A Convolutional Perfectly Matched Layer (CPML) for the Fourth-Order One-Step Leapfrog HIE-FDTD Method
Keywords:
Accuracy, computational efficiency, convolutional perfectly matched layer (CPML), fourth order one-step leapfrog, hybrid implicit and explicitFDTD (HIE-FDTD), relative reflection errorAbstract
A new convolutional perfectly matched layer (CPML) for the fourth-order one-step leapfrog hybrid implicit explicit finite-difference time-domain (HIEFDTD) method for the TE case has been proposed in this paper. When the time step size satisfies with the time stability condition, the maximum reflection error of the proposed method is below -72dB, which demonstrates good absorbing performance of the CPML method. To verify the accuracy and efficiency of the proposed method, we compare the results of the traditional FDTD method and the HIE-FDTD method. Numerical examples demonstrate that the proposed method consumes about 60.13% less CPU time than the traditional FDTD method and 41.60% less CPU time than the existing HIE-FDTD method.
Downloads
References
K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Transactions on Antennas Propagation, vol. 14, pp. 302-307, 1996.
A. Taflove, Computational Electrodynamics. Norwood, MA: Artech House, 1995.
T. Namiki, “A new FDTD algorithm based on alternating-direction implitcit method,” IEEE Trans. Microwave Theory Tech., vol. 47, pp. 2003-2007, 1999.
Q.-X. Chu, L.-N. Wang, and Z.-H. Chen, “A novel numerical dispersion formulation of the 2D ADIFDTD method,” International Journal of RF and Microwave Computer-Aided Engineering, vol. 16, no. 6, pp. 584-587, 2006
X.-T. Zhao, Z.-G. Wang, and X.-K. Ma, “A 3-D unconditionally stable precise integration time domain method for the numerical solutions of Maxwell’s equations in circular cylindrical coordinates,” International Journal of RF and Microwave Computer-Aided Engineering, vol. 19, no. 2, pp. 230-242, 2009.
H. X. Zheng and K. W. Leung, “An efficient method to reduce the numerical dispersion in the ADI-FDTD,” IEEE Trans. Microwave Theory Tech., vol. 53, pp. 2295-2301, 2005.
S. Wang and C. W. Trueman, “An iterative ADIFDTD with reduced splitting error,” IEEE Microw. Compon. Lett., vol. 15, pp. 92-94, 2005.
J. Chen and J. Wang, “Error between unconditionally stable FDTD methods and conventional FDTD method,” Electron. Lett., vol. 42, pp. 1132-1133, 2006.
V. E. Nascimento, F. L.Teixeira, and B. H. V. Borges, “Uncondtionally stable finite-difference time-domain method based on the locally-onedimensional technique,” Proc. 22nd Symp. Brasileiro Telecomun., vol. 9, pp. 288-291, 2005.
J. Shibayama, M. Muraki, J. Yamauchi, et al., “Efficient implicit FDTD algorithm based on locally one-dimensional scheme,” Electron. Lett., vol. 41, pp. 1046-1047, 2005.
B. Huang and G. Wang, “A hybrid implicit-explicit FDTD scheme with weakly conditional stability,” Microwave Opt. Technol. Lett., vol. 39, pp. 97-101, 2003.
J. Chen and J. Wang, “A 3-D hybrid implicitexplicit FDTD scheme with weakly conditional stability,” Microwave Opt. Technol. Lett., vol. 48, pp. 2291-2294, 2006.
J. Chen and J. G. Wang, “A three-dimensional semi-implicit FDTD scheme for calculation of shielding effectiveness of enclosure with thin slots,” IEEE Transactions on Electromagnetic Compatibility, vol. 49, pp. 354-360, 2007.
J. Chen and J. G. Wang, “Numerical simulation using HIE–FDTD method to estimate various antennas with fine scale structures,” IEEE Transactions on Antennas Propagation, vol. 55, pp. 3603-3612, 2007.
J. Wang, B. Zhou, L. Shi, C. Gao, et al., “A novel 3-D HIE-FDTD method with one-step leapfrog scheme,” IEEE Trans. Microw. Theory Tech., vol. 62, pp. 1275-1283, 2014.
M. Dong, A. Zhang, and J. Chen, “The fourth order one-step leapfrog HIE-FDTD method,” Applied Computational Electromagnetics Society Journal, vol. 31, pp.1370-1376, 2016.
D.-W. Zhu, Y.-G. Wang, and H.-L. Chen, “A onestep leapfrog HIE-FDTD method for rotationally symmetric structures,” International Journal of RF and Microwave Computer-Aided Engineering, 2016.
J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Technol. Lett., vol. 27, pp. 334-339, 2002.
M. Krumpholz and L. P. B. Katehi, “MRTD: New time-domain schems based on multiresolution analysis,” IEEE Trans. Microwave Theory Tech., vol. 44, pp. 555-571, 1996.
M. L. Ghrist, “High order difference methods for wave equations,” University of Colorado, 1997.
S. C. Yang, Z. Chen, Y. Yu, et al., “The unconditionally stable one-step leapfrog ADI-FDTD method and its comparisons with other FDTD methods,” IEEE Microw. Wireless Compon. Lett., vol. 21, pp. 640-642, 2011.
S. D. Gedney, “The perfectly matched layer absorbing medium,” Advances in Computational Electrodynamics: The Finite Difference Time Domain, A. Taflove (Editor), Artech House, Boston, MA, pp. 263-340, 1998.
J. Wang, Y. Wang, and D. Zhang, “Truncation of open boundaries of cylindrical waveguides in 2.5- dimensional problems by using the convolutional perfectly matched layer,” IEEE Trans. Plasma Sci., vol. 34, pp. 681-690, 2006.
J. Chen, N. Xu, and A. Zhang, “Using dispersion HIE-FDTD method to simulate the graphene-based polarizer,” IEEE Transaction on Antennas and Propagation, vol. 24, pp. 3011-3017, 2016.
J. Chen and J. Wang, “Three-dimensional dispersive hybrid implicit-explicit finite-difference time-domain method for simulations of graphene,” Computer Physics Communications,vol. 207, pp. 211-216, 2016.
