Reduced Order Methods for Modeling and Computational Reduction

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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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.

• computational mechanics
• model order reduction
• parametrized PDE
• reduced order modeling
• scientific computing

• 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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