Vol. 42

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2012-07-12

Fd2td Analysis of Electromagnetic Field Propagation in Multipole Debye Media with and Without Convolution

By Mauro Feliziani, Silvano Cruciani, Valerio De Santis, and Francesearomana Maradei
Progress In Electromagnetics Research B, Vol. 42, 181-205, 2012
doi:10.2528/PIERB12060109

Abstract

This paper deals with the time-domain numerical calculation of electromagnetic (EM) fields in linearly dispersive media described by multipole Debye model. The frequency-dependent finite-difference time-domain (FD2TD) method is applied to solve Debye equations using convolution integrals or by direct integration. Original formulations of FD2TD methods are proposed using different approaches. In the first approach based on the solution of convolution equations, the exponential analytical behavior of the convolution integrand permits an efficient recursive FD2TD solution. In the second approach, derived by circuit theory, the transient equations are directly solved in time domain by the FD2TD method. A comparative analysis of several FD2TD methods in terms of stability, dispersion, computational time and memory is carried out.

Citation


Mauro Feliziani, Silvano Cruciani, Valerio De Santis, and Francesearomana Maradei, "Fd2td Analysis of Electromagnetic Field Propagation in Multipole Debye Media with and Without Convolution," Progress In Electromagnetics Research B, Vol. 42, 181-205, 2012.
doi:10.2528/PIERB12060109
http://jpier.org/PIERB/pier.php?paper=12060109

References


    1. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media ," IEEE Trans. Antennas Propag., Vol. 14, 302-307, May 1966.
    doi:10.1109/TAP.1966.1138693

    2. Luebbers, R. J., F. P. Hunsberger, K. S. Kunz, R. B. Standler, and M. Schneider, "A frequency-dependent finite-difference time-domain formulation for dispersive materials," IEEE Trans. Electromagn. Compat., Vol. 32, No. 3, 222-227, Aug. 1990.
    doi:10.1109/15.57116

    3. Luebbers, R. J. and F. P. Hunsberger, "FDTD for Nth-order spersive media," IEEE Trans. Antennas Propag., Vol. 40, No. 11, 129-1301, Nov. 1992.

    4. Kelley, D. F. and R. J. Luebbers, "Piecewise linear recursive convolution for dispersive media using FDTD," IEEE Trans. Antennas Propag., Vol. 44, No. 6, 792-797, Jun. 1996.
    doi:10.1109/8.509882

    5. Buccella, C., V. De Santis, M. Feliziani, and F. Maradei, "Fast calculation of dielectric substrate losses in microwave applications by the FD2TD method using a new formalism," IEEE International Symposium on EMC, Fort Lauderdale, USA, Jul. 25-30, 2010.

    6. De Santis, V., M. Feliziani, and F. Maradei, "Safety assessment of UWB radio systems for body area network by the FD2TD method," IEEE Trans. Magn., Vol. 46, No. 8, 3245-3248, Aug. 2010.
    doi:10.1109/TMAG.2010.2046478

    7. Kashiwa, T. and I. Fukai, "A treatment by the FDTD method of the dispersive characteristics associated with electronic polarization," Microw. Opt. Technol. Lett., Vol. 3, No. 6, 203-205, 1990.
    doi:10.1002/mop.4650030606

    8. Joseph, R. M., S. C. Hagness, and A. Taflove, "Direct time integration of Maxwell's equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses," Opt. Lett., Vol. 16, No. 18, 1412-1414, Sept. 1991.
    doi:10.1364/OL.16.001412

    9. Gandhi, O. P., B. Q. Gao, and J. Y. Chen, "A frequency-dependent finite-difference time-domain formulation for general dispersive media," IEEE Trans. Microw. Theory Tech., Vol. 41, No. 4, 658-664, Apr. 1993.
    doi:10.1109/22.231661

    10. Young, J. L., "Propagation in linear dispersive media: Finite difference time-domain methodologies," IEEE Trans. Antennas Propag., Vol. 43, No. 4, 422-426, Apr. 1995.
    doi:10.1109/8.376042

    11. Okoniewski, M., M. Mrozowski, and M. A. Stuchly, "Simple treatment of multi-term dispersion in FDTD," IEEE Microw. Guided Wave Lett., Vol. 7, No. 5, 121-123, 1997.
    doi:10.1109/75.569723

    12. Takayama, Y. and W. Klaus, "Reinterpretation of the auxiliary differential equation method for FDTD," IEEE Microw. Wireless Comp. Lett., Vol. 12, No. 3, 102-104, 2002.
    doi:10.1109/7260.989865

    13. Sullivan, D. M., "Frequency-dependent FDTD methods using Z transforms," IEEE Trans. Antennas Propag., Vol. 40, No. 10, 1223-1230, Oct. 1992.
    doi:10.1109/8.182455

    14. Sullivan, D. M., "Z-transform theory and the FDTD method," IEEE Trans. Antennas Propag., Vol. 44, No. 1, 28-34, Jan. 1996.
    doi:10.1109/8.477525

    15. Weedon, W. H. and C. M. Rappaport, "A general method for FDTD modeling of wave propagation in arbitrary frequency dispersive media," IEEE Trans. Antennas Propag., Vol. 45, 401-410, 1997.
    doi:10.1109/8.558655

    16. Rappaport, C., S. Wu, and S. Winton, "FDTD wave propagation in dispersive soil using a single pole conductivity model," IEEE Trans. Magn., Vol. 35, 1542-1545, May 1999.
    doi:10.1109/20.767262

    17. Kosmas, P., C. Rappaport, and E. Bishop, "Modeling with the FDTD method for microwave breast cancer detection," IEEE Trans. Microwave Theory Tech., Vol. 52, No. 8, 1890-1897, Aug. 2004.
    doi:10.1109/TMTT.2004.831985

    18. Siushansian, R. and J. L. Vetri, "A comparison of numerical techniques for modeling electromagnetic dispersive media," IEEE Microw. Guided Wave Lett., Vol. 5, No. 12, 426-428, 1995.
    doi:10.1109/75.481849

    19. Chen, Q., M. Katsurai, and P. H. Aoyagi, "An FDTD formulation for dispersive media using a current density," IEEE Trans. Antennas Propag., Vol. 46, No. 11, 1739-1746, 1998.
    doi:10.1109/8.736632

    20. Liu, S., N. Yuan, and J. Mo, "A novel FDTD formulation for dispersive media," IEEE Microw. Wireless Comp. Lett., Vol. 13, No. 5, 187-189, 2003.
    doi:10.1109/LMWC.2003.811668

    21. Teixeira, F. L., "Time-domain finite-difference and finite-element methods for Maxwell equations in complex media," IEEE Trans. Antennas Propag., Vol. 56, No. 8, 2150-2166, Aug. 2008.
    doi:10.1109/TAP.2008.926767

    22. Zhang, Y.-Q. and D.-B. Ge, "A unified FDTD approach for electromagnetic analysis of dispersive objects," Progress In Electromagnetics Research, Vol. 96, 155-172, 2009.
    doi:10.2528/PIER09072603

    23. Young, J. L., A. Kittichantphayak, Y. M. Kwok, and D. Sullivan, "On the dispersion errors related to (FD)2TD type schemes," IEEE Trans. Microw. Theory Tech., Vol. 43, No. 8, 1902-1910, Aug. 1995.
    doi:10.1109/22.402280

    24. Young, J. and R. Nelson, "A summary and systematic analysis of FDTD algorithms for linearly dispersive media," IEEE Antennas Propag. Mag., Vol. 43, No. 1, 61-126, Feb. 2001.
    doi:10.1109/74.920019

    25. Kunz, K. and R. Luebbers, The Finite Difference Time Domain Method for Electromagnetics, CRC Press, Boca Raton, FL, 1993.

    26. Petropoulos, P. G., "Stability and phase analysis of FD-TD in dispersive dielectrics," IEEE Trans. Antennas Propag., Vol. 42, No. 1, 62-69, Jan. 1994.
    doi:10.1109/8.272302

    27. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain, 3rd Edition, Artech House, Norwood, MA, 2005.

    28. Bidégaray-Fesquet, B., "Stability of FD-TD schemes for Maxwell-Debye and Maxwell-Lorentz equations," SIAM J. Numer. Anal., Vol. 46, No. 5, 2551-2566, Jun. 2008.
    doi:10.1137/060671255

    29. Mur, G., "Absorbing boundary conditions for the finite-di®erence approximation of the time-domain electromagnetic-field equations," IEEE Trans. Electromagn. Compat., Vol. 23, No. 4, 377-382, Nov. 1981.
    doi:10.1109/TEMC.1981.303970

    30. 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, Dec. 2000.
    doi:10.1002/1098-2760(20001205)27:5<334::AID-MOP14>3.0.CO;2-A