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Multi-parameter dimensional split preconditioner for three-by-three block system of linear equations

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Abstract

For a class of three-by-three block systems of linear equations arising from many practical problems, we develop a multi-parameter dimensional split (MPDS) preconditioner to accelerate the convergence of the Krylov subspace methods. Inasmuch as the preconditioning effect of the MPDS preconditioner depends on the values of its parameters, an effective method for computing the optimal parameters is also proposed. Moreover, the eigenvalue distribution of the preconditioned matrix is carefully analyzed. Numerical examples arising from the discretizations of the Navier–Stokes equations and the partial differential equation (PDE) constraint optimization problems are employed to illustrate the robustness and the efficiency of the MPDS preconditioner.

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Acknowledgements

We thank the anonymous reviewers for their careful reading of the manuscript and for the helpful comments.

Funding

This work is supported by the National Natural Science Foundation of China (grant no. 12161030) and Hainan Provincial Natural Science Foundation of China (grant no. 121RC537 and 523MS039).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hainan Normal University, Haikou, 570000, People’s Republic of China

    Yang Ai-Li

  2. School of Science, Chongqing University of Posts and Telecommunications, Chongqing, 400065, People’s Republic of China

    Zhu Jun-Li

  3. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Wu Yu-Jiang

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  1. Yang Ai-Li
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  2. Zhu Jun-Li
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  3. Wu Yu-Jiang
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Contributions

Ai-Li Yang wrote the main manuscript text, Jun-Li Zhu performed the numerical experiments, and Yu-Jiang Wu reviewed the manuscript and gave some suggestions.

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Correspondence to Yang Ai-Li.

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Ai-Li, Y., Jun-Li, Z. & Yu-Jiang, W. Multi-parameter dimensional split preconditioner for three-by-three block system of linear equations. Numer Algor 95, 721–745 (2024). https://doi.org/10.1007/s11075-023-01587-w

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  • DOI: https://doi.org/10.1007/s11075-023-01587-w

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