Abstract
The reduced basis method (RBM) is a model order reduction technique for parametrized partial differential equations (PDEs) which enables fast and reliable evaluation of the transfer behavior in many-query and real-time settings. We use the RBM to generate a low order model of an electromagnetic system governed by time-harmonic Maxwell’s equations. The reduced order model then makes it feasible to analyze the uncertainty in the model by a Monte-Carlo simulation. Stochastic collocation is employed as a second technique to estimate the statistics. In particular the combination of model order reduction and stochastic collocation allows low computation times compared to Monte-Carlo simulations. We compare the accuracy of Monte-Carlo simulation Hermite Genz-Keister stochastic collocation and the RBM to compute the transfer function under uncertain geometric parameters.
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Acknowledgements
This work is supported by the collaborative project nanoCOPS, Nanoelectronic COupled Problems Solutions, supported by the European Union in the FP7-ICT-2013-11 Program under Grant Agreement Number 619166.
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Benner, P., Hess, M.W. (2016). Reduced Basis Modeling for Uncertainty Quantification of Electromagnetic Problems in Stochastically Varying Domains. In: Bartel, A., Clemens, M., Günther, M., ter Maten, E. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry(), vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-30399-4_21
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DOI: https://doi.org/10.1007/978-3-319-30399-4_21
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