This work presents a two-dimensional (2D) subgrid technology for the geodesic finite different time-domain (FDTD) algorithm, which is applied to solve global extremely low frequency (ELF) electromagnetic EM wave propagation problems in the Earth-ionosphere system. The new technology provides arbitrarily locale resolution to study finer structure without disturb the global grid structure. Combined with the subgrid technique, the new geodesic FDTD algorithm can solve EM propagation problems in specific locale regions without extra computational burden. Based on the original geodesic FDTD formulations, the 2D subgrid technique is developed, and its computational stable relation is derived and analyzed. Then, possible three-dimensional (3D) subgrid structure is proposed. Finally, potential applications for the subgrid technique are suggested.
2. Sevgi, L., F. Akleman, and L. Felsen, "Groundwave propagation modeling: Problem-matched analytical formulations and direct numerical techniques," IEEE Antennas and Propagation Magazine, Vol. 44, 55-75, 2002.
3. Berenger, J., "Long range propagation of lightning pulses using the FDTD method," IEEE Transactions on Electromagnetic, Vol. 47, 1008-1012, 2005.
4. Hu , W. and S. Cummer, "An FDTD model for low and high altitude lightning-generated EM fields," IEEE Transactions on Antennas and Propagation, Vol. 54, 1513-1522, 2006.
5. Soriano, A. , E. Navarro, D. Paul, and J. Porti, "Finite difference time domain simulation of the Earth-ionosphere resonant cavity: Schumann resonances," IEEE Transactions on Antennas and Propagation, Vol. 53, 1535-1541, 2005.
6. Yang, H., V. P. Pasko, and G. Satori, "Seasonal variations of global lightning activity extracted from Schumann resonances using a genetic algorithm method," Journal of Geophysical Research, Vol. 114, 1-10, 2009.
7. Simpson, J. J. and A. Taflove, "E±cient modeling of impulsive ELF antipodal propagation about the earth sphere using an optimized two-dimensional geodesic FDTD grid," IEEE Antennas and Wireless Propagation Letters, Vol. 3, 215-218, 2004.
8. Simpson, J. J. and A. Taflove, "ELF radar system proposed for localized D-region ionospheric anomalies," IEEE Geoscience and Remote Sensing Letters, Vol. 3, 500-503, 2006.
9. Simpson, J. J., R. Heikes, and A. Taflove, "FDTD modeling of a novel ELF radar for major oil deposits using a three-dimensional geodesic grid of the earth-ionosphere waveguide," IEEE Transactions on Antennas and Propagation, Vol. 54, 1734-1741, 2006.
10. Holland , R., "THREDS: A finite-difference time-domain EMP code in 3D spherical coordinates," IEEE Transactions on Nuclear Science, Vol. 30, 4592-4595, 1983.
11. Simpson, J. J., "Electrokinetic effect of the Loma Prieta earthquake calculated by an entire-earth FDTD solution of Maxwell's equations," Geophysical Research Letters, Vol. 32, 1-4, 2005.
12. Simpson, J. J. and A. Taflove, "Two-dimensional FDTD model of antipodal ELF propagation and Schumann resonance of the Earth," IEEE Antennas and Wireless Propagation Letters, Vol. 1, 53-56, 2002.
13. Bannister , P., "ELF propagation update," IEEE Journal of Oceanic Engineering, Vol. 9, 179-188, 1984.
14. Wang, Y. , H. Xia, and Q. Cao, "Analysis of ELF attenuation rate using the geodesic FDTD algorithm," 2010 International Conference on Microwave and Millimeter Wave Technology, 1413-1415, 2010.
15. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House, 2005.
16. Xia, H. , Y. Wang, and Q. Cao, "Local high-resolution technique in FDTD modeling of ELF propagation in the earth ionosphere cavity," IEEE Antennas and Wireless Propagation Letters, Vol. 9, 649-652, 2010.
17. Wang, Y., H. Xia, and Q. Cao, "Analysis of ELF propagation along the earth surface using the FDTD model based on the spherical triangle meshing," IEEE Antennas and Wireless Propagation Letters, Vol. 8, 1017-1020, 2009.