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Structure Exploiting Adjoints for Finite Element Discretizations

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Constrained Optimization and Optimal Control for Partial Differential Equations

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 160))

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Abstract

This paper presents some details for the development, analysis, and implementation of efficient numerical optimization algorithms using algorithmic differentiation (AD) in the context of partial differential equation (PDE) constrained optimization. This includes an error analysis for the discrete adjoints computed with AD and a systematic structure exploitation including efficient checkpointing routines, especially multistage and online checkpointing approaches.

Mathematics Subject Classification (2000). 65Y20, 90C30, 49N90, 68W40.

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References

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Paderborn, Warburgerstr. 100, D-33098, Paderborn, Germany

    Denise Holfeld & Andrea Walther

  2. Fachrichtung Mathematik Institut für Wissenschaftliches Rechnen, TU Dresden, D-01062, Dresden, Germany

    Philipp Stumm

Authors
  1. Denise Holfeld
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  2. Philipp Stumm
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  3. Andrea Walther
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Corresponding author

Correspondence to Denise Holfeld .

Editor information

Editors and Affiliations

  1. , Department Mathematik, Universität Erlangen-Nürnberg, Martensstr. 3, Erlangen, 91058, Germany

    Günter Leugering

  2. , Fakultät Bio- und Chemieingenieurwesen, Technische Universität Dortmund, Geschossbau 2, Dortmund, 44221, Germany

    Sebastian Engell

  3. , Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, Berlin, 12489, Germany

    Andreas Griewank

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

    Michael Hinze

  5. , Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 293, Heidelberg, 69120, Germany

    Rolf Rannacher

  6. , FB 4 - Department Mathematik, Universität Trier, Trier, 54286, Germany

    Volker Schulz

  7. Fakultät für Mathematik, M1, Lehrstuhl für Mathematische Optimierung, Technische Universität München, Boltzmannstr. 3, Garching bei München, 85748, Germany

    Michael Ulbrich

  8. , Fachbereich Mathematik, Technische Universität Darmstadt, Dolivostrasse 15, Darmstadt, 64293, Germany

    Stefan Ulbrich

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Holfeld, D., Stumm, P., Walther, A. (2012). Structure Exploiting Adjoints for Finite Element Discretizations. In: Leugering, G., et al. Constrained Optimization and Optimal Control for Partial Differential Equations. International Series of Numerical Mathematics, vol 160. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0133-1_10

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