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Preconditioners for all-at-once system from the fractional mobile/immobile advection–diffusion model

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Abstract

The all-at-once system arising from fractional mobile/immobile advection–diffusion equations is studied. Firstly, the finite difference method with L1 formula is employed to discretize it. The resulting implicit scheme is a time-stepping scheme, which is not suitable for parallel computing. Based on this scheme, an all-at-once system is established, which will be suitable for parallel computing. Secondly, according to the block lower triangular Toeplitz structure of the all-at-once system, both the block bi-diagonal preconditioner and block stair preconditioner are designed. Finally, numerical examples are presented to show the performances of the proposed preconditioners.

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Acknowledgements

The authors would like to thank the editor and anonymous referees for their valuable comments and detailed revision suggestions that have greatly improved the quality of this paper. This research is supported by the National Natural Science Foundation of China (Nos. 11801463 and 11701522), the Applied Basic Research Program of Sichuan Province (No. 2020YJ0007) and the Fundamental Research Funds for the Central Universities (No. JBK1902028).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, People’s Republic of China

    Yong-Liang Zhao & Huan-Yan Jian

  2. School of Economic Mathematics/Institute of Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, Sichuan, People’s Republic of China

    Xian-Ming Gu

  3. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450001, People’s Republic of China

    Meng Li

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  1. Yong-Liang Zhao
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Correspondence to Xian-Ming Gu.

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Zhao, YL., Gu, XM., Li, M. et al. Preconditioners for all-at-once system from the fractional mobile/immobile advection–diffusion model. J. Appl. Math. Comput. 65, 669–691 (2021). https://doi.org/10.1007/s12190-020-01410-y

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