ISNM International Series of Numerical Mathematics

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2 ISNM International Series of Numerical Mathematics Volume 165 Managing Editors: K.-H. Hoffmann, München, G. Leugering, Erlangen-Nürnberg, Associate Editors: Z. Chen, Beijing, China R.H.W. Hoppe, Augsburg, /Houston, USA N. Kenmochi, Chiba, Japan V. Starovoitov, Novosibirsk, Russia Honorary Editor: J. Todd, Pasadena, USA More information about this series at

3 GRunter Leugering Peter Benner Sebastian Engell Andreas Griewank Helmut Harbrecht Michael Hinze Rolf Rannacher Stefan Ulbrich Editors Trends in PDE Constrained Optimization

4 Editors GRunter Leugering Department Mathematik UniversitRat Erlangen-NRurnberg Erlangen Sebastian Engell Department of Biochemical and Chemical Engineering Technische UniversitRat Dortmund Dortmund Helmut Harbrecht Mathematisches Institut UniversitRat Basel Basel Switzerland Rolf Rannacher Institut frur Angewandte Mathematik Ruprecht-Karls-UniversitRat Heidelberg Heidelberg Peter Benner Institut frur Dynamik komplexer technischer Systeme Max-Planck-Institut Magdeburg Andreas Griewank Department of Mathematics Humboldt-UniversitRat zu Berlin Berlin Michael Hinze Fachbereich Mathematik Optimierung und Approximation UniversitRat Hamburg Hamburg Stefan Ulbrich Fachbereich Mathematik Technische UniversitRat Darmstadt Darmstadt ISSN ISSN (electronic) ISBN ISBN (ebook) DOI / Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: Mathematics Subject Classification (2010): 35K55, 35Q93, 49J20, 49K20, 49M25, 65K10, 65M60, 65N15, 65N30, 76D55, 90C30 Springer International Publishing Switzerland 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (

5 Contents Introduction... 1 Günter Leugering, Andreas Griewank, Stefan Ulbrich, Helmut Harbrecht, Peter Benner, Rolf Rannacher, Michael Hinze, and Sebastian Engell Part I Constrained Optimization, Identification and Control Introduction to Part I Constrained Optimization, Identification and Control... 7 Stefan Ulbrich and Andreas Griewank Optimal Control of Allen-Cahn Systems Luise Blank, M. Hassan Farshbaf-Shaker, Claudia Hecht, Josef Michl, and Christoph Rupprecht Optimal Control of Elastoplastic Processes: Analysis, Algorithms, Numerical Analysis and Applications Roland Herzog, Christian Meyer, and Gerd Wachsmuth One-Shot Approaches to Design Optimzation Torsten Bosse, Nicolas R. Gauger, Andreas Griewank, Stefanie Günther, and Volker Schulz Optimal Design with Bounded Retardation for Problems with Non-separable Adjoints Torsten Bosse, Nicolas R. Gauger, Andreas Griewank, Stefanie Günther, Lena Kaland, Claudia Kratzenstein, Lutz Lehmann, Anil Nemili, Emre Özkaya, and Thomas Slawig On a Fully Adaptive SQP Method for PDAE-Constrained Optimal Control Problems with Control and State Constraints Stefanie Bott, Debora Clever, Jens Lang, Stefan Ulbrich, Jan Carsten Ziems, and Dirk Schröder v

6 vi Contents Optimal Control of Nonlinear Hyperbolic Conservation Laws with Switching Sebastian Pfaff, Stefan Ulbrich, and Günter Leugering Elliptic Mathematical Programs with Equilibrium Constraints in Function Space: Optimality Conditions and Numerical Realization Michael Hintermüller, Antoine Laurain, Caroline Löbhard, Carlos N. Rautenberg, and Thomas M. Surowiec Models and Optimal Control in Freezing and Thawing of Living Cells and Tissues Karl-Heinz Hoffmann, Nikolai D. Botkin, and Varvara L. Turova Optimal Control-Based Feedback Stabilization of Multi-field Flow Problems Eberhard Bänsch, Peter Benner, Jens Saak, and Heiko K. Weichelt Part II Shape and Topology Optimization Introduction to Part II Shape and Topology Optimization Helmut Harbrecht Two-Stage Stochastic Optimization Meets Two-Scale Simulation Sergio Conti, Benedict Geihe, Martin Rumpf, and Rüdiger Schultz On Shape Optimization with Parabolic State Equation Helmut Harbrecht and Johannes Tausch Multi-material Phase Field Approach to Structural Topology Optimization Luise Blank, M. Hassan Farshbaf-Shaker, Harald Garcke, Christoph Rupprecht, and Vanessa Styles Part III Adaptivity and Model Reduction Introduction to Part III Adaptivity and Model Reduction Peter Benner and Rolf Rannacher Model Reduction by Adaptive Discretization in Optimal Control Rolf Rannacher Graded Meshes in Optimal Control for Elliptic Partial Differential Equations: An Overview Thomas Apel, Johannes Pfefferer, and Arnd Rösch Model Order Reduction for PDE Constrained Optimization Peter Benner, Ekkehard Sachs, and Stefan Volkwein

7 Contents vii Adaptive Trust-Region POD Methods in PIDE-Constrained Optimization Ekkehard W. Sachs, Marina Schneider, and Matthias Schu Part IV Discretization: Concepts and Analysis Introduction to Part IV Discretization: Concepts and Analysis Michael Hinze Optimal Control for Two-Phase Flows Malte Braack, Markus Klein, Andreas Prohl, and Benjamin Tews A-Priori Error Bounds for Finite Element Approximation of Elliptic Optimal Control Problems with Gradient Constraints Klaus Deckelnick and Michael Hinze Space-Time Newton-Multigrid Strategies for Nonstationary Distributed and Boundary Flow Control Problems Michael Hinze, Michael Köster, and Stefan Turek Convergence of Adaptive Finite Elements for Optimal Control Problems with Control Constraints Kristina Kohls, Arnd Rösch, and Kunibert G. Siebert Petrov-Galerkin Crank-Nicolson Scheme for Parabolic Optimal Control Problems on Nonsmooth Domains Thomas G. Flaig, Dominik Meidner, and Boris Vexler Part V Applications Introduction to Part V: Applications Optimal Treatment Planning in Radiotherapy Based on Boltzmann Transport Equations Richard C. Barnard, Martin Frank, and Michael Herty Optimal Control of Self-Consistent Classical and Quantum Particle Systems Martin Burger, René Pinnau, Marcisse Fouego, and Sebastian Rau Modeling, Analysis and Optimization of Particle Growth, Nucleation and Ripening by the Way of Nonlinear Hyperbolic Integro-Partial Differential Equations Michael Gröschel, Wolfgang Peukert, and Günter Leugering Stabilization of Networked Hyperbolic Systems with Boundary Feedback Markus Dick, Martin Gugat, Michael Herty, Günter Leugering, Sonja Steffensen, and Ke Wang

8 viii Contents Optimal Control of Surface Acoustic Wave Actuated Sorting of Biological Cells Thomas Franke, Ronald H.W. Hoppe, Christopher Linsenmann, Lothar Schmid, and Achim Wixforth Real-Time PDE Constrained Optimal Control of a Periodic Multicomponent Separation Process Malte Behrens, Hans Georg Bock, Sebastian Engell, Phawitphorn Khobkhun, and Andreas Potschka OPTPDE: A Collection of Problems in PDE-Constrained Optimization Roland Herzog, Arnd Rösch, Stefan Ulbrich, and Winnifried Wollner

9 Contributors Thomas Apel Institute for Mathematics and Civil Engineering Informatics, Universität der Bundeswehr München, Eberhard Bänsch Lehrstuhl für Angewandte Mathematik 3, Friedrich-Alexander- Universität Erlangen-Nürnberg, Erlangen, Richard C. Barnard Institute for Mathematics and Scientific Computing, University of Graz, Graz, Austria Malte Behrens Department of Biochemical and Chemical Engineering, TU Dortmund, Dortmund, Peter Benner Research Group Computational Methods in Systems and Control Theory (CSC), Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg, Magdeburg, Luise Blank Fakultät für Mathematik, Universität Regensburg, Regensburg, Hans Georg Bock Interdisciplinary Center for Scientific Computing, Heidelberg University, Heidelberg, Torsten Bosse Department of Mathematics, Humboldt-Universität zu Berlin, Berlin, Nikolai D. Botkin Zentrum Mathematik, Technische Universität München, München, Stefanie Bott Department of Mathematics and Graduate School of Computational Engineering, Technische Universität Darmstadt, Darmstadt, Malte Braack Mathematical Seminar, Christian-Albrechts-University of Kiel, Kiel, ix

10 x Contributors Martin Burger Institut für Numerische und Angewandte Mathematik, Westfälische Wilhelms-Universität Münster, Münster, Debora Clever Department of Mathematics, Technische Universität Darmstadt, Darmstadt, Sergio Conti Institut für Angewandte Mathematik, Universität Bonn, Bonn, Klaus Deckelnick Institut für Analysis und Numerik, Otto von Guericke Universität Magdeburg, Magdeburg, Markus Dick Department of Mathematics, University of Erlangen-Nuremberg, Erlangen, Sebastian Engell Department of Biochemical and Chemical Engineering, TU Dortmund, Dortmund, M. Hassan Farshbaf-Shaker Weierstraß-Institut, Berlin, Thomas G. Flaig Institut für Mathematik und Bauinformatik, Universität der Bundeswehr München, Neubiberg, Marcisse Fouego Institut für Numerische und Angewandte Mathematik, Westfälische Wilhelms-Universität Münster, Münster, Martin Frank MATHCCES, Department of Mathematics, RWTH Aachen University, Aachen, Thomas Franke Institute of Physics, Universität Augsburg, Augsburg, Harald Garcke Fakultät für Mathematik, Universität Regensburg, Regensburg, Nicolas R. Gauger Department of Mathematics and Center for Computational Engineering Science, RWTH Aachen University, Aachen, Benedict Geihe Institut für Numerische Simulation, Universität Bonn, Bonn, Andreas Griewank Department of Mathematics, Humboldt-Universität zu Berlin, Berlin, Michael Gröschel Institute of Applied Mathematics 2, Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Martin Gugat Department of Mathematics, University of Erlangen-Nuremberg, Erlangen, Stefanie Günther Department of Mathematics and Center for Computational Engineering Science, RWTH Aachen University, Aachen, Helmut Harbrecht Mathematisches Institut, Universität Basel, Basel, Schweiz

11 Contributors xi Claudia Hecht Fakultät für Mathematik, Universität Regensburg, Regensburg, Michael Herty IGPM, Department of Mathematics, RWTH Aachen University, Aachen, Roland Herzog Faculty of Mathematics, Technische Universität Chemnitz, Chemnitz, Michael Hintermüller Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, Michael Hinze Schwerpunkt Optimierung und Approximation, Universität Hamburg, Hamburg, Karl-Heinz Hoffmann Zentrum Mathematik, Technische Universität München, München, Ronald H. W. Hoppe Institute of Mathematics, Universität Augsburg, Augsburg, Department of Mathematics, University of Houston, Houston, TX, USA Lena Kaland Department of Mathematics and Center for Computational Engineering Science, RWTH Aachen University, Aachen, Phawitphorn Khobkhun Department of Biochemical and Chemical Engineering, TU Dortmund, Dortmund, Markus Klein Mathematical Institute, Tübingen University, Tübingen, Kristina Kohl Fachbereich Mathematik, Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Stuttgart, Michael Köster Institute of Applied Mathematics, TU Dortmund, Dortmund, Claudia Kratzenstein Christian-Albrechts-Universität zu Kiel, Kiel, Jens Lang Department of Mathematics and Graduate School of Computational Engineering, Technische Universität Darmstadt, Darmstadt, Antoine Laurain Institut für Mathematik, Technische Universität Berlin, Berlin, Lutz Lehmann Department of Mathematics, Humboldt-Universität zu Berlin, Berlin, Günter Leugering Department of Mathematics, Universität Erlangen-Nürnberg, Erlangen, Christopher Linsenmann Institute of Mathematics, Universität Augsburg, Augsburg,

12 xii Contributors Caroline Löbhard Humboldt-Universität zu Berlin, Berlin, Dominik Meidner Fakultät für Mathematik, Lehrstuhl für Optimale Steuerung, Technische Universität München, Garching b. München, Christian Meyer Faculty of Mathematics, Technical Universität Dortmund, Dortmund, Josef Michl Institut für Theoretische Physik, Universität Regensburg, Regensburg, Anil Nemili Department of Mathematics and Center for Computational Engineering Science, RWTH Aachen University, Aachen, Emre Özkaya Department of Mathematics and Center for Computational Engineering Science, RWTH Aachen University, Aachen, Wolfgang Peukert Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Sebastian Pfaff Department of Mathematics, Technische Universität Darmstadt, Darmstadt, Johannes Pfefferer Universität der Bundeswehr München, München, René Pinnau Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Andreas Potschka Interdisciplinary Center for Scientific Computing, Heidelberg University, Heidelberg, Andreas Prohl Mathematical Institute, Tübingen University, Tübingen, Rolf Rannacher Institut für angewandte Mathematik, Universität Heidelberg, Heidelberg, Sebastian Rau Fachbereich Mathematik, Technische Universität Kaiserslautern, Kaiserslautern, Carlos N. Rautenberg Department of Mathematics and Scientific Computing, Karl-Franzens-University of Graz, Graz, Austria Arnd Rösch Fakultät für Mathematik, Universität Duisburg Essen, Essen, Martin Rumpf Institut für Numerische Simulation, Universität Bonn, Bonn, Christoph Rupprecht Fakultät für Mathematik, Universität Regensburg, Regensburg, Jens Saak Research Group Computational Methods in Systems and Control Theory (CSC), Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg, Magdeburg,

13 Contributors xiii Ekkehard Sachs FB 4 Mathematik, University of Trier, Trier, Lothar Schmid Institute of Physics, Universität Augsburg, Augsburg, Marina Schneider FB IV Department of Mathematics, University of Trier, Trier, Dirk Schröder Department of Mathematics, Technische Universität Darmstadt, Darmstadt, Matthias Schu FB IV Department of Mathematics, University of Trier, Trier, Rüdiger Schultz Fakultät für Mathematik, Universität Duisburg-Essen, Duisburg, Volker Schulz Universität Trier, Trier, Kunibert G. Siebert Fachbereich Mathematik, Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Stuttgart, Thomas Slawig Christian-Albrechts-Universität zu Kiel, Kiel, Sonja Steffensen IGPM, RWTH Aachen University, Aachen, Vanessa Styles Department of Mathematics, University of Sussex, Brighton, UK Thomas M. Surowiec Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, Johannes Tausch Department of Mathematics, Southern Methodist University, Dallas, TX, USA Benjamin Tews Mathematical Seminar, Christian-Albrechts-University of Kiel, Kiel, Stefan Turek Institute of Applied Mathematics, TU Dortmund, Dortmund, Varvara D. Turova Zentrum Mathematik, Technische Universität München, München, Stefan Ulbrich Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Boris Vexler Fakultät für Mathematik, Lehrstuhl für Optimale Steuerung, Technische Universität München, Garching b. München, Stefan Volkwein Department of Mathematics and Statistics, University of Konstanz, Konstanz, Gerd Wachsmuth Faculty of Mathematics, Technische Universität Chemnitz, Chemnitz, Ke Wang School of Mathematical Sciences, Fudan University, Shanghai, China

14 xiv Contributors Heiko K. Weichelt Research Group Mathematics in Industry and Technology (MiIT), Technische Universität Chemnitz, Chemnitz, Achim Wixforth Institute of Physics, Universität Augsburg, Augsburg, Winnifried Wollner Department of Mathematics, Universität Hamburg, Hamburg, Jan Carsten Ziems Department of Mathematics, Technische Universität Darmstadt, Darmstadt,