Interpolatory projection methods for parameterized model reduction

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2011
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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.

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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