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A new preconditioner for elliptic PDE-constrained optimization problems

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Abstract

We propose a preconditioner to accelerate the convergence of the GMRES iterative method for solving the system of linear equations obtained from discretize-then-optimize approach applied to optimal control problems constrained by a partial differential equation. Eigenvalue distribution of the preconditioned matrix as well as its eigenvectors are discussed. Numerical results of the proposed preconditioner are compared with several existing preconditioners to show its efficiency.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and constructive suggestions. The work of Davod Khojasteh Salkuyeh is partially supported by University of Guilan.

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  1. Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

    Hamid Mirchi & Davod Khojasteh Salkuyeh

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  1. Hamid Mirchi
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  2. Davod Khojasteh Salkuyeh
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Correspondence to Davod Khojasteh Salkuyeh.

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Mirchi, H., Salkuyeh, D.K. A new preconditioner for elliptic PDE-constrained optimization problems. Numer Algor 83, 653–668 (2020). https://doi.org/10.1007/s11075-019-00697-8

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  • DOI: https://doi.org/10.1007/s11075-019-00697-8

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