Abstract
In this paper, we propose a certified reduced basis (RB) method for quasilinear elliptic problems together with its application to nonlinear magnetostatics equations, where the later model permanent magnet synchronous motors (PMSM). The parametrization enters through the geometry of the domain and thus, combined with the nonlinearity, drives our reduction problem. We provide a residual-based a-posteriori error bound which, together with the Greedy approach, allows to construct reduced basis spaces of small dimensions. We use the empirical interpolation method (EIM) to guarantee the efficient offline-online computational procedure. The reduced basis solution is then obtained with the surrogate of Newton’s method. The numerical results indicate that the proposed reduced basis method provides a significant computational gain, compared to a finite element method.
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Notes
- 1.
All the computations are performed in MATLAB on Intel Xeon(R) CPU E5-1650 v3, 3.5 GHz x 12 cores, 64 GB RAM.
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Acknowledgements
Both authors acknowledge the support of the collaborative research project PASIROM funded by the German Federal Ministry of Education and Research (BMBF) under grant no. 05M2018.
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Hinze, M., Korolev, D. (2021). Reduced Basis Methods for Quasilinear Elliptic PDEs with Applications to Permanent Magnet Synchronous Motors. In: Benner, P., Breiten, T., Faßbender, H., Hinze, M., Stykel, T., Zimmermann, R. (eds) Model Reduction of Complex Dynamical Systems. International Series of Numerical Mathematics, vol 171. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-72983-7_14
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DOI: https://doi.org/10.1007/978-3-030-72983-7_14
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