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Parallel-in-Time for Parabolic Optimal Control Problems Using PFASST

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Domain Decomposition Methods in Science and Engineering XXIV (DD 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 125))

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Abstract

In gradient-based methods for parabolic optimal control problems, it is necessary to solve both the state equation and a backward-in-time adjoint equation in each iteration of the optimization method. In order to facilitate fully parallel gradient-type and nonlinear conjugate gradient methods for the solution of such optimal control problems, we discuss the application of the parallel-in-time method PFASST to adjoint gradient computation. In addition to enabling time parallelism, PFASST provides high flexibility for handling nonlinear equations, as well as potential extra computational savings from reusing previous solutions in the optimization loop. The approach is demonstrated here for a model reaction-diffusion optimal control problem.

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Acknowledgements

S.G. gratefully acknowledges partial funding by the Deutsche Forschungsgemeinschaft (DFG), Project WE 2937/6-1. The work of M.M. was supported by the Applied Mathematics Program of the DOE Office of Advanced Scientific Computing Research under the U.S. Department of Energy under contract DE-AC02-05CH11231.

Author information

Authors and Affiliations

  1. Zuse Institute Berlin, Berlin, Germany

    Sebastian Götschel

  2. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Michael L. Minion

Authors
  1. Sebastian Götschel
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  2. Michael L. Minion
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Corresponding authors

Correspondence to Sebastian Götschel or Michael L. Minion .

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Petter E. Bjørstad

  2. Department of Mathematics, Louisana State University, Baton Rouge, LA, USA

    Susanne C. Brenner

  3. Laboratoire Analyse, Géométrie et Applications, Université Paris 13, Villetaneuse, France

    Lawrence Halpern

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

    Hyea Hyun Kim

  5. FB Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany

    Ralf Kornhuber

  6. Western Norway University of Applied Sciences, Bergen, Norway

    Talal Rahman

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

    Olof B. Widlund

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Götschel, S., Minion, M.L. (2018). Parallel-in-Time for Parabolic Optimal Control Problems Using PFASST. In: Bjørstad, P., et al. Domain Decomposition Methods in Science and Engineering XXIV . DD 2017. Lecture Notes in Computational Science and Engineering, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-319-93873-8_34

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