameter selection.By replacing Toeplitz matrices in the correspanding TPS preconditioner with circulant matrices,we introduce a two-parameter splitting circulant(TPSC)preconditioner.This novel preconditioner is the product of two circulant matrices,so it is easy to be inverted by using fast Fourier transform.In addition,the spectral property of the preconditioned coefficient matrix is carefully analyzed.Numerical experiments show that the TPSC preconditioner can significantly improve the efficiency of the Krylov subspace iteration methods.