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

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  • Xiaofeng Guo

    (School of Data Science, Fudan University, Shanghai 200433, China
    Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China)

Abstract

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.

Suggested Citation

  • Xiaofeng Guo, 2024. "Efficient Preconditioning Based on Scaled Tridiagonal and Toeplitz-like Splitting Iteration Method for Conservative Space Fractional Diffusion Equations," Mathematics, MDPI, vol. 12(15), pages 1-22, August.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:15:p:2405-:d:1448473
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