volume | PIER Journals

Abstract

Implementing appropriate absorbing boundary conditions (ABCs) in finite-difference time-domain (FDTD) simulations is essential. Optimal ABCs can help minimize or even eliminate spurious reflections in simulations involving waves impinging on the edges of simulation grid boundaries. In this work, 2D FDTD code facilitating ABCs were implemented and incorporated under plug-and-play conditions. Using this FDTD code, two different types of ABCs were evaluated: a differential ABC and a perfectly matched layer (PML) for the anisotropic medium of the ionosphere. Furthermore, numerical experiments were conducted to examine the efficiencies of both these ABCs; a total of n = 2000 iterations were adopted, under grid conditions of 120 in the y-direction, 600 in the x-direction of spatial step, and Δx = 1000 km. Additionally, n was set as a time-equivalent variable in these simulations. For the interval Δx=1 km between any two adjacent grid points, active conditions for the grid simulation were determined within 120 km in the y-direction (vertical) and 600 km in the x-direction (horizontal). Furthermore, numerical experiments revealed that the PML platform yielded excellent efficiency, as compared with the differential ABC.

1. Engquist, B. and A. Majda, "Absorbing boundary conditions for numerical simulation of waves," Proc. Natl. Acad. Sci., Vol. 74, 1765-1766, 1977.
doi:10.1073/pnas.74.5.1765 Google Scholar

2. Mur, G., "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations," IEEE Trans. Electromagn. Compat., Vol. 23, 377-382, 1981.
doi:10.1109/TEMC.1981.303970 Google Scholar

3. Taflove, A., Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House, 1995.

4. Berenger, J. P., "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys., Vol. 114, No. 2, 185-200, Oct. 1994, doi: 10.1006/jcph.1994.1159.
doi:10.1006/jcph.1994.1159 Google Scholar

5. Yu, T. B., B. H. Zhou, and B. Chen, "An unsplit formulation of the Berenger's PML absorbing boundary condition for FDTD meshes," IEEE Microw. Wirel. Components Lett., Vol. 13, 348-350, 2003. Google Scholar

6. Abdulkareem, B., J. P. Bérenger, F. Costen, R. Himeno, and H. Yokota, "An operator absorbing boundary condition for the absorption of electromagnetic waves in dispersive media," IEEE Trans. Antennas Propag., Vol. 66, 2147-2150, 2018.
doi:10.1109/TAP.2018.2796386 Google Scholar

7. Chen, Y. and N. Feng, "Learning unsplit-field-based PML for the FDTD method by deep differentiable forest," arXiv:2004.04815, Jun. 16, 2021. [Online]. Available: http://arxiv.org/abs/2004.04815. Google Scholar

8. Tan, E. L., "A leapfrog scheme for complying-divergence implicit finite-difference time-domain method," IEEE Antennas Wirel. Propag. Lett., Vol. 20, 853-857, 2021.
doi:10.1109/LAWP.2021.3065520 Google Scholar

9. Valagiannopoulos, C. A. and N. K. Uzunoglu, "Rigorous analysis of a metallic circular post in a rectangular waveguide with step discontinuity of sidewalls," IEEE Trans. Microw. Theory Tech., Vol. 55, No. 8, 1673-1684, Aug. 2007.
doi:10.1109/TMTT.2007.901597 Google Scholar

10. Sun, Y.-C., H. Ren, K. Yamazaki, et al. "Semi-analytical solutions of seismo-electromagnetic signals arising from the motional induction in 3-D multi-layered media: Part I - Theoretical formulations," Earth, Planets and Space, Vol. 73, No. 1, 1-26, 2021.
doi:10.1186/s40623-020-01327-7 Google Scholar

11. Bérenger, J. P., "An implicit FDTD scheme for the propagation of VLF-LF radio waves in the Earth-ionosphere waveguide," Comptes Rendus Physique, 2014. Google Scholar

12. Samimi, A. and J. J. Simpson, "Introducing a new method for FDTD modeling of electromagnetic wave propagation in magnetized plasma," 2014 USNC-URSI Radio Science Meeting (Joint with AP-S Symposium), USNC-URSI 2014 - Proceedings, 158, Nov. 2014. Google Scholar

13. Fang, Y., X. L. Xi, J. M. Wu, J. F. Liu, and Y. R. Pu, "A J-E collocated WLP-FDTD model of wave propagation in isotropic cold plasma," IEEE Trans. Microw. Theory Tech., Vol. 64, No. 7, Pt. 1, 1957-1965, 2016. Google Scholar

14. Pokhrel, S., J. J. Simpson, D. T. Welling, and M. W. Liemohn, "Regional FDTD modeling of GICs during the 2003 `Halloween' solar storm," AGUFM, Vol. 2018, IN33D-0884, Feb. 23, 2021. [Online]. Available: https://ui.adsabs.harvard.edu/abs/2018AGUFMIN33D0884P/abstract. Google Scholar

15. Pokhrel, S., V. Shankar, and J. J. Simpson, "Simplified FDTD model of electromagnetic wave propagation in magnetized plasma," 2018 International Applied Computational Electromagnetics Society Symposium (ACES), IEEE, Denver, CO, USA, May 2018. Google Scholar

16. Valagiannopoulos, C., "An overview of the Watson transformation presented through a simple example," Progress In Electromagnetics Research, Vol. 75, 137-152, 2007.
doi:10.2528/PIER07052502 Google Scholar

17. Li, M.-K. and W. C. Chew, "A new Sommerfeld-Watson transform in 3D," IEEE Antennas and Propagation Society Symposium, 2004, Vol. 2, IEEE, 2004. Google Scholar

18. Chen, Q., M. Katsurai, and P. H. Aoyagi, "An FDTD formulation for dispersive media using a current density," IEEE Trans. Antennas Propag., Vol. 46, 1739-1746, 1998.
doi:10.1109/8.736632 Google Scholar

19. Yang, L., Y. Xie, and P. Yu, "Study of bandgap characteristics of 2D magnetoplasma photonic crystal by using M-FDTD method," Microw. Opt. Technol. Lett., Vol. 53, 1778-1784, 2011.
doi:10.1002/mop.26143 Google Scholar

20. Courant, R., K. Friedrichs, and H. Lewy, "On the partial difference equations of mathematical physics," IBM J. Res. Dev., Vol. 11, 215-234, 1967.
doi:10.1147/rd.112.0215 Google Scholar

21. Berenger, J. P., "Improved PML for the FDTD solution of wave-structure interaction problems," IEEE Trans. Antennas Propag., Vol. 45, 466-473, 1997.
doi:10.1109/8.558661 Google Scholar

22. Yee, K., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag., Vol. 14, No. 3, 302-307, 1966.
doi:10.1109/TAP.1966.1138693 Google Scholar

23. Rickard, Y. S. and N. K. Georgieva, "Problem-independent enhancement of PML ABC for the FDTD method," IEEE Trans. Antennas Propag., Vol. 51, No. 10, 3002-3006, 2003.
doi:10.1109/TAP.2003.818000 Google Scholar

Dr. Md Yusoff Siti Harwani

Dr. Tiem Leong Yoon