Model Order Reduction: Theory, Research Aspects and ApplicationsWilhelmus H. Schilders, Henk A. van der Vorst, Joost Rommes 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. |
Contents
| 3 | |
Linear Systems Eigenvalues and Projection | 33 |
Department of Computer Science Sint Pietersnieuwstraat | 41 |
StructurePreserving Model Order Reduction of RCL Circuit Equations | 49 |
A Unified Krylov Projection Framework for StructurePreserving | 74 |
Model Reduction via Proper Orthogonal Decomposition | 95 |
A Family of Approximate Principalcomponentslike | 110 |
A Survey on Model Reduction of Coupled Systems | 133 |
Singular Value Analysis and Balanced Realizations for Nonlinear | 251 |
Matrix Functions | 274 |
Model Reduction of Interconnected Systems | 305 |
Quadratic Inverse Eigenvalue Problem and Its Applications | 322 |
DataDriven Model Order Reduction Using Orthonormal Vector Fitting | 341 |
ModelOrder Reduction of HighSpeed Interconnects Using Integrated | 361 |
Methodology and Computational | 402 |
Model Order Reduction of Large RC Circuits | 421 |
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Common terms and phrases
algorithm analysis applications approach approximation assume balanced balanced realization balanced truncation basis block bound circuit columns complex computed consider construct Control convergence corresponding coupled defined definite denotes derived described diagonal differential dimension direction discussed dominant dynamical eigenvalues elements equations equivalent error estimate example Figure first formulation frequency given gives Gramians Hence IEEE important initial input integral interconnect iteration Krylov subspace linear systems mapping matrix method minimal model order reduction model reduction nodes nonlinear Note numerical observability obtained operator optimization original orthogonal output parameters poles positive presented preserve problem procedure projection properties rational reachability reduced model reduced-order refer respectively samples shown shows SIAM simulation singular value solution solving space stable step structure subsystems symmetric techniques Theorem tion transfer function transformation vector