volume | PIER Journals

Abstract

Based on the conventional finite-difference time-domain (FDTD) method, a novel dual-meshed technique is presented to deal with the underwater detection problems applying in low frequency electromagnetic wave. A transformation surface connecting the coarse cell with the fine cell is implemented by applying a total-field scattered-field source (TSS) technique, which is carried out by two-step FDTD simulation. The ratio of a coarse cell size to a fine cell size can be set as an arbitrary integer, such as N=10. Moreover, it is illustrates that non-physical reflection fields from the TSS surface are avoided by introducing the TSS surface. We have derived, in detail, the update equations of fields on grids of the TSS surface. Three cases of dealing with different underwater electromagnetic problems are discussed. Numerical results show that by analyzing the magnitude and phase of scattered fields from obstacles underwater we can distinguish the category of the obstacles which belongs to either a high resistivity body or a low resistivity body. Therefore, the proposed method provides us an effective tool for analyzing the electromagnetic response of materials underwater.

1. Allen, T., Computational Electrodynamics: The Finite-difference Time-domain Method, 2nd Edition, Boston, 2000.

2. Yee, K., "Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media," IEEE Transactions Antennas and Propagation, Vol. 14, 6-10, 1966.
doi:10.1109/TAP.1966.1138620

3. Xia, Y. and D. M. Sullivan, "Underwater FDTD simulation at extremely low frequencies," IEEE Antennas and Wireless Propagation Letters, Vol. 7, 661-664, 2008.
doi:10.1109/LAWP.2008.2010066

4. Furse, C. M., "Faster than Fourier: Ultra-efficient time-to-frequency-domain conversions for FDTD simulations," IEEE Antennas and Propagation Magazine, Vol. 42, 24-34, 2000.
doi:10.1109/74.894179

5. Loach, P. D., J. J. Kazik, and R. C. Ireland, "Numerical modelling of underwater electromagnetic propagation," Recent Advances in Applied and Theoretical Mathematics, 220-225, 2000.

6. Chen, J. and A. Zhang, "A subgridding scheme based on the FDTD method and HIE-FDTD method," Applied Computational Electromagnetics Society Journal, Vol. 26, No. 1, 1-7, 2011.

7. Yu, W. and R. Mittra, "New subgridding method for the finite-difference time-domain (FDTD) algorithm," Microwave and Optical Technology Letters, Vol. 21, No. 5, 330-333, 1999.
doi:10.1002/(SICI)1098-2760(19990605)21:5<330::AID-MOP7>3.0.CO;2-N

8. Mock, A., "Subgridding scheme for FDTD in cylindrical coordinates," PIERS Proceedings, 1053-1057, Suzhou, China, Sep. 12-16, 2011.

9. Berenger, J. P., "A Huygens subgridding for the FDTD method," IEEE Transactions on Antennas and Propagation, Vol. 54, No. 12, 3797-3804, 2006.
doi:10.1109/TAP.2006.886519

10. Berenger, J. P., "Extension of the FDTD huygens subgridding algorithm to two dimensions," IEEE Transactions on Antennas and Propagation, Vol. 57, No. 12, 3860-3867, 2009.
doi:10.1109/TAP.2009.2031906

11. Berenger, J. P., "The Huygens subgridding for the numerical solution of the Maxwell equations," Journal of Computational Physics, Vol. 230, No. 14, 5635-5659, 2011.
doi:10.1016/j.jcp.2011.03.046

12. Abalenkovs, M., "Huygens subgridding for 3-D frequency-dependent finite-difference time-domain method," IEEE Transactions on Antennas and Propagation, Vol. 60, No. 9, 4336-434, 2012.
doi:10.1109/TAP.2012.2207039

13. Xia, Y. and D. M. Sullivan, "Dual problem space FDTD simulation for underwater ELF applications," IEEE Antennas and Wireless Propagation Letters, Vol. 8, 498-501, 2009.

14. Sullivan, D. M. and Y. Xia, "A perfectly matched layer for lossy media at extremely low frequencies," 2009 IEEE International Symposium on Antennas and Propagation and USNC/URSI National Radio Science Meeting, Institute of Electrical and Electronics Engineers Inc., North Charleston, SC, United States, Jun. 1-5, 2009.

15. Roden, J. A. and S. D. Gedney, "Convolution PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media," Microwave and Optical Technology Letters, Vol. 27, No. 5, 334-339, 2000.
doi:10.1002/1098-2760(20001205)27:5<334::AID-MOP14>3.0.CO;2-A

16. Harrington, R. F., Time-harmonic Electromagnetic Fields, 106-108, 228–230, 2001.
doi:10.1109/9780470546710

Dr. Kuisong Zheng

Dr. Hui Yu

Dr. Huan Luo

Dr. Tengjiang Ding