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Titel
Two-sided moment matching methods for nonlinear model reduction / Peter Benner, Tobias Breiten
VerfasserBenner, Peter ; Breiten, Tobias
KörperschaftMax-Planck-Institut für Dynamik Komplexer Technischer Systeme
ErschienenMagdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, June 29, 2012
Umfang1 Online-Ressource (25 Seiten = 0,92 MB) : Diagramme
SpracheEnglisch
SerieMax Planck Institute Magdeburg Preprints ; 12-12
URNurn:nbn:de:gbv:3:2-64035 
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Two-sided moment matching methods for nonlinear model reduction [0.92 mb]
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Abstract: In this paper, we discuss a recently introduced approach for nonlinear model order reduction. The new method is motivated by the concept of moment matching known from model reduction techniques for linear systems and can be generalized by means of generalized transfer functions arising for a large class of smooth nonlinear control affine dynamical systems. We will extend the existing concepts by making use of some basic tools known from tensor theory. This will allow a more efficient computation of the reduced-order model as well as the possibility of constructing two-sided projection methods which are theoretically shown to yield more accurate reduced-order models. Moreover, we will test both, one-sided and two-sided projection methods, on several semi-discretized nonlinear partial differential equations which already have been used as test examples in the context of nonlinear model reduction and compare them with the common nonlinear reduction technique proper orthogonal decomposition. We will further point out the main advantages and drawbacks of our new method.

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Abstract: In this paper we discuss a recently introduced approach for nonlinear model order reduction. The new method is motivated by the concept of moment matching known from model reduction techniques for linear systems and can be generalized by means of generalized transfer functions arising for a large class of smooth nonlinear control affine dynamical systems. We will extend the existing concepts by making use of some basic tools known from tensor theory. This will allow a more efficient computation of the reduced-order model as well as the possibility of constructing two-sided projection methods which are theoretically shown to yield more accurate reduced-order models. Moreover we will test both one-sided and two-sided projection methods on several semi-discretized nonlinear partial differential equations which already have been used as test examples in the context of nonlinear model reduction and compare them with the common nonlinear reduction technique proper orthogonal decomposition. We will further point out the main advantages and drawbacks of our new method.