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Efficient Solvers for Some Classes of Time-Periodic Eddy Current Optimal Control Problems

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Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 45))

Abstract

In this paper, we present and discuss the results of our numerical studies of preconditioned MinRes methods for solving the optimality systems arising from the multiharmonic finite element approximations to time-periodic eddy current optimal control problems in different settings including different observation and control regions, different tracking terms, as well as box constraints for the Fourier coefficients of the state and the control. These numerical studies confirm the theoretical results published by the first author in a recent paper.

Mathematics Subject Classification (2010): 49J20, 65T40, 65M60, 65F08

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Notes

  1. 1.

    http://www.numa.uni-linz.ac.at/P19255/software.shtml.

  2. 2.

    http://www.cise.ufl.edu/research/sparse/umfpack/.

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Acknowledgements

The authors gratefully acknowledge the financial support by the Austrian Science Fund (FWF) under the grants P19255 and W1214 (project DK04). The authors also thank the Austria Center of Competence in Mechatronics (ACCM), which is a part of the COMET K2 program of the Austrian Government, for supporting their work on eddy current problems.

Author information

Authors and Affiliations

  1. DK Computational Mathematics, Johannes Kepler University Linz, Altenberger Str. 69, 4040, Linz, Austria

    Michael Kolmbauer

  2. Institute of Computational Mathematics, Johannes Kepler University Linz, Altenberger Str. 69, 4040, Linz, Austria

    Ulrich Langer

Authors
  1. Michael Kolmbauer
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  2. Ulrich Langer
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Corresponding author

Correspondence to Ulrich Langer .

Editor information

Editors and Affiliations

  1. , Dept. of Flow and Material Simulation, Fraunhofer Institute for Industrial Math, Fraunhofer-Platz 1, Kaiserslautern, 67663, Germany

    Oleg P. Iliev

  2. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. 25A, Sofia, 1113, Bulgaria

    Svetozar D. Margenov

  3. , Dept. of Mathematical and Statistical Sc, University of Alberta, 677 Central Academic Building, Edmonton, T6G 2G1, Alberta, Canada

    Peter D Minev

  4. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, East Avenue 7000, Livermore, 94550, California, USA

    Panayot S. Vassilevski

  5. , Department of Mathematics, Pennsylvania State University, 310 McAllister Building, University Park, 16802, Pennsylvania, USA

    Ludmil T Zikatanov

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Kolmbauer, M., Langer, U. (2013). Efficient Solvers for Some Classes of Time-Periodic Eddy Current Optimal Control Problems. In: Iliev, O., Margenov, S., Minev, P., Vassilevski, P., Zikatanov, L. (eds) Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications. Springer Proceedings in Mathematics & Statistics, vol 45. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7172-1_11

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