Research
Nonlinear eigenvalue and frequency response problems in industrial practice
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* Corresponding author: Volker Mehrmann mehrmann@math.tu-berlin.de
Institut für Mathematik, Ma 4-5, TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
Journal of Mathematics in Industry 2011, 1:7 doi:10.1186/2190-5983-1-7
The electronic version of this article is the complete one and can be found online at: http://www.mathematicsinindustry.com/content/1/1/7
| Received: | 21 February 2011 |
| Accepted: | 27 July 2011 |
| Published: | 27 July 2011 |
© 2011 Mehrmann and Schröder; licensee Springer.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Background
We discuss the numerical solution of large scale nonlinear eigenvalue problems and frequency response problems that arise in the analysis, simulation and optimization of acoustic fields. We report about the cooperation with the company SFE in Berlin. We present the challenges in the current industrial problems and the state-of-the-art of current methods.
Results
The difficulties that arise with current off-the-shelf methods are discussed and several industrial examples are presented.
Conclusions
It is documented that industrial cooperation is by no means a one-way street of transfer from academia to industry but the challenges arising in industrial practice also lead to new mathematical questions which actually change the mathematical theory and methods.
AMS classification: 65F18, 15A18.
Keywords:
nonlinear eigenvalue problem; frequency response problem; complex symmetric linear system; block-Arnoldi method; acoustic field computation; automotive industryPublisher note
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