Simultaneous Reduced Basis Approximation of Parameterized Elliptic\n Eigenvalue Problems

2015/06/30 by Thomas Horger, Barbara Wohlmuth, Horger, Thomas +3 · 1 citation
Physics and Astronomy · Engineering · #Model Reduction and Neural Networks #Numerical methods in engineering #Fatigue and fracture mechanics

paper · pdf · doi:10.48550/arxiv.1506.09200

Abstract

The focus is on a model reduction framework for parameterized elliptic\neigenvalue problems by a reduced basis method. In contrast to the standard\nsingle output case, one is interested in approximating several outputs\nsimultaneously, namely a certain number of the smallest eigenvalues. For a fast\nand reliable evaluation of these input-output relations, we analyze a\nposteriori error estimators for eigenvalues. Moreover, we present different\ngreedy strategies and study systematically their performance. Special attention\nneeds to be paid to multiple eigenvalues whose appearance is\nparameter-dependent. Our methods are of particular interest for applications in\nvibro-acoustics.\n

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