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Book Cover
E-book
Author MODRED (Workshop) (5th : 2019 : Graz, Austria)

Title Model reduction of complex dynamical systems / Peter Benner [and more], editors
Published Cham, Switzerland : Birkhäuser, 2021

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Description 1 online resource
Series International Series of Numerical Mathematics ; v. 171
International series of numerical mathematics ; v. 171.
Contents Intro -- Preface -- Contents -- *-20pt Methods and Techniques of Model Order Reduction -- On Bilinear Time-Domain Identification and Reduction in the Loewner Framework -- 1 Introduction -- 1.1 Outline of the Paper -- 2 System Theory Preliminaries -- 2.1 Linear Systems -- 2.2 Nonlinear Systems -- 3 The Loewner Framework -- 3.1 The Loewner Matrix -- 3.2 Construction of Interpolants -- 4 The Special Case of Bilinear Systems -- 4.1 The Growing Exponential Approach -- 4.2 The Kernel Separation Method -- 4.3 Identification of the Matrix N -- 4.4 A Separation Strategy for the second Kernel
4.5 The Loewner-Volterra Algorithm for Time-Domain Bilinear Identification and Reduction -- 4.6 Computational Effort of the Proposed Method -- 5 Numerical Examples -- 6 Conclusion -- References -- Balanced Truncation for Parametric Linear Systems Using Interpolation of Gramians: A Comparison of Algebraic and Geometric Approaches -- 1 Introduction -- 2 Balanced Truncation for Parametric Linear Systems and Standard Interpolation -- 2.1 Balanced Truncation -- 2.2 Interpolation of Gramians for Parametric Model Order Reduction -- 2.3 Offline-Online Decomposition
3 Interpolation on the Manifold mathcalS+(k, n) -- 3.1 A Quotient Geometry of mathcalS+(k, n) -- 3.2 Curve and Surface Interpolation on Manifolds -- 4 Numerical Examples -- 4.1 A model for heat conduction in solid material -- 4.2 An Anemometer Model -- 5 Conclusion -- References -- Toward Fitting Structured Nonlinear Systems by Means of Dynamic Mode Decomposition -- 1 Introduction -- 2 Dynamic Mode Decomposition -- 2.1 Dynamic Mode Decomposition with Control (DMDc) -- 2.2 Input-Output Dynamic Mode Decomposition -- 3 The Proposed Extensions -- 3.1 Bilinear Systems -- 3.2 Quadratic-Bilinear Systems
4 Numerical Experiments -- 4.1 The Viscous Burgers' Equation -- 4.2 Coupled van der Pol Oscillators -- 5 Conclusion -- 6 Appendix -- 6.1 Computation of the Reduced-Order Matrices for the Quadratic-Bilinear Case -- References -- Clustering-Based Model Order Reduction for Nonlinear Network Systems -- 1 Introduction -- 2 Preliminaries -- 2.1 Graph Theory -- 2.2 Graph Partitions -- 2.3 Linear Multi-agent Systems -- 2.4 Clustering-Based Model Order Reduction -- 2.5 Model Reduction for Non-asymptotically Stable Systems -- 3 Clustering for Linear Multi-agent Systems
4 Clustering for Nonlinear Multi-agent Systems -- 4.1 Nonlinear Multi-agent Systems -- 4.2 Clustering by Projection -- 5 Numerical Examples -- 5.1 Small Network Example -- 5.2 van der Pol Oscillators -- 6 Conclusions -- References -- Adaptive Interpolatory MOR by Learning the Error Estimator in the Parameter Domain -- 1 Introduction -- 2 Interpolatory MOR -- 3 Greedy Method for Choosing Interpolation Points -- 4 Adaptive Training by Learning the Error Estimator in the Parameter Domain -- 4.1 Radial Basis Functions -- 4.2 Learning the Error Estimator over the Parameter Domain
Summary 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
Subject System theory -- Congresses
Dynamics -- Congresses
Teoría de sistemas
Dinámica
Dynamics
System theory
Genre/Form proceedings (reports)
Conference papers and proceedings
Conference papers and proceedings.
Actes de congrès.
Form Electronic book
Author Benner, Peter
Breiten, Tobias
Fassbender, Heike
Hinze, Michael
Stykel, Tatjana
Zimmermann, Ralf
ISBN 9783030729837
3030729834