Interpolatory Projection Methods for Parameterized Model Reduction
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 n...
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Published in | SIAM journal on scientific computing Vol. 33; no. 5; pp. 2489 - 2518 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Philadelphia
Society for Industrial and Applied Mathematics
01.01.2011
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 1064-8275 1095-7197 |
DOI: | 10.1137/090776925 |