Interpolatory Projection Methods for Parameterized Model Reduction

• Published in: SIAM journal on scientific computing Vol. 33; no. 5; pp. 2489 - 2518
• Main Authors: Baur, Ulrike, Beattie, Christopher, Benner, Peter, Gugercin, Serkan
• Format: Journal Article
• Language: English
• Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2011
• Subjects: CAE; Computer aided engineering; Design optimization; Dynamical systems; Simulation
• ISSN: 1064-8275; 1095-7197
• DOI: 10.1137/090776925

We provide a unifying projection-based framework for structure-preserving interpolatory model reduction of parameterized linear dynamical systems, i.e., systems having a structured dependence on parameters that we wish to retain in the reduced-order model. The parameter dependence may be linear or nonlinear and is retained in the reduced-order model. Moreover, we are able to give conditions under which the gradient and Hessian of the system response with respect to the system parameters is matched in the reduced-order model. We provide a systematic approach built on established interpolatory $\mathcal{H}_2$ optimal model reduction methods that will produce parameterized reduced-order models having high fidelity throughout a parameter range of interest. For single input/single output systems with parameters in the input/output maps, we provide reduced-order models that are optimal with respect to an $\mathcal{H}_2\otimes\mathcal{L}_2$ joint error measure. The capabilities of these approaches are illustrated by several numerical examples from technical applications.