Abstract
When Co-simulation is applied to coupled differential algebraic equations, convergence can only be guaranteed if certain properties are fulfilled. However, introducing uncertainties in this mode may have great impact on these contraction properties and may destroy convergence. Hence one is interested to analyze the stochastic behavior of those properties. Within this paper we compare the Kernel Density Estimation technique and the spectral approach based on polynomial chaos expansion to measure the density of the contraction factor which may occur for coupled systems. Using the new R-splitting approach in a field/circuit coupled problem as benchmark, we clarify the benefits of both schemes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arnold, M., Günther, M.: Preconditioned dynamic iteration for coupled differential-algebraic systems. BIT 41, 1–25 (2001)
Bartel, A., Brunk, M., Günther, M., Schöps, S.: Dynamic iteration for coupled problems of electric circuits and distributed devices. SIAM J. Sci. Comput. 35(2), B315–B335 (2013)
Burrage, K.: Parallel Methods for Systems of Ordinary Differential Equations. Clarendon Press, Oxford (1995)
Scott, D.W.: Multivariate Density Estimation: Theory, Practice, and Visualization, 2nd edn. Wiley, Hoboken (2015)
Kornatka, M.: The weighted kernel density estimation methods for analysing reliability of electricity supply. In: 17th International Scientific Conference on Electric Power Engineering (EPE), Prague, pp. 1–4 (2016)
Li, J., Marzouk, Y.: Multivariate semi-parametric density estimation using polynomial chaos expansion (2013, in preparation)
Xiu, D.: Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, Princeton (2010)
Schöps, S., De Gersem, H., Bartel, A.: A cosimulation framework for multirate time integration of field/circuit coupled problems. IEEE Trans. Magn. 46(8), 3233–3236 (2010)
Graybill, F.A., Mood, A.M., Boes, D.C.: Introduction to the Theory of Statistics, International 3rd revised edn. Mcgraw-Hill Education, New York (1974)
Acknowledgements
This work is supported by the German Federal Ministry of Education and Research (BMBF) in the research projects SIMUROM (05M13PXB) and KoSMos (05M13PXA).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Gausling, K., Bartel, A. (2018). Density Estimation Techniques in Cosimulation Using Spectral- and Kernel Methods. In: Langer, U., Amrhein, W., Zulehner, W. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry(), vol 28. Springer, Cham. https://doi.org/10.1007/978-3-319-75538-0_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-75538-0_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-75537-3
Online ISBN: 978-3-319-75538-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)