A Fast Preconditioned Algorithm For Nonlocal Diffusion Model

The variable coefficient non-local diffusion model is a modeling method that can be used to describe phenomena such as abnormal diffusion and porous media flow.It can be ef-fectively numerically discretized by a fast configuration method.After discretization,a dense linear equation system with a coefficient matrix with Toeplitz structure is obtained.Since the coefficient matrix is asymmetric,the system of linear equations can be solved by the gener-alized minimal residual method(GMRES).In order to improve the convergence rate of the GMRES method,the Toeplitz and cyclic preconditioner of the coefficient matrix are con-structed,and the preconditioned GMRES method is proposed to solve the linear equations.Numerical examples also show the effectiveness of the preconditioned algorithm.