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Reduced Order Methods for Modeling and Computational Reduction

  • Book
  • © 2014

Overview

Editors:
  1. Alfio Quarteroni

    1. CMCS-MATHICSE, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
      MOX, Department of Mathematics “F. Brioschi”, Politecnico di Milano, Milan, Italy

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    You can also search for this editor in PubMed   Google Scholar

  2. Gianluigi Rozza

    1. SISSA mathLab, International School for Advanced Studies, Trieste, Italy

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • A complete review on the state of the art of model order reduction advances and developments
  • A gallery of application examples on reduced order modeling in computational science and engineering
  • It covers several topics and techniques by leading experts
  • Includes supplementary material: sn.pub/extras

Part of the book series: MS&A (MS&A, volume 9)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-x
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  2. A Novel Approach to Model Order Reduction for Coupled Multiphysics Problems

    • Wil H. A. Schilders, Agnieszka Lutowska
    Pages 1-49

  3. Case Study: Parametrized Reduction Using Reduced-Basis and the Loewner Framework

    • Antonio C. Ionita, Athanasios C. Antoulas
    Pages 51-66

  4. Comparison of Some Reduced Representation Approximations

    • Mario Bebendorf, Yvon Maday, Benjamin Stamm
    Pages 67-100

  5. Application of the Discrete Empirical Interpolation Method to Reduced Order Modeling of Nonlinear and Parametric Systems

    • Harbir Antil, Matthias Heinkenschloss, Danny C. Sorensen
    Pages 101-136

  6. Greedy Sampling Using Nonlinear Optimization

    • Karsten Urban, Stefan Volkwein, Oliver Zeeb
    Pages 137-157

  7. A Robust Algorithm for Parametric Model Order Reduction Based on Implicit Moment Matching

    • Peter Benner, Lihong Feng
    Pages 159-185

  8. On the Use of Reduced Basis Methods to Accelerate and Stabilize the Parareal Method

    • Feng Chen, Jan S. Hesthaven, Xueyu Zhu
    Pages 187-214

  9. On the Stability of Reduced-Order Linearized Computational Fluid Dynamics Models Based on POD and Galerkin Projection: Descriptor vs Non-Descriptor Forms

    • David Amsallem, Charbel Farhat
    Pages 215-233

  10. Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

    • Toni Lassila, Andrea Manzoni, Alfio Quarteroni, Gianluigi Rozza
    Pages 235-273

  11. Window Proper Orthogonal Decomposition: Application to Continuum and Atomistic Data

    • Leopold Grinberg, Mingge Deng, George Em Karniadakis, Alexander Yakhot
    Pages 275-303

  12. Reduced Order Models at Work in Aeronautics and Medicine

    • Michel Bergmann, Thierry Colin, Angelo Iollo, Damiano Lombardi, Olivier Saut, Haysam Telib
    Pages 305-332

  13. Back Matter

    Pages 333-334
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Keywords

About this book

This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.

Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects.

This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

Editors and Affiliations

  • CMCS-MATHICSE, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Alfio Quarteroni

  • MOX, Department of Mathematics “F. Brioschi”, Politecnico di Milano, Milan, Italy

    Alfio Quarteroni

  • SISSA mathLab, International School for Advanced Studies, Trieste, Italy

    Gianluigi Rozza

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