Solving parameter-dependent Lyapunov equations using reduced basis method with application to parametric model order reduction

  • Our aim is to numerically solve parameter-dependent Lyapunov equations using reduced basis method. Such equations arise in parametric model order reduction. We restrict ourselves to systems that affinely depend on the parameter as our main ingredient is the min-Theta approach. In those cases, we derive various a posteriori error estimates. Based on these estimates, Greedy algorithms for constructing reduced basis are formulated. Thanks to the derived results, a novel so-called parametric balanced truncation model reduction method is developed. Numerical examples are presented.

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Metadaten
Author:Nguyen Thanh Son, Tatjana StykelGND
URN:urn:nbn:de:bvb:384-opus4-31557
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/3155
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2015-05)
Type:Preprint
Language:English
Publishing Institution:Universität Augsburg
Release Date:2015/06/26
Tag:parameter-dependent Lyapunov equations; reduced basis method; affine dependence; error estimates; greedy algorithm; model order reduction; parametric balanced truncation
GND-Keyword:Ljapunov-Gleichung; Fehlerabschätzung; A-posteriori-Abschätzung; Greedy-Algorithmus; Ordnungsreduktion; Numerisches Verfahren
Note:
Erschienen in: SIAM J. Matrix Anal. Appl., 38(2), 2017, pp. 478–504, https://doi.org/10.1137/15M1027097
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht