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Constrained Optimization and Optimal Control for Partial Differential Equations pp 611–622Cite as

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On the Influence of Constitutive Models on Shape Optimization for Artificial Blood Pumps

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

Abstract

We report on a shape optimization framework that couples a highlyparallel finite element solver with a geometric kernel and different optimization algorithms. The entire optimization framework is transformed with automatic differentiation techniques, and the derivative code is employed to compute derivatives of the optimal shapes with respect to viscosity. This methodology provides a powerful tool to investigate the necessity of intricate constitutive models by taking derivatives with respect to model parameters

Mathematics Subject Classification (2000). Primary 76D55; Secondary 90C31.

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Authors and Affiliations

  1. Chair for Computational Analysis of Technical Systems (CATS) Center for Computational Engineering Science (CCES), RWTH Aachen University, D-52056, Aachen, Germany

    Markus Probst, Mike Nicolai & Marek Behr

  2. Institute for Scientific Computing (SC) Center for Computational Engineering Science (CCES), RWTH Aachen University, D-52056, Aachen, Germany

    Michael Lülfesmann, H. Martin Bücker & Christian H. Bischof

Authors
  1. Markus Probst
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  2. Michael Lülfesmann
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  3. Mike Nicolai
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  4. H. Martin Bücker
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  5. Marek Behr
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  6. Christian H. Bischof
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Corresponding author

Correspondence to Markus Probst .

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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Probst, M., Lülfesmann, M., Nicolai, M., Bücker, H.M., Behr, M., Bischof, C.H. (2012). On the Influence of Constitutive Models on Shape Optimization for Artificial Blood Pumps. 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_32

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