Abstract
We consider a model of an electric circuit, where differential algebraic equations for a circuit part are coupled to partial differential equations for an electromagnetic field part. An uncertainty quantification is performed by changing physical parameters into random variables. A random quantity of interest is expanded into the (generalised) polynomial chaos using orthogonal basis polynomials. We investigate the determination of sparse representations, where just a few basis polynomials are required for a sufficiently accurate approximation. Furthermore, we apply model order reduction with proper orthogonal decomposition to obtain a low-dimensional representation in an alternative basis.
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References
Antoulas, A.: Approximation of Large-Scale Dynamical Systems. SIAM Publications, Philadelphia (2005)
Blatman, G., Sudret, B.: Adaptive sparse polynomial chaos expansion based on least angle regression. J. Comput. Phys. 230(6), 2345–2367 (2011)
Doostan, A., Owhadi, H.: A non-adapted sparse approximation of PDEs with stochastic inputs. J. Comput. Phys. 230(8), 3015–3034 (2011)
Ho, C.W., Ruehli, A., Brennan, P.: The modified nodal approach to network analysis. IEEE Trans. Circ. Syst. 22(6), 504–509 (1975)
Jakeman, J.D., Narayan, A., Zhou, T.: A generalized sampling and preconditioning scheme for sparse approximation of polynomial chaos expansions. SIAM J. Sci. Comput. 39(3), A1114–A1144 (2017)
Pulch, R.: Model order reduction and low-dimensional representations for random linear dynamical systems. Math. Comput. Simulat. 144, 1–20 (2018)
Pulch, R.: Model order reduction for random nonlinear dynamical systems and low-dimensional representations for their quantities of interest. Math. Comput. Simulat. 166, 76–92 (2019)
Schöps, S.: Multiscale Modeling and Multirate Time-Integration of Field/Circuit Coupled Problems. VDI Verlag. Fortschritt-Berichte VDI, Reihe 21, Nr. 398 (2011)
Schöps, S., De Gersem, H., Weiland, T.: Winding functions in transient magnetoquasistatic field-circuit coupled simulations. COMPEL 29(2), 2063–2083 (2013)
Stroud, A.J.: Approximate Calculation of Multiple Integrals. Prentice-Hall, Englewood Cliffs (1971)
Tsukerman, I.A., Konrad, A., Meunier, G., Sabonnadiere, J.C.: Coupled field-circuit problems: trends and accomplishments. IEEE Trans. Magn. 29(2), 1701–1704 (1993)
Xiu, D.: Numerical Methods for Stochastic Computations: a Spectral Method Approach. Princeton University Press, Princeton (2010)
Acknowledgements
The research of the second author is supported by the Excellence Initiative of the German Federal and State Governments and by the Graduate School of Computational Engineering at Technische Universität Darmstadt.
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Pulch, R., Schöps, S. (2019). Sparse Representations for Uncertainty Quantification of a Coupled Field-Circuit Problem. In: Faragó, I., Izsák, F., Simon, P. (eds) Progress in Industrial Mathematics at ECMI 2018. Mathematics in Industry(), vol 30. Springer, Cham. https://doi.org/10.1007/978-3-030-27550-1_2
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DOI: https://doi.org/10.1007/978-3-030-27550-1_2
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