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.

Accepted:

DOI: 10.1051/m2an/2016025

Keywords: A posteriori error estimation, eigenvalue problem, finite element method, model reduction, multiple eigenvalues, parameter-dependent partial differential equation, reduced basis method

^{1}; Wohlmuth, Barbara

^{1}; Dickopf, Thomas

^{1}

@article{M2AN_2017__51_2_443_0, author = {Horger, Thomas and Wohlmuth, Barbara and Dickopf, Thomas}, 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}, mrnumber = {3626406}, zbl = {1362.65121}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2016025/} }

TY - JOUR AU - Horger, Thomas AU - Wohlmuth, Barbara AU - Dickopf, Thomas TI - Simultaneous reduced basis approximation of parameterized elliptic eigenvalue problems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 443 EP - 465 VL - 51 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016025/ DO - 10.1051/m2an/2016025 LA - en ID - M2AN_2017__51_2_443_0 ER -

%0 Journal Article %A Horger, Thomas %A Wohlmuth, Barbara %A Dickopf, Thomas %T Simultaneous reduced basis approximation of parameterized elliptic eigenvalue problems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 443-465 %V 51 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016025/ %R 10.1051/m2an/2016025 %G en %F M2AN_2017__51_2_443_0

Horger, Thomas; Wohlmuth, Barbara; Dickopf, Thomas. Simultaneous reduced basis approximation of parameterized elliptic eigenvalue problems. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 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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