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arXiv · 1506.09200

Simultaneous Reduced Basis Approximation of Parameterized Elliptic Eigenvalue Problems

Thomas Horger·Barbara Wohlmuth·Thomas Dickopf
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Abstract

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.

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Thomas Horger, Barbara Wohlmuth, Thomas Dickopf. 2015-06-30. Simultaneous Reduced Basis Approximation of Parameterized Elliptic Eigenvalue Problems. https://arxiv.org/abs/1506.09200

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