Simultaneous reduced basis approximation of parameterized elliptic eigenvalue problems
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 443-465.

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
Mots clés : 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},
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     pages = {443--465},
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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. http://www.numdam.org/articles/10.1051/m2an/2016025/

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