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On the Time-Domain Decomposition of Parabolic Optimal Control Problems

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Domain Decomposition Methods in Science and Engineering XXIII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 116))

Abstract

Discretized parabolic control problems lead to very large systems of equations, because trajectories must be approximated forward and backward in time. It is therefore of interest to devise parallel solvers for such systems. In this paper, we propose an optimized Schwarz type method for decomposing the parabolic control problem in time, and show how to choose the optimized parameters to obtain the fastest convergence in the two subdomain case. The method of energy estimates is used to deduce the contraction rate. We illustrate the method for a problem constrained by the advection-diffusion equation.

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Acknowledgements

The author is grateful to the anonymous referee, whose suggestions led to a better presentation of the paper. We would also like to thank Martin J. Gander for the inspiring collaboration and discussions on this topic. This work is partially supported by Grant No. ECS-22300115 from the Research Grants Council of Hong Kong.

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Authors and Affiliations

  1. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Felix Kwok

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  1. Felix Kwok
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Correspondence to Felix Kwok .

Editor information

Editors and Affiliations

  1. Dept. of Mathematical Sciences, KAIST, Daejeon, Korea (Republic of)

    Chang-Ock Lee

  2. Dept. of Computer Science, University of Colorado, Boulder, Colorado, USA

    Xiao-Chuan Cai

  3. Applied Math & Computational Science, KAUST, Thuwal, Saudi Arabia

    David E. Keyes

  4. Dept. of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. Mathematisches Institut, Universität zu Köln, Köln, Germany

    Axel Klawonn

  6. Dept. of Computational Science & Engineering, Yonsei University, Seoul, Korea (Republic of)

    Eun-Jae Park

  7. Courant Institute of Mathematical Sciences, New York University, New York, New York, USA

    Olof B. Widlund

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Kwok, F. (2017). On the Time-Domain Decomposition of Parabolic Optimal Control Problems. In: Lee, CO., et al. Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering, vol 116. Springer, Cham. https://doi.org/10.1007/978-3-319-52389-7_5

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