Bock / Hoog / Friedman Model Order Reduction: Theory, Research Aspects and Applications

1. Auflage 2008
ISBN: 978-3-540-78841-6
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 466 Seiten

The idea for this book originated during the workshop 'Model order reduction, coupled problems and optimization' held at the Lorentz Center in Leiden from S- 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 ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd 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 de?ned during the discussion sessions at the workshop, is three-fold: ?rst, 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 appli- 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.

Wil Schilders received the MSc degree in pure and applied mathematics from Nijmegen University in 1978, and a PhD in numerical analysis from Trinity College Dublin in 1980. Since 1980, he has been with Philips Electronics, where he developed algorithms for semiconductor device simulation, electronic circuit simulation, and electromagnetics problems. He wrote two volumes on the numerical simulation of semiconductor devices, and published a special volume on Numerical Methods in Electromagnetics. Since 1999, he is part-time professor in numerical analysis for industry at Eindhoven University of Technology. He developed a novel method known as the Schilders factorization for the solution of indefinite linear systems. Since more than a decade, his interest is in model order reduction, and he is a frequent organizer of workshops and symposia on this topic. Currently, he is with NXP Semiconductors, heading the Mathematics group. Henk van der Vorst is a leading expert in numerical linear algebra, in particular in iterative methods for linear systems and eigenproblems. The techniques developed and used in these areas are of very high interest in model order reduction. Van der Vorst was the (co-) author of novel and highly important techniques, including incomplete decompositions, Bi-CGSTAB, and the Jacobi-Davidson method. The Bi-CGSTAB paper was the most cited paper in mathematics  of the 1990's according to ISI in 2000. For the Jacobi-Davidson method he received, together with co-author Sleijpen  a SIAG-LA Award for the best paper in numerical linear algebra over a three year period. Van der Vorst is Editor in Chief of the SIAM Journal SIMAX and he is member of the Netherlands Royal Academy of Sciences. Joost Rommes received the M.Sc. degree in computational science, the M.Sc.
degree in computer science, and the Ph.D. degree in mathematics from Utrecht
University, Utrecht, The Netherlands, in 2002, 2003, and 2007, respectively. During his PhD studies he worked on eigensolution methods with applications in model order reduction. Some of his developed methods are now used in software for circuit simulation and power system analysis. Joost Rommes currently works at NXP Semiconductors on model order reduction. In the electronics industry, an increase in complexity at transistor level leads to much large models that can not be simulated without accurate reduction techniques. Due to specific properties of the models, there is also need for different reduction techniques that can deal with these properties. This book provides a wide range of reduction techniques.

Autoren/Hrsg.

Bock, Hans-Georg

Hoog, Frank

Friedman, Avner

Gupta, Arvind

Neunzert, Helmut

Rommes, Joost

Inhaltsverzeichnis

1;Preface;5
2;Contents;7
3;List of Contributors;9
4;Part I Basic Concepts;13
4.1;Introduction to Model Order Reduction;14
4.1.1;1 Introduction;14
4.1.2;2 Transfer Function, Stability and Passivity;23
4.1.3;3 A Short Account of Techniques for Model Order Reduction;29
4.1.4;References;42
4.2;Linear Systems, Eigenvalues, and Projection;44
4.2.1;1 Introduction;44
4.2.2;2 Linear Systems;48
4.2.3;3 Subspace Methods;49
4.2.4;References;55
5;Part II Theory;58
5.1;Structure-Preserving Model Order Reduction of RCL Circuit Equations;60
5.1.1;1 Introduction;60
5.1.2;2 Formulation of General RCL Circuits as Integro-DAEs;62
5.1.3;3 Structure-Preserving Model Order Reduction;65
5.1.4;4 Equivalent First-Order Form of Integro-DAEs;68
5.1.5;5 Krylov-Subspace Projection and PRIMA;72
5.1.6;6 The SPRIM Algorithm;74
5.1.7;7 Pade-Type Approximation Property of SPRIM;77
5.1.8;8 Numerical Examples;78
5.1.9;9 Concluding Remarks;81
5.1.10;Acknowledgement;82
5.1.11;References;82
5.2;A Unified Krylov Projection Framework for Structure- Preserving Model Reduction;86
5.2.1;1 Introduction;86
5.2.2;2 A unified Krylov Projection Structure-Preserving Model Order Reduction Framework;87
5.2.3;3 Structure of Krylov Subspace and Arnoldi Process;93
5.2.4;4 RCL and RCS Systems;94
5.2.5;References;103
5.3;Model Reduction via Proper Orthogonal Decomposition;106
5.3.1;1 Introduction;106
5.3.2;2 Proper Orthogonal Decomposition;107
5.3.3;3 POD in Radiative Heat Transfer;113
5.3.4;4 Conclusions and Future Perspectives;116
5.3.5;Acknowledgments;118
5.3.6;References;118
5.4;PMTBR: A Family of Approximate Principal- components- like Reduction Algorithms;122
5.4.1;1 Introduction;122
5.4.2;2 Basic Algorithm;124
5.4.3;3 Algorithmic Variants;128
5.4.4;4 Analysis and Comparisons;134
5.4.5;5 Experimental Results;136
5.4.6;6 Conclusions;141
5.4.7;References;142
5.5;A Survey on Model Reduction of Coupled Systems.;144
5.5.1;1 Introduction;144
5.5.2;2 Coupled Systems;145
5.5.3;3 Model Reduction Approaches for Coupled Systems;148
5.5.4;4 Numerical Examples;157
5.5.5;References;164
5.6;Space Mapping and Defect Correction;168
5.6.1;1 Introduction;168
5.6.2;2 Fine and Coarse Models in Optimization;169
5.6.3;3 Space-Mapping Optimization;171
5.6.4;4 Defect Correction and Space Mapping;175
5.6.5;5 Manifold Mapping, the Improved Space Mapping Algorithm;178
5.6.6;6 Examples;181
5.6.7;7 Conclusions;186
5.6.8;References;186
5.7;Modal Approximation and Computation of Dominant Poles;188
5.7.1;1 Introduction;188
5.7.2;2 Transfer Functions, Dominant Poles and Modal Equivalents;188
5.7.3;3 Computing Dominant Poles;190
5.7.4;4 Generalizations;197
5.7.5;5 Numerical Examples;199
5.7.6;6 Conclusions;203
5.7.7;Acknowledgement;203
5.7.8;References;203
5.8;Some Preconditioning Techniques for Saddle Point Problems;206
5.8.1;1 Introduction;206
5.8.2;2 Properties of Saddle Point Systems;207
5.8.3;3 Preconditioned Krylov Subspace Methods;208
5.8.4;4 Block Preconditioners;210
5.8.5;5 Augmented Lagrangian Formulations;212
5.8.6;6 Constraint Preconditioning;213
5.8.7;7 Other Techniques;216
5.8.8;8 Numerical Examples;217
5.8.9;9 Conclusions;219
5.8.10;References;220
5.9;Time Variant Balancing and Nonlinear Balanced Realizations;224
5.9.1;1 Introduction;224
5.9.2;2 Time Varying Linear Systems;225
5.9.3;3 Sliding Interval Balancing;230
5.9.4;4 Nonlinear Balancing;235
5.9.5;5 Global Balancing;250
5.9.6;6 Mayer-Lie Interpolation;253
5.9.7;7 Nonlinear Model Reduction;255
5.9.8;8 How Far Can You Go?;256
5.9.9;9 Conclusions;258
5.9.10;References;259
5.10;Singular Value Analysis and Balanced Realizations for Nonlinear Systems;262
5.10.1;1 Introduction;262
5.10.2;2 Singular Value Analysis of Nonlinear Operators;263
5.10.3;3 Balanced Realization for Linear Systems;266
5.10.4;4 Basics of Nonlinear Balanced Realizations;269
5.10.5;5 Balanced Realizations Based on Singular Value Analysis of Hankel Operators;273
5.10.6;6 Model Order Reduction;276
5.10.7;7 Numerical Example;278
5.10.8;8 Conclusion;282
5.10.9;References;282
6;Part III Research Aspects and Applications;284
6.1;Matrix Functions;286
6.1.1;1 Introduction;286
6.1.2;2 Matrix Functions;286
6.1.3;3 Computational Aspects;289
6.1.4;4 The Exponential Function;296
6.1.5;5 The Matrix Sign Function;304
6.1.6;References;311
6.2;Model Reduction of Interconnected Systems;316
6.2.1;1 Introduction;316
6.2.2;2 Interconnected Systems Balanced Truncation;319
6.2.3;3 Krylov Techniques for Interconnected Systems;323
6.2.4;4 Examples of Structured Model Reduction Problems;327
6.2.5;5 Concluding Remarks;330
6.2.6;Acknowledgment;331
6.2.7;References;331
6.3;Quadratic Inverse Eigenvalue Problem and Its Applications to Model Updating — An Overview;334
6.3.1;1 Introduction;334
6.3.2;2 Challenges;336
6.3.3;3 Quadratic Inverse Eigenvalue Problem;338
6.3.4;4 Spill-Over Phenomenon;347
6.3.5;5 Least Squares Update;349
6.3.6;6 Conclusions;350
6.3.7;References;350
6.4;Data-Driven Model Order Reduction Using Orthonormal Vector Fitting;352
6.4.1;1 Identi.cation Problem;353
6.4.2;2 Vector Fitting;355
6.4.3;3 Orthonormal Vector Fitting;358
6.4.4;4 Example;362
6.4.5;5 Conclusion;364
6.4.6;6 Acknowledgements;364
6.4.7;A Sanathanan-Koerner Iteration;364
6.4.8;B Real-Valued State Space;366
6.4.9;References;368
6.5;Model-Order Reduction of High-Speed Interconnects Using Integrated Congruence Transform;372
6.5.1;1 High-Speed Interconnects and Its Effects on Signal Propagation;372
6.5.2;2 Time-Domain Macromodeling of High-Speed Interconnects;375
6.5.3;3 Time-Domain Macromodeling Through MOR;383
6.5.4;4 Numerical Computations;404
6.5.5;5 Conclusion;410
6.5.6;References;410
6.6;Model Order Reduction for MEMS: Methodology and Computational Environment for Electro- Thermal Models;414
6.6.1;1 Introduction;414
6.6.2;2 Applications;415
6.6.3;3 Model Order Reduction: Method and Numerical Results;416
6.6.4;4 Computational Environment;418
6.6.5;5 Error Estimation;420
6.6.6;6 Coupling of the Reduced Models;421
6.6.7;7 Model Order Reduction as a Fast Solver;423
6.6.8;8 Advanced Development;425
6.6.9;9 Summary;427
6.6.10;References;427
6.7;Model Order Reduction of Large RC Circuits;432
6.7.1;1 Introduction;432
6.7.2;2 Gaussian Elimination Background;433
6.7.3;3 RC-in RC-out Reduction;439
6.7.4;4 Elimination for Synthesis;446
6.7.5;5 Computational Aspects;451
6.7.6;6 Conclusion;455
6.7.7;References;456
6.8;Reduced Order Models of On-Chip Passive Components and Interconnects, Workbench and Test Structures;458
6.8.1;1 Extraction of the EM-FW State Models for Passive Components;458
6.8.2;2 Finite States Representation by Finite Integrals Technique;461
6.8.3;3 State Representation of the Boundary Conditions;465
6.8.4;4 ROMWorkBench;468
6.8.5;5 All Levels Reduced Order Modelling;470
6.8.6;6 Test Structures;471
6.8.7;7 Conclusions;476
6.8.8;Acknowledgment;478
6.8.9;References;478
7;Index;480