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Implementation and analysis of multigrid schemes with finite elements for elliptic optimal control problems

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Abstract

The detailed implementation and analysis of a finite element multigrid scheme for the solution of elliptic optimal control problems is presented. A particular focus is in the definition of smoothing strategies for the case of constrained control problems. For this setting, convergence of the multigrid scheme is discussed based on the BPX framework. Results of numerical experiments are reported to illustrate and validate the optimal efficiency and robustness of the performance of the present multigrid strategy.

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Authors and Affiliations

  1. Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität, Heinrichstraße 36, 8010, Graz, Austria

    O. Lass, M. Vallejos & A. Borzi

  2. Institute of Mathematics, College of Science, University of the Philippines, Diliman, Philippines

    M. Vallejos

  3. Dipartimento e Facoltà di Ingegneria, Università degli Studi del Sannio, Palazzo Dell’Aquila Bosco Lucarelli, Corso Garibaldi 107, 82100, Benevento, Italy

    A. Borzi

  4. Mathematics Department, University of Wyoming, Dept. 3036, 1000 E. University Avenue Laramie, Laramie, WY, 82071, USA

    C. C. Douglas

Authors
  1. O. Lass
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  2. M. Vallejos
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  3. A. Borzi
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  4. C. C. Douglas
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Corresponding author

Correspondence to A. Borzi.

Additional information

Supported in part by the Austrian Science Fund FWF project P18136-N13 “Quantum optimal control of semiconductor nanostructures” and F3205-N18 “Fast Multigrid Methods for Inverse Problems” and American NSF grants OISE-0405349, ACI-0305466, ACI-0324876, and CNS-0720454.

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Lass, O., Vallejos, M., Borzi, A. et al. Implementation and analysis of multigrid schemes with finite elements for elliptic optimal control problems. Computing 84, 27–48 (2009). https://doi.org/10.1007/s00607-008-0024-5

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  • DOI: https://doi.org/10.1007/s00607-008-0024-5

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