Geodesic
Simultaneous reduced basis approximation of parameterized elliptic eigenvalue problems
Horger, Thomas1 ; Wohlmuth, Barbara1  ; Dickopf, Thomas1 
1 Lehrstuhl für Numerische Mathematik, Technische Universität München, Boltzmannstraße 3, 85748 Garching, Germany.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 443-465

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The focus is on a model reduction framework for parameterized elliptic eigenvalue problems by a reduced basis method. In contrast to the standard single output case, one is interested in approximating several outputs simultaneously, namely a certain number of the smallest eigenvalues. For a fast and reliable evaluation of these input-output relations, we analyze a posteriori error estimators for eigenvalues. Moreover, we present different greedy strategies and study systematically their performance. Special attention needs to be paid to multiple eigenvalues whose appearance is parameter-dependent. Our methods are of particular interest for applications in vibro-acoustics.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2016025
Classification : 35B30, 65N15, 65N25, 65N30, 74S10
Keywords: A posteriori error estimation, eigenvalue problem, finite element method, model reduction, multiple eigenvalues, parameter-dependent partial differential equation, reduced basis method

Horger, Thomas 1 ; Wohlmuth, Barbara 1 ; Dickopf, Thomas 1

1 Lehrstuhl für Numerische Mathematik, Technische Universität München, Boltzmannstraße 3, 85748 Garching, Germany. 
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     title = {Simultaneous reduced basis approximation of parameterized elliptic eigenvalue problems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {443--465},
     publisher = {EDP-Sciences},
     volume = {51},
     number = {2},
     year = {2017},
     doi = {10.1051/m2an/2016025},
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     zbl = {1362.65121},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2016025/}
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Horger, Thomas; Wohlmuth, Barbara; Dickopf, Thomas. Simultaneous reduced basis approximation of parameterized elliptic eigenvalue problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 443-465. doi: 10.1051/m2an/2016025

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