Simultaneous reduced basis approximation of parameterized elliptic eigenvalue problems∗
Lehrstuhl für Numerische Mathematik, Technische Universität München, Boltzmannstraße 3, 85748 Garching, Germany.
Received: 10 June 2015
Revised: 2 March 2016
Accepted: 12 April 2016
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.
Mathematics Subject Classification: 35B30 / 65N15 / 65N25 / 65N30 / 74S10
Key words: A posteriori error estimation / eigenvalue problem / finite element method / model reduction / multiple eigenvalues / parameter-dependent partial differential equation / reduced basis method
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