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Two Ways to Treat Time in Reduced Basis Methods Read chapter Read first chapter

2017 | Supplement | Chapter

6. Reduced Basis Isogeometric Mortar Approximations for Eigenvalue Problems in Vibroacoustics

Authors : Thomas Horger, Barbara Wohlmuth, Linus Wunderlich

Published in: Model Reduction of Parametrized Systems

Publisher: Springer International Publishing

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Abstract

We simulate the vibration of a violin bridge in a multi-query context using reduced basis techniques. The mathematical model is based on an eigenvalue problem for the orthotropic linear elasticity equation. In addition to the nine material parameters, a geometrical thickness parameter is considered. This parameter enters as a 10th material parameter into the system by a mapping onto a parameter independent reference domain. The detailed simulation is carried out by isogeometric mortar methods. Weakly coupled patch-wise tensorial structured isogeometric elements are of special interest for complex geometries with piecewise smooth but curvilinear boundaries. To obtain locality in the detailed system, we use the saddle point approach and do not apply static condensation techniques. However within the reduced basis context, it is natural to eliminate the Lagrange multiplier and formulate a reduced eigenvalue problem for a symmetric positive definite matrix. The selection of the snapshots is controlled by a multi-query greedy strategy taking into account an error indicator allowing for multiple eigenvalues.

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previous chapter A Reduced Basis Method for Parameter Functions Using Wavelet Approximations
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Metadata
Title
Reduced Basis Isogeometric Mortar Approximations for Eigenvalue Problems in Vibroacoustics
Authors
Thomas Horger
Barbara Wohlmuth
Linus Wunderlich
Copyright Year
2017
Book
Model Reduction of Parametrized Systems

Print ISBN: 978-3-319-58785-1

Electronic ISBN: 978-3-319-58786-8

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-58786-8_6

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