Interpolatory projection methods for parameterized model reduction

Files

Main article (1.34 MB)
Downloads: 1138

TR Number

Date

2011

Journal Title

Journal ISSN

Volume Title

Publisher

Siam Publications

Abstract

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 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 H(2) circle times L(2) joint error measure. The capabilities of these approaches are illustrated by several numerical examples from technical applications.

Description

Keywords

parameterized model reduction, interpolation, rational krylov, partial-differential-equations, nonlinear dynamical-systems, reduced, basis method, order reduction, approximation, optimization, macromodels, algorithm, networks, mathematics, applied

Citation

Baur, U.; Beattie, C.; Benner, P.; Gugercin, S., "Interpolatory projection methods for parameterized model reduction," SIAM J. Sci. Comput., 33(5), 2489-2518, (2011). DOI: 10.1137/090776925