In this paper we compare current implementations of commonly used numerical techniques - the Finite-Difference Time-Domain (FDTD) method, the Finite-Integration Technique (FIT), and Time-Domain Integral Equations (TDIE) - to solve the canonical problem of a horizontal dipole antenna radiating over lossless and lossy half-spaces. These types of environment are important starting points for simulating many Ground Penetrating Radar (GPR applications which operate in the near-field of the antenna, where the interaction among the antenna, the ground, and targets is important. We analysed the simulated current at the centre of the dipole antenna, as well as the electric field at different distances from the centre of the antenna inside the half-space. We observed that the results from the simulations using the FDTD and FIT methods agreed well with each other in all of the environments. Comparisons of the electric field showed that the TDIE technique agreed with the FDTD and FIT methods when observation distances were towards the far-field of the antenna but degraded closer to the antenna. These results provide evidence necessary to develop a hybridisation of current implementations of the FDTD and TDIE methods to capitalise on the strengths of each technique.
2. Bretones, A. R. and A. G. Tijhuis, "Transient excitation of a straight thin wire segment over an interface between two dielectric half spaces," Radio Science, Vol. 30, No. 6, 1723-1738, 1995.
3. Cassidy, N. J. and T. M. Millington, "The application of finite-difference time-domain modelling for the assessment of GPR in magnetically lossy materials," Journal of Applied Geophysics, Vol. 67, No. 4, 296-308, 2009.
4. Chen, H. T., J.-X. Luo, and D.-K. Zhang, "An analytic formula of the current distribution for the vlf horizontal wire antenna above lossy half-space," Progress In Electromagnetics Research Letters, Vol. 1, 149-158, 2008.
5. Elsevier, Scopus, the largest abstract and citation database of peer-reviewed literature, [online], http://www.scopus.com, Mar. 24, 2017.
6. Giannopoulos, A., "Modelling ground penetrating radar by gprMax," Construction and Building Materials, Vol. 19, No. 10, 755-762, 2005.
7. Gwangju Institute of Science and Technology, GMES - Gist Maxwell's equations solver, [online], http://sourceforge.net/projects/gmes/, Mar. 24, 2017.
8. Liu, L. and S. A. Arcone, "Propagation of radar pulses from a horizontal dipole in variable dielectric ground: A numerical approach," Subsurface Sensing Technologies and Applications, Vol. 6, No. 1, 5-24, 2005.
9. Lumerical Solutions, Inc., FDTD solutions, [online], https://www.lumerical.com/tcadproducts/fdtd/, Mar. 24, 2017.
10. Massachusetts Institute of Technology, Meep - Mit electromagnetic equation propagation, [online], http://ab-initio.mit.edu/wiki/index.php/Meep, Mar. 24, 2017.
11., Mentor Graphics, Electromagnetic simulation solutions, [online], https://www.mentor.com/pcb/nimbic/, Mar. 24, 2017.
12. Miller, E. K., A. J. Poggio, and G. J. Burke, "An integro-differential equation technique for the time domain analysis of thin wire structures. I. The numerical method," Journal of Computational Physics, Vol. 12, No. 1, 24-48, 1973.
13. Moore, R. K. and W. E. Blair, "Dipole radiation in a conducting half-space," Journal of Research of the National Bureau of Standards - D. Radio Propagation, Vol. 65, No. 6, 547-563, 1961.
14. Poljak, D., S. Sesnic, D. Paric, and K. El Khamlichi Drissi, "Direct time domain modeling of the transient field transmitted in a dielectric half-space for gpr applications," 2015 International Conference on IEEE Electromagnetics in Advanced Applications (ICEAA), 345-348, 2015.
15. Poljak, D., Advanced Modeling in Computational Electromagnetic Compatibility, John Wiley & Sons, 2007.
16. Poljak, D. and V. Roje, "Time domain calculation of the parameters of thin wire antennas and scatterers in a half-space configuration," IEE Proceedings - Microwaves, Antennas and Propagation, Vol. 145, No. 1, 57-63, 1998.
17. Rančić, M. P. and P. D. Rančić, "Horizontal linear antennas above a lossy half-space: A new model for the Sommerfeld’s integral kernel," International Journal of Electronics and Communications (AEU), Vol. 65, No. 10, 879-887, 2011.
18., Remcom, Xfdtd em simulation software, [online], http://www.remcom.com/xf7, Mar. 24, 2017.
19. Rynne, B. P. and P. D. Smith, "Stability of time marching algorithms for the electric field integral equation," Journal of Electromagnetic Waves and Applications, Vol. 4, No. 12, 1181-1205, 1990.
20. Shangguan, P. and I. L. Al-Qadi, "Calibration of fdtd simulation of GPR signal for Asphalt pavement compaction monitoring," IEEE Transactions on Geoscience and Remote Sensing, Vol. 53, No. 3, 1538-1548, 2015.
21. Shoory, A., R. Moini, and S. H. H. Sadeghi, "Direct use of discrete complex image method for evaluating electric field expressions in a lossy half space," IET Microwaves, Antennas & Propagation, Vol. 4, No. 2, 258-268, 2010.
22. Slob, E. and J. Fokkema, "Coupling effects of two electric dipoles on an interface," Radio Science, Vol. 37, No. 5, 2002.
23. Slob, E., M. Sato, and G. Olhoeft, "Surface and borehole ground-penetrating-radar developments," Geophysics, Vol. 75, No. 5, 75A103-75A120, 2010.
24. Soldovieri, F., J. Hugenschmidt, R. Persico, and G. Leone, "A linear inverse scattering algorithm for realistic GPR applications," Near Surface Geophysics, Vol. 5, No. 1, 29-42, 2007.
25. Solla, M., R. Asorey-Cacheda, X. Núñez-Nieto, and B. Conde-Carnero, "Evaluation of historical bridges through recreation of gpr models with the FDTD algorithm," NDT & E International, Vol. 77, 19-27, 2016.
26. Sommerfeld, A., "Über die ausbreitung der wellen in der drahtlosen telegraphie," Annalen der Physik, Vol. 333, 665-736, 1909.
27. Sommerfeld, A., "Über die ausbreitung der wellen in der drahtlosen telegraphie," Annalen der Physik, Vol. 386, No. 25, 1135-1153, 1926.
28. Tran, A. P., F. Andre, and S. Lambot, "Validation of near-field groundpenetrating radar modeling using full-wave inversion for soil moisture estimation," IEEE Transactions on Geoscience and Remote Sensing, Vol. 52, No. 9, 5483-5497, 2014.
29. Wait, J. R., "The electromagnetic fields of a horizontal dipole in the presence of a conducting half-space," Canadian Journal of Physics, Vol. 39, No. 7, 1017-1028, 1961.
30. Warren, C., A. Giannopoulos, and I. Giannakis, "GPRMAX: Open source software to simulate electromagnetic wave propagation for ground penetrating radar," Computer Physics Communications, Vol. 209, 163-170, 2016.
31. Weiland, T., "A discretization model for the solution of Maxwell’s equations for six-component fields," Archiv Elektronik und Uebertragungstechnik, Vol. 31, 116-120, 1977.
32. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Transactions on Antennas and Propagation, Vol. 14, No. 3, 302-307, 1966.