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A reordering-based preconditioner for elliptic PDE-constrained optimization problems with small Tikhonov parameters

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Abstract

In this paper, I present an efficient reordering-based preconditioner for the elliptic PDE-constrained optimization problems. The proposed preconditioner is extracted from a stationary iterative method which is convergent under certain suitable conditions. In addition, the spectral properties of the corresponding preconditioned matrix are studied. The resulting preconditioner is efficient for solving problems with small Tikhonov parameters (less than \(1e{-}6\)). Numerical experiments are presented to illustrate the effectiveness of the proposed preconditioner.

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Acknowledgements

The author would like to thank the reviewers for their detailed comments and suggestions that led to considerable improvements in the quality of the present manuscript.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, China University of Petroleum-Beijing, Beijing, 102249, China

    Qingqing Zheng

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  1. Qingqing Zheng
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Correspondence to Qingqing Zheng.

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Communicated by Xiang Wang.

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The author was supported by National Natural Science Foundation of China Grant (No. 12001311), Science Foundation of China University of Petroleum, Beijing (No. 2462021YJRC025), and the State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum

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Zheng, Q. A reordering-based preconditioner for elliptic PDE-constrained optimization problems with small Tikhonov parameters. Comp. Appl. Math. 42, 169 (2023). https://doi.org/10.1007/s40314-023-02317-7

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  • DOI: https://doi.org/10.1007/s40314-023-02317-7

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