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Model Order Reduction of Nonlinear Eddy Current Problems Using Missing Point Estimation

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Model Reduction of Parametrized Systems

Part of the book series: MS&A ((MS&A,volume 17))

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Abstract

In electromagnetics, the finite element method has become the most used tool to study several applications from transformers and rotating machines in low frequencies to antennas and photonic devices in high frequencies. Unfortunately, this approach usually leads to (very) large systems of equations and is thus very computationally demanding. This contribution compares three model order reduction techniques for the solution of nonlinear low frequency electromagnetic applications (in the so-called magnetoquasistatic regime) to efficiently reduce the number of equations—leading to smaller and faster systems to solve.

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References

  1. Amsallem, D.: Interpolation on manifolds of CFD-based fluid and finite element-based structural reduced-order models for on-line aeroelastic predictions. Ph.D. dissertation, Stanford, USA (2010)

    Google Scholar 

  2. Astrid, P., et al.: Missing point estimation in models described by proper orthogonal decomposition. IEEE Trans. Autom. Control, 53(10), 2237–2251 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Barrault, M., et al.: An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations. C. R. Math. 339(9), 667–672 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bossavit, A.: Computational Electromagnetism: Variational Formulations, Complementarity, Edge Elements. Academic Press, San Diego (1998)

    MATH  Google Scholar 

  5. Bui-Thanh, T., Damodaran, M., Willcox, K.E.: Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition. AIAA J. 42, 1505–1516 (2004)

    Article  Google Scholar 

  6. Chaturantabut, S., Sorensen, D.C.: Nonlinear model reduction via discrete empirical interpolation. SIAM J. Sci. Comput. 32(5), 2737–2764 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Clenet, S., et al.: Model order reduction of non-linear magnetostatic problems based on POD and DEI methods. IEEE Trans. Magn. 50, 33–36 (2014)

    Article  Google Scholar 

  8. Cohen, A., DeVore, R.: Kolmogorov widths under holomorphic mappings. IMA J. Numer. Anal. (2015)

    Google Scholar 

  9. Dular, P., et al.: A general environment for the treatment of discrete problems and its application to the finite element method. IEEE Trans. Magn. 34(5), 3395–3398 (1998)

    Article  Google Scholar 

  10. Gyselinck, J.: Twee-Dimensionale Dynamische Eindige-Elementenmodellering van Statische en Roterende Elektromagnetische Energieomzetters. PhD thesis (1999)

    Google Scholar 

  11. Gyselinck, J., et al.: Calculation of eddy currents and associated losses in electrical steel laminations. IEEE Trans. Magn. 35(3), 1191–1194 (1999)

    Article  Google Scholar 

  12. Hiptmair, R., Xu, J.-C.: Nodal auxiliary space preconditioning for edge elements. In: 10th International Symposium on Electric and Magnetic Fields, France (2015)

    Google Scholar 

  13. Kolmogoroff, A.: Über die beste Annäaherung von Funktionen einer gegebenen Funktionen-klasse. Ann. Math. Second Ser. 37, 107–110 (1936)

    Article  MATH  Google Scholar 

  14. Maday, Y., Patera, A., Turinici, G.: A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations. J. Sci. Comput. 17, 437–446 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  15. Montier, L., et al: Robust model order reduction of a nonlinear electrical machine at start-up through reduction error estimation. In: 10th International Symposium on Electric and Magnetic Fields, France (2015)

    Google Scholar 

  16. Paquay, Y., Brüls, O., Geuzaine, C.: Nonlinear interpolation on manifold of reduced order models in magnetodynamic problems. IEEE Trans. Magn. 52(3), 1–4 (2016)

    Google Scholar 

  17. Ryckelynck, D.: A priori hyperreduction method: an adaptive approach. J. Comput. Phys. 202(1), 346–366 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  18. Schilders, W., et al.: Model Order Reduction: Theory, Research Aspects and Applications, vol. 13. Springer, Berlin (2008)

    Book  MATH  Google Scholar 

  19. Sirovich, L.: Turbulence and the dynamics of coherent structures. Part I: Coherent structures. Q. Appl. Math. 45(3), 561–571 (1987)

    MathSciNet  MATH  Google Scholar 

  20. Sorensen, D. Private discussions (2015)

    Google Scholar 

  21. Volkwein, S.: Proper orthogonal decomposition and singular value decomposition. Universität Graz/Technische Universität Graz. SFB F003-Optimierung und Kontrolle (1999)

    Google Scholar 

  22. Zlatko, D., Gugercin, S.: A New Selection Operator for the Discrete Empirical Interpolation Method–improved a priori error bound and extensions. SIAM J. Sci. Comput. 38(5), A631–A648 (2016)

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was funded in part by the Belgian Science Policy under grant IAP P7-02 (Multiscale Modelling of Electrical Energy Systems) and by the F.R.S.—FNRS (Belgium).

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Authors and Affiliations

  1. Montefiore Institute, University of Liège, Allée de la découverte B28, B-4000, Liège, Belgium

    Y. Paquay & C. Geuzaine

  2. Department of Aerospace and Mechanical Engineering, University of Liège, Allée de la dècouverte B52, B-4000, Liège, Belgium

    O. Brüls

Authors
  1. Y. Paquay
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  2. O. Brüls
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  3. C. Geuzaine
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Corresponding author

Correspondence to Y. Paquay .

Editor information

Editors and Affiliations

  1. Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany

    Peter Benner

  2. Institute for Computational and Applied Mathematics, University of Münster , Münster, Germany

    Mario Ohlberger

  3. Massachusetts Institute of Technology, MIT , Cambridge, Massachusetts, USA

    Anthony Patera

  4. SISSA MathLab, International School for Adv. Studies , Trieste, Italy

    Gianluigi Rozza

  5. Institute of Numerical Mathematics, Ulm University , Ulm, Germany

    Karsten Urban

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Paquay, Y., Brüls, O., Geuzaine, C. (2017). Model Order Reduction of Nonlinear Eddy Current Problems Using Missing Point Estimation. In: Benner, P., Ohlberger, M., Patera, A., Rozza, G., Urban, K. (eds) Model Reduction of Parametrized Systems. MS&A, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-58786-8_27

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