Uncertainty Analysis of Reflection Coefficient for a Coating with Random Flaws Using Adaptive Mesh and DGTD Method
Keywords:
AM-DGTD method, reflection coefficient, statistical analysis, uncertainty quantificationAbstract
An imperfect coating shall cause uncertainties in the analysis of electromagnetic properties. To quantify the influence of irregularity, complexity, and uncertainty of the coatings for electronic devices, an adaptive mesh algorithm combined with the discontinuous Galerkin time domain (AM-DGTD) method is developed. The uncertain variations are incorporated into the proposed algorithm by an appropriate parameterization. The standard statistical analysis is performed to calculate the appropriate moments, i.e., mean and variance. The developed method is validated by modeling a dielectric coating with uncertain flaws in an adaptive mesh grid. The computed quantities of interest from numerical estimations are compared with the analytical values, these results agree with the physical explanation, and are in good agreement with the exact values, as demonstrated by numerical experiments.
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References
D. Satas, A. A. Tracton, and A. J. Rafanelli, Coatings Technology Handbook. 2nd ed., Charleston Advisor, pp. 12-14, 2002.
M. P. Schultz, “Effects of coating roughness and biofouling on ship resistance and powering,” Biofouling, vol. 23, no. 5, pp. 331-341, Sep. 2007.
L. R. A. X. De Menezes, A. Ajayi, et al., “Efficient extraction of statistical moments in electromagnetic problems solved with the method of moments,” in Microwave and Optoelectronics Conference, pp. 757-760, 2007.
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, Feb. 2010.
A. C. M. Austin and C. D. Sarris, “Efficient analysis of geometrical uncertainty in the FDTD method using polynomial chaos with application to microwave circuits,” IEEE Transactions on Microwave Theory & Techniques, vol. 61, no. 12, pp. 4293-4301, Sep. 2013.
S. M. Smith and C. Furse, “Stochastic FDTD for analysis of statistical variation in electromagnetic fields,” IEEE Transactions on Antennas & Propagation, vol. 60, iss. 7, pp. 3343-3350, May 2012.
B. Navaneetha Raj, N. G. R. Iyengar, and D. Yadav, “Response of composite plates with random material properties using FEM and Monte-Carlo simulation,” Advanced Composite Materials, vol. 7, no. 3, pp. 34-39, Apr. 2012.
S. Sarkar and D. Ghosh, “A hybrid method for stochastic response analysis of a vibrating structure,” Archive of Applied Mechanics, vol. 85, iss. 11, pp. 1607-1626, Nov. 2015.
C. Chauvi, J. S. Hesthaven, and L. Lurati, “Computational modeling of uncertainty in timedomain electromagnetics,” Siam Journal on Scientific Computing, vol. 28, no. 2, pp. 751-775, Jan. 2006.
P. Li and L. J. Jiang, “Uncertainty quantification for electromagnetic systems using ASGC and DGTD method,” IEEE Transactions on Electromagnetic Compatibility, vol. 57, no. 4, pp. 754- 763, Feb. 2015.
L. D. Angulo, J. Alvarez, et al., “Discontinuous Galerkin time domain methods in computational electrodynamics: State of the art,” Forum for Electromagnetic Research Methods and Application Technologies, vol. 10, no. 004, pp. 34-39, Aug. 2015.
S. P. Gao, Y. Lu, and Q. Cao, “Hybrid method combining DGTD and TDIE for wire antennadielectric interaction,” Applied Computational Electromagnetics Society Journal, vol. 60, no. 6, pp. 677-681, June 2015.
H. Li, I. Hussain, Y. Wang, et al., “Analysis the electromagnetic properties of dielectric coatings with uncertain flaws using DGTD method,” International Applied Computational Electromagnetics Society (ACES) Symposium, Aug. 2017.
L. Zhao, G. Chen, and W. Yu, “An efficient algorithm for SAR evaluation from anatomically realistic human head model using DGTD with hybrid meshes,” Applied Computational Electromagnetics Society Journal, vol. 31, no. 6, pp. 629- 635, June 2016.
S. Yan and J. M. Jin, “A dynamic p-adaptation algorithm for the DGTD simulation of nonlinear EM-plasma interaction,” IEEE/ACES International Conference on Wireless Information Technology and Systems, IEEE, pp. 1-2, May 2016.
H. Edelsbrunner, Geometry and Topology for Mesh Generation. Cambridge University Press, 2001.
L. Freitag and C. Ollivier-Gooch, “Tetrahedral mesh improvement using swapping and smoothing,” International Journal for Numerical Methods in Engineering, vol. 40, no. 21, pp. 3979-4002, Mar. 1997.
S. Swain, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences. Springer-Verlag, 1983.
E. L. Bronaugh and J. D. M. Osburn, “A process for the analysis of the physics of measurement and determination of measurement uncertainty in EMC test procedures,” in Electromagnetic Compatibility, pp. 245-249, Aug. 1996.
D. L. Rumpf, Statistics for Dummies. John Wiley & Sons Inc., 2004.
J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Springer Publishing Company, Incorporated, 2008.
I. Hussain, H. Li, Y. Wang, and Q. Cao, “Modeling of structures using adaptive mesh in DGTD method for EM solver,” presented at Progress in Electromagnetics Research Symposium, 2017.
T. Warburton, “An explicit construction of interpolation nodes on the simplex,” Journal of Engineering Mathematics, vol. 56, no. 3, pp. 247- 262, Sep. 2006.
R. Diehl, K. Busch, and J. Niegemann, “Comparison of low-storage Runge-Kutta schemes for discontinuous Galerkin time-domain simulations of Maxwell’s equations,” Journal of Computational & Theoretical Nanoscience, vol. 7, no. 8, pp. 1572- 1580, Aug. 2010.
G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time domain electromagnetic field equations,” IEEE Trans. Electromagnetic Compatibility, vol. 23, no. 4, pp. 277-382, Nov. 1981.
