Vol. 131
Latest Volume
All Volumes
PIERC 144 [2024] PIERC 143 [2024] PIERC 142 [2024] PIERC 141 [2024] PIERC 140 [2024] PIERC 139 [2024] PIERC 138 [2023] PIERC 137 [2023] PIERC 136 [2023] PIERC 135 [2023] PIERC 134 [2023] PIERC 133 [2023] PIERC 132 [2023] PIERC 131 [2023] PIERC 130 [2023] PIERC 129 [2023] PIERC 128 [2023] PIERC 127 [2022] PIERC 126 [2022] PIERC 125 [2022] PIERC 124 [2022] PIERC 123 [2022] PIERC 122 [2022] PIERC 121 [2022] PIERC 120 [2022] PIERC 119 [2022] PIERC 118 [2022] PIERC 117 [2021] PIERC 116 [2021] PIERC 115 [2021] PIERC 114 [2021] PIERC 113 [2021] PIERC 112 [2021] PIERC 111 [2021] PIERC 110 [2021] PIERC 109 [2021] PIERC 108 [2021] PIERC 107 [2021] PIERC 106 [2020] PIERC 105 [2020] PIERC 104 [2020] PIERC 103 [2020] PIERC 102 [2020] PIERC 101 [2020] PIERC 100 [2020] PIERC 99 [2020] PIERC 98 [2020] PIERC 97 [2019] PIERC 96 [2019] PIERC 95 [2019] PIERC 94 [2019] PIERC 93 [2019] PIERC 92 [2019] PIERC 91 [2019] PIERC 90 [2019] PIERC 89 [2019] PIERC 88 [2018] PIERC 87 [2018] PIERC 86 [2018] PIERC 85 [2018] PIERC 84 [2018] PIERC 83 [2018] PIERC 82 [2018] PIERC 81 [2018] PIERC 80 [2018] PIERC 79 [2017] PIERC 78 [2017] PIERC 77 [2017] PIERC 76 [2017] PIERC 75 [2017] PIERC 74 [2017] PIERC 73 [2017] PIERC 72 [2017] PIERC 71 [2017] PIERC 70 [2016] PIERC 69 [2016] PIERC 68 [2016] PIERC 67 [2016] PIERC 66 [2016] PIERC 65 [2016] PIERC 64 [2016] PIERC 63 [2016] PIERC 62 [2016] PIERC 61 [2016] PIERC 60 [2015] PIERC 59 [2015] PIERC 58 [2015] PIERC 57 [2015] PIERC 56 [2015] PIERC 55 [2014] PIERC 54 [2014] PIERC 53 [2014] PIERC 52 [2014] PIERC 51 [2014] PIERC 50 [2014] PIERC 49 [2014] PIERC 48 [2014] PIERC 47 [2014] PIERC 46 [2014] PIERC 45 [2013] PIERC 44 [2013] PIERC 43 [2013] PIERC 42 [2013] PIERC 41 [2013] PIERC 40 [2013] PIERC 39 [2013] PIERC 38 [2013] PIERC 37 [2013] PIERC 36 [2013] PIERC 35 [2013] PIERC 34 [2013] PIERC 33 [2012] PIERC 32 [2012] PIERC 31 [2012] PIERC 30 [2012] PIERC 29 [2012] PIERC 28 [2012] PIERC 27 [2012] PIERC 26 [2012] PIERC 25 [2012] PIERC 24 [2011] PIERC 23 [2011] PIERC 22 [2011] PIERC 21 [2011] PIERC 20 [2011] PIERC 19 [2011] PIERC 18 [2011] PIERC 17 [2010] PIERC 16 [2010] PIERC 15 [2010] PIERC 14 [2010] PIERC 13 [2010] PIERC 12 [2010] PIERC 11 [2009] PIERC 10 [2009] PIERC 9 [2009] PIERC 8 [2009] PIERC 7 [2009] PIERC 6 [2009] PIERC 5 [2008] PIERC 4 [2008] PIERC 3 [2008] PIERC 2 [2008] PIERC 1 [2008]
2023-03-20
Analyses of Absorbing Boundary Conditions in 2D FDTD Simulations for Electromagnetic Wave Propagation in Anisotropic Ionosphere
By
Progress In Electromagnetics Research C, Vol. 131, 103-117, 2023
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.
Citation
Md Yusoff Siti Harwani, and Tiem Leong Yoon, "Analyses of Absorbing Boundary Conditions in 2D FDTD Simulations for Electromagnetic Wave Propagation in Anisotropic Ionosphere," Progress In Electromagnetics Research C, Vol. 131, 103-117, 2023.
doi:10.2528/PIERC22112302
References

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

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

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

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.

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

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.

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

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

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

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.

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.

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.

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.

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.

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

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.

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

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

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

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

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

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