Uncertainty Analysis of the EMC Simulation Based on the Non-Intrusive Galerkin Method
Keywords:Non-Intrusive Galerkin Method, Stochastic Galerkin Method, Uncertainty Analysis, EMC simulation
Recently, as a high-efficient uncertainty analysis method, the Stochastic Galerkin Method has been widely applied in EMC simulations. In this method, the original solver must be changed during uncertainty analysis. Thus, the realization of the Stochastic Galerkin Method may become impossible in some cases. In this paper, a novel method named Non-Intrusive Galerkin method is proposed in order to sove this problem. The performance of the proposed method can be clearly shown by calculating a published example.
R. S. Edwards, A. C. Marvin, and S. J. Porter, “Uncertainty analyses in the finite-difference timedomain method,” IEEE Transactions on Electromagnetic Compatibility, vol. 52, no. 1, pp. 155-163, 2010.
D. Bellan and S. A. Pignari, “Efficient estimation of crosstalk statistics in random wire bundles with lacing cords,” IEEE Transactions on Electro magnetic Compatibility, vol. 53, no. 1, pp. 209-218, 2011.
C. Jullien, P. Besnier, M. Dunand, et al., “Advanced modeling of crosstalk between an unshielded twisted pair cable and an unshielded wire above a ground plane,” IEEE Transactions on Electromagnetic Compatibility, vol. 55, no. 1, pp. 183-194, 2013.
R. W. Walters and L. Huyse, “Uncertainty analysis for fluid dynamics with applications,” ICASE Report no. 2002-1, NASA/CR-2002-211449, REC Warangal, Feb. 2002.
P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations. Springer-Verlag, Berlin, 1999.
D. Xiu, “Numerical methods for stochastic computations,” Princeton University Press, pp. 1- 23, 2010.
D. Xiu and G. E. Karniadakis, “The Wiener Askey polynomial chaos for stochastic differential equations,” SIAM Journal on Scientific Computing, vol. 24, no. 2, pp. 619-644, 2002.
P. Manfredi and F. G. Canavero, “Numerical calculation of polynomial chaos coefficients for stochastic per-unit-length parameters of circular conductors,” IEEE Transactions on Magnetics, vol. 50, no. 3, pp. 74-82, 2014.
P. Manfredi and F. G. Canavero, “Polynomial chaos for random field coupling to transmission lines,” IEEE Transactions on Electromagnetic Compatibility, vol. 54, no. 3, pp. 677-680, 2012.
R. S. Edwards, “Uncertainty analyses in computational electromagnetism,” University of York, 2009.
R. A. Perez, “Uncertainty analysis of computational fluid dynamics via polynomial chaos,” Virginia Polytechnic Institute and State University, 2008.
B. Jinjun, Z. Gang, et al., “Uncertainty analysis in EMC simulation based on Stochastic collocation method,” 2015 IEEE International Symposium on Electromagnetic Compatibility, pp. 930-934, 2015.
IEEE Recommended Practice for Validation of Computational Electromagnetics Computer Modeling and Simulations, IEEE STD 15972-2010, pp. 1-124, 2011.