Model reduction of parametrized systems

✍ Scribed by Benner, Peter

• Publisher: Springer
• Year: 2017
• Tongue: English
• Leaves: 503
• Series: MS&A 17
• Category: Library

✦ Synopsis

The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems.

The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts, guaranteeing a wide range of expertise and topics. Further, it reflects an important effor

t, carried out over the last 12 years, to build a growing research community in this field.

Though not a textbook, some of the chapters can be used as reference materials or lecture notes for classes and tutorials (doctoral schools, master classes).

✦ Table of Contents

Front Matter ....Pages i-xii
Two Ways to Treat Time in Reduced Basis Methods (Silke Glas, Antonia Mayerhofer, Karsten Urban)....Pages 1-16
Simultaneous Empirical Interpolation and Reduced Basis Method: Application to Non-linear Multi-Physics Problem (Cécile Daversin, Christophe Prud’homme)....Pages 17-35
A Certified Reduced Basis Approach for Parametrized Optimal Control Problems with Two-Sided Control Constraints (Eduard Bader, Martin A. Grepl, Karen Veroy)....Pages 37-54
A Reduced Basis Method with an Exact Solution Certificate and Spatio-Parameter Adaptivity: Application to Linear Elasticity (Masayuki Yano)....Pages 55-76
A Reduced Basis Method for Parameter Functions Using Wavelet Approximations (Antonia Mayerhofer, Karsten Urban)....Pages 77-90
Reduced Basis Isogeometric Mortar Approximations for Eigenvalue Problems in Vibroacoustics (Thomas Horger, Barbara Wohlmuth, Linus Wunderlich)....Pages 91-106
Reduced Basis Approximations for Maxwell’s Equations in Dispersive Media (Peter Benner, Martin Hess)....Pages 107-119
Offline Error Bounds for the Reduced Basis Method (Robert O’Connor, Martin Grepl)....Pages 121-136
ArbiLoMod: Local Solution Spaces by Random Training in Electrodynamics (Andreas Buhr, Christian Engwer, Mario Ohlberger, Stephan Rave)....Pages 137-148
Reduced-Order Semi-Implicit Schemes for Fluid-Structure Interaction Problems (Francesco Ballarin, Gianluigi Rozza, Yvon Maday)....Pages 149-167
True Error Control for the Localized Reduced Basis Method for Parabolic Problems (Mario Ohlberger, Stephan Rave, Felix Schindler)....Pages 169-182
Efficient Reduction of PDEs Defined on Domains with Variable Shape (Andrea Manzoni, Federico Negri)....Pages 183-199
Localized Reduced Basis Approximation of a Nonlinear Finite Volume Battery Model with Resolved Electrode Geometry (Mario Ohlberger, Stephan Rave)....Pages 201-212
A-Posteriori Error Estimation of Discrete POD Models for PDE-Constrained Optimal Control (Martin Gubisch, Ira Neitzel, Stefan Volkwein)....Pages 213-234
Hi-POD Solution of Parametrized Fluid Dynamics Problems: Preliminary Results (Davide Baroli, Cristina Maria Cova, Simona Perotto, Lorenzo Sala, Alessandro Veneziani)....Pages 235-254
Adaptive Sampling for Nonlinear Dimensionality Reduction Based on Manifold Learning (Thomas Franz, Ralf Zimmermann, Stefan Görtz)....Pages 255-269
Cross-Gramian-Based Model Reduction: A Comparison (Christian Himpe, Mario Ohlberger)....Pages 271-283
Truncated Gramians for Bilinear Systems and Their Advantages in Model Order Reduction (Peter Benner, Pawan Goyal, Martin Redmann)....Pages 285-300
Leveraging Sparsity and Compressive Sensing for Reduced Order Modeling (J. Nathan Kutz, Syuzanna Sargsyan, Steven L. Brunton)....Pages 301-315
A HJB-POD Approach to the Control of the Level Set Equation (Alessandro Alla, Giulia Fabrini, Maurizio Falcone)....Pages 317-331
Model Order Reduction Approaches for Infinite Horizon Optimal Control Problems via the HJB Equation (Alessandro Alla, Andreas Schmidt, Bernard Haasdonk)....Pages 333-347
Interpolatory Methods for (\mathcal{H}_{\infty }) Model Reduction of Multi-Input/Multi-Output Systems (Alessandro Castagnotto, Christopher Beattie, Serkan Gugercin)....Pages 349-365
Model Reduction of Linear Time-Varying Systems with Applications for Moving Loads (M. Cruz Varona, B. Lohmann)....Pages 367-386
Interpolation Strategy for BT-Based Parametric MOR of Gas Pipeline-Networks (Y. Lu, N. Marheineke, J. Mohring)....Pages 387-401
Energy Stable Model Order Reduction for the Allen-Cahn Equation (Murat Uzunca, Bülent Karasözen)....Pages 403-419
MOR-Based Uncertainty Quantification in Transcranial Magnetic Stimulation (Lorenzo Codecasa, Konstantin Weise, Luca Di Rienzo, Jens Haueisen)....Pages 421-437
Model Order Reduction of Nonlinear Eddy Current Problems Using Missing Point Estimation (Y. Paquay, O. Brüls, C. Geuzaine)....Pages 439-454
On Efficient Approaches for Solving a Cake Filtration Model Under Parameter Variation (S. Osterroth, O. Iliev, R. Pinnau)....Pages 455-470
Model Reduction for Coupled Near-Well and Reservoir Models Using Multiple Space-Time Discretizations (Walid Kheriji, Yalchin Efendiev, Victor Manuel Calo, Eduardo Gildin)....Pages 471-490
Time-Dependent Parametric Model Order Reduction for Material Removal Simulations (Michael Baumann, Dominik Hamann, Peter Eberhard)....Pages 491-504

✦ Subjects

Mathematical models;Mathematical optimization;Computational complexity;MATHEMATICS / General