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Model Reduction of Complex Dynamical Systems

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  • © 2021

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Editors:
  1. Peter Benner

    1. Dynamics of Complex Technical Systems, Max Planck Institute, Magdeburg, Germany

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  2. Tobias Breiten

    1. Institute of Mathematics, Technical University of Berlin, Berlin, Germany

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  3. Heike Faßbender

    1. Institute for Numerical Analysis, TU Braunschweig, Braunschweig, Germany

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  4. Michael Hinze

    1. Mathematisches Institut, Universität Koblenz-Landau, Campus Koblenz, Koblenz, Germany

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  5. Tatjana Stykel

    1. Institut für Mathematik, Universität Augsburg, Augsburg, Germany

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  6. Ralf Zimmermann

    1. Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark

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  • Presents the latest research on model order reduction of complex dynamical systems
  • Features contributions from leading researchers and users of model order reduction techniques
  • Offers an ideal resource for graduate students and researchers in all areas of model reduction, as well as those working in applied mathematics and theoretical informatics

Part of the book series: International Series of Numerical Mathematics (ISNM, volume 171)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xii
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  2. Methods and Techniques of Model Order Reduction

    1. Front Matter

      Pages 1-1
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    2. On Bilinear Time-Domain Identification and Reduction in the Loewner Framework

      • D. S. Karachalios, I. V. Gosea, A. C. Antoulas
      Pages 3-30

    3. Balanced Truncation for Parametric Linear Systems Using Interpolation of Gramians: A Comparison of Algebraic and Geometric Approaches

      • Nguyen Thanh Son, Pierre-Yves Gousenbourger, Estelle Massart, Tatjana Stykel
      Pages 31-51

    4. Toward Fitting Structured Nonlinear Systems by Means of Dynamic Mode Decomposition

      • Ion Victor Gosea, Igor Pontes Duff
      Pages 53-74

    5. Clustering-Based Model Order Reduction for Nonlinear Network Systems

      • Peter Benner, Sara Grundel, Petar Mlinarić
      Pages 75-96

    6. Adaptive Interpolatory MOR by Learning the Error Estimator in the Parameter Domain

      • Sridhar Chellappa, Lihong Feng, Valentín de la Rubia, Peter Benner
      Pages 97-117

    7. A Link Between Gramian-Based Model Order Reduction and Moment Matching

      • C. Bertram, H. Faßbender
      Pages 119-139

    8. Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms

      • Christian Himpe
      Pages 141-164

    9. Optimization-Based Parametric Model Order Reduction for the Application to the Frequency-Domain Analysis of Complex Systems

      • Rupert Ullmann, Stefan Sicklinger, Gerhard Müller
      Pages 165-189

    10. On Extended Model Order Reduction for Linear Time Delay Systems

      • Sajad Naderi Lordejani, Bart Besselink, Antoine Chaillet, Nathan van de Wouw
      Pages 191-215

  3. Applications of Model Order Reduction

    1. Front Matter

      Pages 217-217
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    2. A Practical Method for the Reduction of Linear Thermo-Mechanical Dynamic Equations

      • Artur Jungiewicz, Christoph Ludwig, Shuwen Sun, Utz Wever, Roland Wüchner
      Pages 219-235

    3. Reduced-Order Methods in Medical Imaging

      • Saifon Chaturantabut, Thomas Freeze, Elias Salomão Helou, Nicole Hemming-Schroeder, Charles H. Lee
      Pages 237-258

    4. Efficient Krylov Subspace Techniques for Model Order Reduction of Automotive Structures in Vibroacoustic Applications

      • Harikrishnan K. Sreekumar, Rupert Ullmann, Stefan Sicklinger, Sabine C. Langer
      Pages 259-282

    5. Model-Based Adaptive MOR Framework for Unsteady Flows Around Lifting Bodies

      • Gaetano Pascarella, Marco Fossati
      Pages 283-305

    6. Reduced Basis Methods for Quasilinear Elliptic PDEs with Applications to Permanent Magnet Synchronous Motors

      • Michael Hinze, Denis Korolev
      Pages 307-326

    7. Structure-Preserving Reduced- Order Modeling of Non-Traditional Shallow Water Equation

      • Süleyman Yildiz, Murat Uzunca, Bülent Karasözen
      Pages 327-345

  4. Benchmarks and Software of Model Order Reduction

    1. Front Matter

      Pages 347-347
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    2. A Non-stationary Thermal-Block Benchmark Model for Parametric Model Order Reduction

      • Stephan Rave, Jens Saak
      Pages 349-356
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Keywords

About this book

This contributed volume presents some of the latest research related to model order reduction of complex dynamical systems with a focus on time-dependent problems.  Chapters are written by leading researchers and users of model order reduction techniques and are based on presentations given at the 2019 edition of the workshop series Model Reduction of Complex Dynamical Systems – MODRED, held at the University of Graz in Austria.  The topics considered can be divided into five categories:


  • system-theoretic methods, such as balanced truncation, Hankel norm approximation, and reduced-basis methods; 
  • data-driven methods, including Loewner matrix and pencil-based approaches, dynamic mode decomposition, and kernel-based methods;
  • surrogate modeling for design and optimization, with special emphasis on control and data assimilation;
  • model reduction methods in applications, such as control and network systems, computational electromagnetics, structural mechanics, and fluid dynamics; and
  • model order reduction software packages and benchmarks.



This volume will be an ideal resource for graduate students and researchers in all areas of model reduction, as well as those working in applied mathematics and theoretical informatics.


Editors and Affiliations

  • Dynamics of Complex Technical Systems, Max Planck Institute, Magdeburg, Germany

    Peter Benner

  • Institute of Mathematics, Technical University of Berlin, Berlin, Germany

    Tobias Breiten

  • Institute for Numerical Analysis, TU Braunschweig, Braunschweig, Germany

    Heike Faßbender

  • Mathematisches Institut, Universität Koblenz-Landau, Campus Koblenz, Koblenz, Germany

    Michael Hinze

  • Institut für Mathematik, Universität Augsburg, Augsburg, Germany

    Tatjana Stykel

  • Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark

    Ralf Zimmermann

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