In this paper, the uniaxial anisotropic perfectly matched layer (UPML) absorbing boundary condition in unconditionally stable five-step locally one-dimensional finite-difference time-domain (LOD5-FDTD) method is deduced. The UPML absorbing boundary condition (ABC) is validated based on comparison with a simulation in larger domain (and thus without reflection) in the first test. Then using a sinusoidal source, target field phase distribution surrounded by the UPML-ABC is analyzed. The results further illustrate the stability and efficiency of the UPML absorbing boundary condition.
1. Saxena, A. K. and K. V. Srivastava, "A three-dimensional unconditionally stable five-step LOD-FDTD method," IEEE Trans. Antenna Propag., Vol. 62, No. 3, 1321-1329, Mar. 2014. doi:10.1109/TAP.2013.2293790
2. Courant, R., K. Friedrichs, and H. Lewy, "On the partial difference equations of mathematical physics," IBMJ, Vol. 11, 215-234, Mar. 1967. doi:10.1147/rd.112.0215
3. Namiki, T., "A new FDTD algorithm based on alternating-direction implicit method," IEEE Trans. Microw. Theory. Tech., Vol. 47, No. 10, 2003-2007, Oct. 1999. doi:10.1109/22.795075
4. Zheng, F., Z. Chen, and J. Zhang, "A finite-difference time-domain method without the Courant stability conditions," IEEE Microw. Guided Wave Lett., Vol. 9, No. 11, 441-443, Nov. 1999. doi:10.1109/75.808026
5. Tan, E. L., "Unconditionally stable LOD-FDTD method for 3-D Maxwell's equations," IEEE Microwave and Wireless Components Letters, Vol. 17, No. 2, 85-87, Feb. 2007. doi:10.1109/LMWC.2006.890166
6. Ahmed, I., E. K. Chua, E. P. Li, and Z. Chen, "Development of the three dimensional unconditionally stable LOD-FDTD method," IEEE Trans. Antenna Propag., Vol. 56, No. 11, 3596-3600, Nov. 2008. doi:10.1109/TAP.2008.2005544
7. Do Nascimento, V. E., B. H. V. Borges, and F. L. Teixeira, "Split-field PML implementations for the unconditionally stable LOD-FDTD method," IEEE Microwave and Wireless Components Letters, Vol. 16, No. 7, 398-400, Jul. 2006. doi:10.1109/LMWC.2006.877132
8. Ahmed, I., E. Li, and K. Krohne, "Convolutional perfectly matched layer for an unconditionally stable LOD-FDTD method," IEEE Microwave and Wireless Components Letters, Vol. 17, No. 12, 816-819, Dec. 2007. doi:10.1109/LMWC.2007.910458
9. Gedney, S. D., "An Anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices," IEEE Trans. Antenna Propag., Vol. 44, No. 12, 1630-1639, Dec. 1996. doi:10.1109/8.546249
10. Sun, W., N. G. Loeb, and Q. Fu, "Finite-difference time domain solution of light scattering and absorption by particles in an absorbing medium," Appl. Opt., Vol. 41, 5728-5743, Sep. 2002. doi:10.1364/AO.41.005728
11. Sun, W., H. Pan, and G. Videen, "General finite-difference time-domain solution of an arbitrary electromagnetic source interaction with an arbitrary dielectric surface," Appl. Opt., Vol. 48, 6015-6025, Nov. 2009.
12. Wei, B., S. Zhang, F. Wang, and D. Ge, "A novel UPML FDTD absorbing boundary condition for dispersive media," Waves in Random and Complex Media, Vol. 20, 511-527, Aug. 2010. doi:10.1080/17455030.2010.496005
13. Liang, F. and G. Wang, "Study of Mur's and UPML absorbing boundary condition for the LOD-FDTD method," ICMMT, Vol. 2, 947-949, 2008.
14. Ahmed, I., E. H. Khoo, and L. Erping, "Development of the CPML for three-dimensional unconditionally stable LOD-FDTD method," IEEE Trans. Antenna Propag., Vol. 58, No. 3, 832-837, Mar. 2010. doi:10.1109/TAP.2009.2039334
15. Omar, R., "Efficient LOD-SC-PML formulations for electromagnetic fields in dispersive media," IEEE Microwave and Wireless Components Letters, Vol. 22, No. 6, 297-299, 2012. doi:10.1109/LMWC.2012.2197819
16. Taflove, A. and S. C. Hagness, Computational electrodynamics the finite-difference time-domain method, 3rd Ed., 293, Artech House, Norwood, MA, 2005.