Interpolatory projection methods for parameterized model reduction


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Siam Publications


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.



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


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