Model Order Reduction: Theory, Research Aspects and Applications

463 Pages·2008·6.09 MB·English

MATHEMATICS IN INDUSTRY 13
Editors
Hans-Georg Bock
Frank de Hoog
Avner Friedman
Arvind Gupta
Helmut Neunzert
William R. Pulleyblank
Torgeir Rusten
Fadil Santosa
Anna-Karin Tornberg
THE EUROPEAN CONSORTIUM
FOR MATHEMATICS IN INDUSTRY
SUBSERIES
Managing Editor
Vincenzo Capasso
Editors
Luis L. Bonilla
Robert Mattheij
Helmut Neunzert
Otmar Scherzer
Wilhelmus H.A. Schilders
Henk A. van der Vorst
Joost Rommes
Editors
Model Order Reduction:
Theory, Research Aspects
and Applications
With 133 Figures , 53 in color and 9 Tables
123
Authors and Editors
Wilhelmus H.A. Schilders Joost Rommes
NXP Semiconductors NXP Semiconductors
Corporate I&T/DTF/Design Methods Corporate I&T/DTF/Design Methods
Physical Design Methods − Mathematics Physical Design Mothods
High Tech Campus 37 High Tech Campus 37
5656 AE Eindhoven 5656 AE Eindhoven
The Netherlands The Netherlands
Preface
The idea for this book originated during the workshop “Model order reduction,
coupled problems and optimization” held at the Lorentz Center in Leiden from Sep-
tember 19–23, 2005. During one of the discussion sessions, it became clear that a
book describing the state of the art in model order reduction, starting from the very
basics and containing an overview of all relevant techniques, would be of great use
for students, young researchers starting in the field, and experienced researchers. The
observation that most of the theory on model order reduction is scattered over many
good papers, making it difficult to find a good starting point, was supported by most
of the participants. Moreover, most of the speakers at the workshop were willing to
contribute to the book that is now in front of you.
The goal of this book, as defined during the discussion sessions at the workshop,
is three-fold: first, it should describe the basics of model order reduction. Second,
both general and more specialized model order reduction techniques for linear and
nonlinear systems should be covered, including the use of several related numerical
techniques. Third, the use of model order reduction techniques in practical applica-
tions and current research aspects should be discussed.
We have organized the book according to these goals. In Part I, the rationale
behind model order reduction is explained, and an overview of the most common
methods is described. Furthermore, in the second chapter, an introduction is given
to background material from numerical linear algebra needed to assess the theory
and methods presented later in the book. This is very important and useful informa-
tion, as advances in numerical linear algebra often lead to new results in the area of
model order reduction. Thus, the first two chapters serve as an introduction to readers
who are not familiar with the subject. In Part II, model order reduction techniques
and related numerical problems are described from different points of view: both
frameworks for structure-preserving techniques and more specialized techniques are
presented, while numerical methods for (closely) related problems and approaches
for nonlinear systems are considered as well. This part serves as the theoretical back-
bone of the book, containing an overview of techniques used and areas covered. In
Part III the focus is on research aspects and applications of model order reduction. A
variety of experiments with real-life examples shows that different problems require
VI Preface
different techniques, while application of the techniques leads to new research topics
that are described as well.
Despite the fact that the workshop was organized already in 2005, this book con-
tains many recent advances in model order reduction. Moreover, it presents several
open problems for which techniques are still in development, related to both linear
systems, which become larger and more complex mainly due to industrial require-
ments, and nonlinear systems, which demand a completely new theory. The latter
illustrates the final and most important goal of this book, namely to serve as a source
of inspiration for its readers, who will discover that model order reduction is a very
exciting and lively field.
At this point we would like to thank all authors of the chapters in this book.
Without the contributions of these experts, it would not be possible to cover the wide
and rapidly developing field of model order reduction in one book.
Leiden, Utrecht, Eindhoven Wil Schilders
September 2005 – May 2008 Henk van der Vorst
Joost Rommes
Contents
Part I Basic Concepts
Introduction to Model Order Reduction
Wil Schilders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Linear Systems, Eigenvalues, and Projection
Henk van der Vorst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Part II Theory
Structure-Preserving Model Order Reduction of RCL Circuit Equations
Roland W. Freund . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
A Unified Krylov Projection Framework for Structure-Preserving
Model Reduction
Zhaojun Bai, Ren-cang Li, and Yangfeng Su . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Model Reduction via Proper Orthogonal Decomposition
Rene´ Pinnau . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
PMTBR: A Family of Approximate Principal-components-like
Reduction Algorithms
Joel R. Phillips, Zhenhai Zhu, and L. Miguel Silveira . . . . . . . . . . . . . . . . . . . . . 111
A Survey on Model Reduction of Coupled Systems
Timo Reis and Tatjana Stykel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Space Mapping and Defect Correction
David Echeverr´ıa, Domenico Lahaye, and Piet W. Hemker . . . . . . . . . . . . . . . . . 157
Modal Approximation and Computation of Dominant Poles
Joost Rommes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
VIII Contents
Some Preconditioning Techniques for Saddle Point Problems
Michele Benzi and Andrew J. Wathen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
Time Variant Balancing and Nonlinear Balanced Realizations
E.I. Verriest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Singular Value Analysis and Balanced Realizations for Nonlinear
Systems
Kenji Fujimoto and Jacquelien M.A. Scherpen. . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Part III Research Aspects and Applications
Matrix Functions
Andreas Frommer and Valeria Simoncini . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
Model Reduction of Interconnected Systems
Antoine Vandendorpe and Paul Van Dooren . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
Quadratic Inverse Eigenvalue Problem and Its Applications
to Model Updating — An Overview
∗∗
Moody T. Chu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
Data-Driven Model Order Reduction Using Orthonormal Vector Fitting
Dirk Deschrijver and Tom Dhaene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
Model-Order Reduction of High-Speed Interconnects Using Integrated
Congruence Transform
Emad Gad, Michel Nakhla, and Ram Achar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
Model Order Reduction for MEMS: Methodology and Computational
Environment for Electro-Thermal Models
Tamara Bechtold, Evgenii B. Rudnyi, and Jan G. Korvink . . . . . . . . . . . . . . . . . . 403
Model Order Reduction of Large RC Circuits
Nick P. van der Meijs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
Reduced Order Models of On-Chip Passive Components
and Interconnects, Workbench and Test Structures
Daniel Ioan and Gabriela Ciuprina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
List of Contributors
Ram Achar Gabriela Ciuprina
Deptartment of Electronics Politehnica University of Bucharest
Carleton University Romania
Ottawa, ON, Canada, K1S 5B6
X List of Contributors
Andreas Frommer Nick P. van der Meijs
Department of Mathematics and Faculty of EEMCS
Science Delft University of Technology
University of Wuppertal Delft, The Netherlands
D-42097 Wuppertal, Germany