Fast MGM For Two Dimensional Caputo-Riesz Fractional Diffusion Equation

In this paper,the two-dimensional time-space Caputo-Riesz fractional diffu-sion equation is discretized by an implicit Second-order finite difference scheme. The scheme is unconditionally stable and the coefficient matrix possesses the Toeplitz-Block-Like structure. A multigrid method is proposed to solve the result-ing system.Meanwhile,the fast Toeplitz matrix-vector multiplication is utilized to lower the computational cost with O(NxNylog2(NxNy)) complexity,where Nx, Ny are the numbers of grid point in x and y direction respectively. Numerical experiments are given to demonstrate the efficiency of the method.