Efficient and Accurate Double Fast Algorithm for Solving High-Dimensional Time-Space Fractional Diffusion Problems with Spectral Fractional Laplacian

This paper presents an efficient and accurate double fast algorithm to solve high-dimensional time-space fractional diffusion problems with spectral fractional Laplacian. The proposed scheme uses linear finite element or fourth-order compact difference method combined with matrix transfer technique to approximate the spectral fractional Laplacian, and introduces a fast time-stepping L1 scheme for time discretization. The algorithm can exactly evaluate the fractional power of matrices and perform matrix-vector multiplication efficiently using discrete sine transform, significantly reducing the computational cost and memory requirement.