Efficient Preconditioning Based on Scaled Tridiagonal and Toeplitz-like Splitting Iteration Method for Conservative Space Fractional Diffusion Equations

The purpose of this work is to study the efficient numerical solvers for time-dependent conservative space fractional diffusion equations. Specifically, for the discretized Toeplitz-like linear system, we aim to study efficient preconditioning based on a matrix-splitting iteration method. We propose a scaled tridiagonal and Toeplitz-like splitting iteration method. Its asymptotic convergence property is first established. Further, based on the induced preconditioner, a fast circulant-like preconditioner is developed to accelerate the convergence of the Krylov Subspace iteration methods. Theoretical results suggest that the fast preconditioner can inherit the effectiveness of the original induced preconditioner. Numerical results also demonstrate its efficiency.