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Nested multigrid methods for time-periodic, parabolic optimal control problems

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Computing and Visualization in Science

Abstract

We present a nested multigrid method to optimize time-periodic, parabolic, partial differential equations (PDE). We consider a quadratic tracking objective with a linear parabolic PDE constraint. The first order optimality conditions, given by a coupled system of boundary value problems can be rewritten as an Fredholm integral equation of the second kind, which is solved by a multigrid of the second kind. The evaluation of the integral operator consists of solving sequentially a boundary value problem for respectively the state and the adjoints. Both problems are solved efficiently by a time-periodic space-time multigrid method.

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Authors and Affiliations

  1. Department of Computer science, K. U. Leuven, Celestijnenlaan 200, 3001, Heverlee, Belgium

    Dirk Abbeloos & Stefan Vandewalle

  2. Electrical Engineering Department ESAT, K. U. Leuven, Kasteelpark Arenberg 10, 3001, Heverlee, Belgium

    Moritz Diehl

  3. Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, 20146, Hamburg, Germany

    Michael Hinze

Authors
  1. Dirk Abbeloos
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  2. Moritz Diehl
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  3. Michael Hinze
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  4. Stefan Vandewalle
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Corresponding author

Correspondence to Dirk Abbeloos.

Additional information

Communicated by: C. W. Oosterlee and A. Borzi.

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Abbeloos, D., Diehl, M., Hinze, M. et al. Nested multigrid methods for time-periodic, parabolic optimal control problems. Comput. Visual Sci. 14, 27 (2011). https://doi.org/10.1007/s00791-011-0158-4

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  • DOI: https://doi.org/10.1007/s00791-011-0158-4

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