2011-05-27
A Hybrid Higher Order FDTD Scheme for Modeling Radar Cross Section of Electrically Large Targets
By
Progress In Electromagnetics Research M, Vol. 18, 143-157, 2011
Abstract
This paper proposes a hybrid higher order finite difference time domain (FDTD) scheme that combines the classical FDTD scheme and the higher order FDTD scheme with second order accuracy in time and fourth order accuracy in space for analyzing the three-dimensional electrically large scattering problems. The classical FDTD stencils were used as buffers in the scattered field region to make the higher order FDTD stencils not intrude inside the absorbing boundary condition's regions. The superior performance of the hybrid higher order FDTD scheme has been compared with the classical FDTD one. Numerical results demonstrate that the proposed scheme would improve the accuracy and save the computer resources significantly compared to the classical FDTD scheme involved in the radar cross section (RCS) calculation. The obtained computational efficiency allows this proposed scheme to model the RCS of electrically large targets using the number of higher order FDTD cells which are much less than that of the classical FDTD cells required by three-dimensional FDTD scheme.
Citation
Xia Ai, Yiping Han, Zhuyang Chen, and Xiao-Wei Shi, "A Hybrid Higher Order FDTD Scheme for Modeling Radar Cross Section of Electrically Large Targets," Progress In Electromagnetics Research M, Vol. 18, 143-157, 2011.
doi:10.2528/PIERM11042904
References

1. Ishimaru, A. and Ed., Wave Propagation and Scattering in Random Media, 2nd edition, Academic, New York, 1978.

2. 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, 302-307, 1966.
doi:10.1109/TAP.1966.1138693        Google Scholar

3. Taflove, A. and S. Hagness, Computational Electromagnetics: The Finite-difference Time-domain Method, 3nd Edition, Artech House, Boston, MA, 2005.

4. Taflove, A., K. R. Umashankar, and T. G. Jurgens, "Validation of FDTD modeling of the radar cross-section of three-dimensional structures spanning up to 9 wavelengths," IEEE Transactions on Antennas and Propagation, Vol. 33, 662-666, 1985.
doi:10.1109/TAP.1985.1143644        Google Scholar

5. Li, X., A. Taflove, and V. Backman, "Modified FDTD near-to-far-field transformation for improved backscattering calculation of strongly forward-scattering objects," IEEE Antennas and Wireless Propagation Letters, Vol. 4, 35-38, 2005.
doi:10.1109/LAWP.2005.845038        Google Scholar

6. Umashankar, K. R. and A. Taflove, "A novel method to analyze electromagnetic scattering of complex objects," IEEE Transactions on Electromagnetic Compatibility, Vol. 24, 397-405, 1982.
doi:10.1109/TEMC.1982.304054        Google Scholar

7. Shlager, K. L. and J. B. Schneider, "Comparison of the dispersion properties of several low-dispersion finite-difference time-domain algorithms," IEEE Transactions on Antennas and Propagation, Vol. 51, 642-653, 2003.
doi:10.1109/TAP.2003.808532        Google Scholar

8. Nehrbass, J. W., J. O. Jevtc, and R. Lee, "Reducing the phase error for finite-difference methods without increasing the order," IEEE Transactions on Antennas and Propagation, Vol. 46, 1194-1201, 1998.
doi:10.1109/8.718575        Google Scholar

9. Cole, J. B., "High-accuracy realization of the Yee algorithm using non-standard finite differences," IEEE Transactions on Microwave Theory and Techniques, Vol. 45, 991-996, 1997.
doi:10.1109/22.588615        Google Scholar

10. Kim, W.-T., I.-S. Koh, and J.-G. Yook, "3D isotropic dispersion (ID)-FDTD algorithm: Update equation and characteristics analysis," IEEE Transactions on Antennas and Propagation, Vol. 58, 1251-1259, 2010.
doi:10.1109/TAP.2010.2041311        Google Scholar

11. Lan, K., Y. Liu, and W. Lin, "Higher order (2, 4) scheme for reducing dispersion in FDTD algorithm," IEEE Transactions on Electromagnetic Compatibility, Vol. 41, 160-165, 1999.
doi:10.1109/15.765109        Google Scholar

12. Georgakopoulos, S. V., C. R. Birtcher, C. A. Balanis, and R. A. Renaut, "Higher-order finite-difference schemes for electromagnetic radiation, scattering, and penetration. Part 1: Theory," IEEE Antennas and Propagation Magazine, Vol. 44, 134-142, 2002.
doi:10.1109/74.997945        Google Scholar

13. Georgakopoulos, S. V., C. R. Birtcher, and C. A. Balanis, "Higher-order finite-difference schemes for electromagnetic radiation, scattering, and penetration, Part 2: Applications," IEEE Antennas and Propagation Magazine, Vol. 44, 92-101, 2002.
doi:10.1109/MAP.2002.1003639        Google Scholar

14. Abd El-Raouf, H. E., E. A. El-Diwani, A. E.-H. Ammar, and F. El-Hefnawi, "A low-dispersion 3-D second-order in time fourth- order in space FDTD scheme (M3d24)," IEEE Transactions on Antennas and Propagation, Vol. 52, 1638-1646, 2004.
doi:10.1109/TAP.2004.831286        Google Scholar

15. Zygiridis, T. T. and T. D. Tsiboukis, "Low-dispersion algorithms based on the higher order (2, 4) FDTD method," IEEE Transactions on Microwave Theory and Techniques, Vol. 52, 1321-1327, 2004.
doi:10.1109/TMTT.2004.825695        Google Scholar

16. Zygiridis, T. T. and T. D. Tsiboukis, "A dispersion-reduction scheme for the higher order (2, 4) FDTD method," IEEE Transactions on Magnetics, Vol. 40, 1464-1467, 2004.
doi:10.1109/TMAG.2004.824779        Google Scholar

17. Hadi, M. F. and S. F. Mahmoud, "A high-order compact- FDTD algorithm for electrically large waveguide analysis," IEEE Transactions on Antennas and Propagation, Vol. 56, 2589-2598, 2008.
doi:10.1109/TAP.2008.927545        Google Scholar

18. Georgakopoulos, S. V. and R. A. Renaut, "A hybrid forth-order FDTD utilizing a second-order FDTD subgrid," IEEE Microwave and Wireless Components Letters, Vol. 11, 462-464, 2001.
doi:10.1109/7260.966042        Google Scholar

19. Fang, J., "Time domain finite difference computation for Maxwell's equations,", Ph.D. Dissertation, University of California, Berkeley, CA, USA, 1989.        Google Scholar

20. Hadi, M. F., "A finite volumes-based 3-D low dispersion FDTD algorithm," IEEE Transactions on Antennas and Propagation, Vol. 55, 2287-2293, 2007.
doi:10.1109/TAP.2007.901996        Google Scholar

21. Berenger, J. P., "A perfectly matched layer for the absorption of electromagnetic waves," Journal of Computional Physics, Vol. 114, 185-200, 1994.
doi:10.1006/jcph.1994.1159        Google Scholar

22. Zygiridis, T. T. and T. D. Tsiboukis, "Development of higher order FDTD schemes with controllable dispersion error," IEEE Transactions on Antennas and Propagation, Vol. 53, 2952-2960, 2005.
doi:10.1109/TAP.2005.854559        Google Scholar

23. Hadi, M. F. and M. Piket-May, "Modified FDTD (2, 4) scheme for modeling electrically large structures with high-phase accuracy," IEEE Transactions on Antennas and Propagation, Vol. 45, 254-264, 1997.
doi:10.1109/8.560344        Google Scholar

24. Ogurtsov, S. and S. V. Georgakopoulos, "FDTD schemes with minimal numerical dispersion," IEEE Transactions on Advanced Packaging, Vol. 32, 199-204, 2009.
doi:10.1109/TADVP.2008.2008100        Google Scholar

25. Hadi, M. F. and R. K. Dib, "Phase-matching the hybrid FV24/S22 FDTD algorithm," Progress In Electromagnetics Research, Vol. 72, 307-323, 2007.
doi:10.2528/PIER07031601        Google Scholar