volume | PIER Journals

Abstract

Finite-Difference Time-Domain (FDTD) subgridding schemes can significantly improve efficiency of various electromagnetic circuit simulations. However, numerous subgridding schemes suffer from issues associated with stability, efficiency, and material traverse capability. These issues limit general applicability of FDTD subgridding schemes to realistic problems. Herein, a robust nonuniform subgridding scheme is presented that overcomes those weaknesses. The scheme improves simulation accuracy with the aid of greatly increased stability margin and an optimal interpolation technique. It also improves simulation efficiency by allowing the use of time step factors as close as the Courant-Friedrichs-Lewy (CFL) limit. In addition, latetime stability and general applicability are verified through practical microstrip circuit simulation examples.

1. Elsherbeni, A. and V. Demir, The Finite-difference Time-domain Method for Electromagnetics with MATLAB Simulations, SciTech Publishing, Inc., Raleigh, NC, 2009.

2. Courant, R., K. Friedrichs, and H. Lewy, "On the partial difference equations of mathematical physics," IBM Journal of Research and Development, Vol. 11, No. 2, 215-234, 1967.
doi:10.1147/rd.112.0215

3. Thoma, P. and T. Weiland, "A consistent subgridding scheme for the finite difference time domain method," Int. J. Numer. Modeling: Electron. Networks, Devices Fields, Vol. 9, 359-374, 1996.
doi:10.1002/(SICI)1099-1204(199609)9:5<359::AID-JNM245>3.0.CO;2-A

4. Krishnaiah, K. and C. Railton, "A stable subgridding algorithm and its application to eigenvalue problems," IEEE Trans. Microw. Theory Tech., Vol. 47, No. 5, 620-628, May 1999.
doi:10.1109/22.763164

5. Xiao, K., D. Pommerenke, and J. Drewniak, "A three dimensional FDTD subgridding algorithm based on interpolation of current density," Proc. IEEE EMC Symp., Vol. 1, 118-123, Santa Clara,CA, 2004.

6. Xiao, K., D. Pommerenke, and J. Drewniak, "A three-dimensional FDTD subgridding algorithm with separated temporal and spatial interfaces and related stability analysis," IEEE Trans. Antennas Propagat., Vol. 55, No. 7, 1981-1990, Jul. 2007.
doi:10.1109/TAP.2007.900180

7. Monk, P., "Subgridding FDTD schemes," Appl. Comput. Electromagn. Society J., Vol. 11, No. 1, 37-46, 1996.

8. Chilton, R. A. and R. Lee, "Conservative and provably stable FDTD subgridding," IEEE Trans. Antennas Propagat., Vol. 55, No. 9, 2537-254, Sep. 2007.
doi:10.1109/TAP.2007.904092

9. Chevalier, M. W., R. J. Luebbers, and V. P. Cable, "FDTD local grid with material traverse," IEEE Trans. Antennas Propagat., Vol. 45, 411-421, Mar. 1997.
doi:10.1109/8.558656

10. White, M. J., Z. Yun, and M. F. Iskander, "A new 3-D FDTD multigrid technique with dielectric traverse capabilities," IEEE Trans. Microw. Theory Tech., Vol. 49, 422-430, 2001.
doi:10.1109/22.910545

11. Vaccari, A., R. Pontalti, C. Malacarne, and L. Cristoforetti, "A robust and efficient subgridding algorithm for finite-difference time-domain simulations of Maxwell's equations," J. Comp. Phys., Vol. 194, 117-139, 2004.
doi:10.1016/j.jcp.2003.09.002

12. Donderici, B. and F. L. Teixeira, "Improved FDTD subgridding algorithms via digital filtering and domain overriding," IEEE Trans. Antennas Propagat., Vol. 53, No. 9, 2938-2951, 2005.
doi:10.1109/TAP.2005.854558

13. Kulas, L. and M. Mrozowski, "Low reflection subgridding," IEEE Trans. Microw. Theory Tech., Vol. 53, No. 5, 1587-1592, 2005.
doi:10.1109/TMTT.2005.847048

14. Berenger, J.-P., "A Huygens subgridding for the FDTD method," IEEE Trans. Antennas Propagat., Vol. 54, 3797-3804, 2006.
doi:10.1109/TAP.2006.886519

15. Moler, C., Numerical Computing with MATLAB, 2004, Available: http://www.mathworks.com/moler/index ncm.html.

16. Okoniewski, M., E. Okoniewska, and M. A. Stuchly, "Three-dimensional subgridding algorithm for FDTD," IEEE Trans. Antennas Propagat., Vol. 45, No. 3, 422-429, 1997.
doi:10.1109/8.558657

17. Kermani, M. H. and O. M. Ramahi, "The complementary derivatives method: A second-order accurate interpolation scheme for nonuniform grid in FDTD simulation," IEEE Microw. Wireless Compon. Lett., Vol. 16, 60-62, Feb. 2006.
doi:10.1109/LMWC.2005.863253

18. "Sonnet User's Guide --- Release 12," Sonnet Software Inc., North Syracuse, NY, Apr. 2009.

19. Liu, Y. and C. D. Sarris, "Efficient modeling of microwave integrated circuit geometries via a dynamically adaptive mesh refinement (AMR) --- FDTD technique," IEEE Trans. Microw. Theory Tech., Vol. 54, No. 2, 689-703, Feb. 2006.
doi:10.1109/TMTT.2005.862660

20. Sheen, D. M., S. M. Ali, M. D. Abouzahra, and J. A. Kong, "Application of the three-dimensional finite-difference time-domain method to the analysis of planar microstrip circuits," IEEE Trans. Microw. Theory Tech., Vol. 38, 849-857, Jul. 1990.

Dr. Gyusub Kim

Dr. Ercument Arvas

Dr. Veysel Demir

Professor Atef Elsherbeni