Efficient Z-Transform Implementation of the D-B CFS-PML for Truncating Multi-Term Dispersive FDTD Domains

Authors

  • Naixing Feng Institute of Electromagnetics and Acoustics Xiamen University, Xiamen 361005, P. R. China
  • Yongqing Yue Institute of Electromagnetics and Acoustics Xiamen University, Xiamen 361005, P. R. China
  • Chunhui Zhu Institute of Electromagnetics and Acoustics Xiamen University, Xiamen 361005, P. R. China
  • Qing Huo Liu Department of Electrical and Computer Engineering Duke University, Durham, NC 27708, USA
  • Liangtian Wan Department of Information and Communication Engineering Harbin Engineering University, Harbin 150001, P. R. China

Keywords:

D-B constitutive relations, Finite-Difference Time-Domain (FDTD), multi-term Lorentz, Perfectly Matched Layer (PML) and Z-transform

Abstract

Efficient Z-transform implementation of the Complex Frequency-Shifted Perfectly Matched Layer (CFS-PML) using the D-B formulations are proposed to truncate open region multi-term dispersive Finite-Difference Time-Domain (FDTD) lattices. These formulations are independent of material properties of the FDTD domains and hence can be used for modeling general media because of the D-B constitutive relations. A Three-Dimensional (3-D) simulation of the two-term Lorentz dispersive FDTD domain has been carried out to demonstrate the validity of the proposed formulations. Furthermore, in order to show the validity of the proposed algorithm, the second 3D inhomogeneous problem has also been used for validating the proposed formulations. It is clearly shown that the new formulations with the CFS-PML scheme are efficient in attenuating evanescent waves and reducing late-time reflections.

Downloads

Download data is not yet available.

References

J. P. Bérenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Computat. Phys., vol. 114, no. 2, pp. 185-200, October 1994.

W. C. Chew and W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett., vol. 7, no. 13, pp.599-603, September. 1994.

J. A. Roden and S. D. Gedney, “Convolution PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Technol. Lett., vol. 27, no. 5, pp. 334-339, December 2000.

G. X. Fan and Q. H. Liu, “A well-posed PML absorbing boundary condition for lossy media,” in Proc. IEEE Antennas Propagat. Soc. Int. Symp. Dig., vol. 3, pp. 2-5, Boston, MA, July 8-13, 2001, Also published in Antennas Wireless Propag. Lett., vol. 2, pp. 97-100, 2003.

O. Ramadan, “Auxiliary differential equation formulation: an efficient implementation of the perfectly matched layer,” IEEE Microw. Wireless Compon. Lett., vol. 13, no. 2, pp. 69-71, February 2003.

J. Li and J. Dai, “An efficient implementation of the stretched coordinate perfectly matched layer,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 5, pp. 322-324, May 2007.

O. Ramadan and A. Y. Oztoprak, “DSP techniques for implementation of perfectly matched layer for truncating FDTD domains,” Electron. Lett., vol. 38, no. 5, pp. 211-212, 2002.

D. M. Sullivan, “Frequency-dependent FDTD methods using z transforms,” IEEE Trans. Antennas Propag., vol. 40, no. 10, pp. 1223-1230, 1992.

J. Li and J. Dai, “Efficient implementation of stretched coordinate perfectly matched layer using DSP techniques,” Electron. Lett., vol. 42, no. 17, pp. 953-955, 2006.

J. Li and J. Dai, “Efficient implementation of the stretched coordinate perfectly matched layer based on the z-transform method,” IET Microw. Antennas Propag., vol. 1, no. 3, pp. 645-650, 2007.

O. Ramadan and A. Y. Oztoprak, “Z-transform implementation of the perfectly matched layer for truncating FDTD domains,” IEEE Microw. Wireless Compon. Lett., vol. 13, no. 9, pp. 402-404, September 2003.

J. P. Bérenger, “Evanescent waves in PMLs: origin of numerical reflection in wave-structure interaction problems,” IEEE Trans. Antennas Propag., vol. 47, pp. 1497-1503, 1999.

J. De Moerloose and M. A. Stuchley, “Behavior of Berenger’s ABC for evanescent waves,” IEEE Microwave Guided Wave Lett., vol. 5, pp. 344-346, October 1995.

M. Kuzuoglu and R. Mittra, “Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers,” IEEE Microw. Guided Wave Lett., vol. 6, no. 12, pp. 447-449, December 1996.

J. Li and J. Dai, “Z-transform implementation of the CFS-PML for arbitrary media,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 8, pp. 437-439, August 2006.

J. Li and C. Miao, “An efficient FDTD implementation of the CFS-PML based on the ADE method and its validation along with the PLRC method in dispersive media,” ICMMT, pp. 766-769, April 2008.

D. Correia and J. M. Jin, “A simple and efficient implementation of CFS-PML in the FDTD analysis of periodic structures,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 7, pp. 487-489, July 2005.

O. Ramadan, “General ADE formulations of SC-PML for modeling multi-term dispersive FDTD applications,” Electron. Lett., vol. 47, no. 20, pp. 1122-1124, 2011.

J. G. Proakis and D. G. Manolakis, “Digital signal processing: principles, algorithms and applications,” Prentice Hall International Editions, 3rd edn, 1996.

N. Feng, J. Li and X. Zhao, “Efficient FDTD implementation of the higher-order PML using DSP techniques for arbitrary media,” IEEE Trans. Antennas Propag., vol. 61, no. 5, pp. 2623-2629, May 2013.

Downloads

Published

2021-09-03

How to Cite

[1]
N. . Feng, Y. . Yue, C. . Zhu, Q. H. . Liu, and L. . Wan, “Efficient Z-Transform Implementation of the D-B CFS-PML for Truncating Multi-Term Dispersive FDTD Domains”, ACES Journal, vol. 29, no. 03, pp. 190–196, Sep. 2021.

Issue

2014: Vol 29 Iss 3

Section

Articles