Normal Directionaly NURBS Arithmetic of Conformal PML
Keywords:
Common normal direction, conformal PML, finite element modeling, NURBS arithmeticAbstract
Conformal Perfectly Matched Layer (PML) is a high-efficiency absorbing boundary condition for the finite element analysis of electromagnetic fields. Accurate calculation of normal direction of conformal PML is essential for the geometric modelling of conformal shell elements and constitutive parameters of conformal PML, especially for sophisticated and arbitrary shape scatterers. Consequently, a Non-Uniform Rational B-Splines (NURBS) arithmetic is proposed for describing the conformal surface accurately in this study. Based on the NURBS arithmetic, four weighted average formulas are presented for calculating the common normal direction of adjacent surface elements of conformal shell. Numerical experiments show the availability of NURBS arithmetic and precision of weighted average formulas in the geometrical modelling of conformal PML.
Downloads
References
M. Kuzuoglu and R. Mittra, “Investigation of nonplanar perfectly matched absorbers for finiteelement mesh truncation,” IEEE Transactions on Antennas and Propagation, vol. 45, no. 3, pp. 474- 486, March 1997.
F. L. Teixeira and W. C. Chew, “Analytical derivation of a conformal perfectly matched absorber for electromagnetic waves,” Microwave and Optical Technology Letters, vol. 17, no. 4, pp. 231-236, March 1998.
O. Ozgun and M. Kuzuoglu, “Non-maxwellian locally-conformal PML absorbers for finite element mesh truncation,” IEEE Transactions on Antennas and Propagation, vol. 55, no. 3, pp. 931- 937, March 2007.
B. Donderici and F. L. Teixeira, “Conformal perfectly matched layer for the mixed finite element time-domain method,” IEEE Transactions on Antennas and Propagation, vol. 56, no. 4, pp. 1017-1026, April 2008.
K. P. Hwang and J. M. Jin, “Application of a hyperbolic grid generation technique to a conformal PML implementation,” IEEE Microwave and Guided Wave Letters, vol. 9, no. 4, pp. 137-139, April 1999.
F. L. Teixeira and W. C. Chew, “On causality and dynamic stability of perfectly matched layers for FDTD simulations,” IEEE Transactions on Microwave Theory and Techniques, vol. 47, no. 6, pp. 775-785, June 1999.
F. L. Teixeira, K. P. Hwang, W. C. Chew, and J. M. Jin, “Conformal PML-FDTD schemes for electromagnetic field simulations: a dynamic stability study,” IEEE Transactions on Antennas and Propagation, vol. 49, no. 6, pp. 902-907, June 2001.
Y. J. Zhang and Q. Sun, “Layer-based integration arithmetic of conformal PML,” Applied Computational Electromagnetics Society Journal, vol. 24, no. 5, pp. 518-522, October 2009.
P. Liu, J. D. Xu, and W. Wan, “A finite-element realization of a 3-D conformal PML,” Microwave and Optical Technology Letters, vol. 30, no. 3, pp. 170-173, August 2001.
P. Liu and Y. Q. Jin, “Numerical simulation of bistatic scattering from a target at low altitude above rough sea surface under an EM-wave incidence at low grazing angle by using the finite element method,” IEEE Transactions on Antennas and Propagation, vol. 52, no. 5, pp. 1205-1210, May 2004.
R. Sevilla, S. Fernandez-Mendez, and A. Huerta, “3D NURBS-enhanced finite element method (NEFEM),” International Journal for Numerical Methods in Engineering, vol. 88, no. 2, pp. 103- 125, October 2011.
B. Lai, H. B. Yuan, and C. H. Liang, “Analysis of NURBS surfaces modeled geometries with higherorder mom based aim,” Journal of Electromagnetic Waves and Applications, vol. 25, no. 5-6, pp. 683- 691, 2011.
L. Z. Liu and J. Yang, “Analysis of electromagnetic scattering with higher-order moment method and NURBS model,” Progress in Electromagnetics Research-Pier, vol. 96, pp. 83- 100, 2009.
L. Valle, F. Rivas, and M. F. Citedra, “Combining the moment method with geometrical modelling by NURBS surfaces and bezier patches,” IEEE Transactions on Antennas and Propagation, vol. 42, no. 3, pp. 373-381, March 1994.
L. A. Piegl and W. Tiller, “The NURBS book,” 2 nd edition, Springer-Verlag, New York, 1997.
