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Fast and improved scaled HSS preconditioner for steady-state space-fractional diffusion equations

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Abstract

For the discrete linear system resulted from the considered steady-state space-fractional diffusion equations, we propose an improved scaled HSS (ISHSS) iteration method and discuss its convergence theory. Then, we construct a fast ISHSS (FISHSS) preconditioner to accelerate the convergence rates of the Krylov subspace iteration methods. We discuss the spectral properties of the FISHSS preconditioning matrix. Numerical experiments show the good performance of the FISHSS preconditioner.

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Funding

This study was supported by The National Natural Science Foundation (No. 11501038) and The Science and Technology Planning Projects of Beijing Municipal Education Commission (Nos. KM201911232010, KM202011232019 and KM201811232020), P.R. China.

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Authors and Affiliations

  1. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, People’s Republic of China

    Fang Chen & Tian-Yi Li

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  1. Fang Chen
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  2. Tian-Yi Li
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Correspondence to Fang Chen.

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Chen, F., Li, TY. Fast and improved scaled HSS preconditioner for steady-state space-fractional diffusion equations. Numer Algor 87, 651–665 (2021). https://doi.org/10.1007/s11075-020-00982-x

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  • DOI: https://doi.org/10.1007/s11075-020-00982-x

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