High-order Staggered Finite Difference Time Domain Method for Dispersive Debye Medium
Keywords:
Accuracy, backward differentiation, central finite difference, Debye model, dispersive media, finite difference time domain, stabilityAbstract
In this paper, a high order accuracy Finite Difference Time Domain method was proposed for the simulation of electromagnetic waves in the Debye dispersive medium. The proposed method was based on the use of the third order Backward Differentiation scheme for the approximation of the time derivatives and the use of the fourth order Central Finite Difference scheme for the approximation of space derivatives. The stability of the present method was analyzed by using the Root-Locus method. The accuracy of the proposed method was analyzed in the case of free space and the dispersive media, in the case of plane wave and the case of a Hertzian dipole source. The proposed method offered high performance regarding the accuracy and the stability in comparison with the other methods.
Downloads
References
K. Yee, “Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media,” IEEE Trans. Antennas Propagat., vol. 14, no. 3, pp. 302-307, 1966.
M. Pieraccini, A. Bicci, D. Mecatti, G. Macaluso and C. Atzeni, “Propagation of large bandwidth microwave signals in water,” IEEE Trans. Antennas Propagat., vol. 57, no. 11, pp. 3612-3618, 2009.
S. Mustafa, A. Abbosh, and P. Nguyen, “Modeling human head tissues using fourth-order Debye model in convolution-based three-dimensional finitedifference time-domain,” IEEE Trans. Antennas Propagat., vol. 62, no. 3, pp. 1354-1361, 2014.
C. Gabriel, “Compilation of the Dielectric Properties of Body Tissues at RF and Microwave Frequencies,” Brooks Air Force, Tech. Rep. AL/OE-TR-19960037, 1996.
P. Bia, L. Mescia, and D. Caratelli, “Fractional calculus-based modeling of electromagnetic field propagation in arbitrary biological tissue,” Mathematical Problems in Engineering, vol. 2016, pp. 1- 11, 2016.
J. Li, L.-X. Guo, Y.-C. Jiao, and R. Wang, “Composite scattering of a plasma-coated target above dispersive sea surface by the ADE-FDTD method,” IEEE Geoscience and Remote Sensing Letters, vol. 10, no. 1, pp. 4-8, 2013.
S. Liu, S. Liu, and S. Liu, “Finite-difference timedomain algorithm for plasma based on trapezoidal recursive convolution technique,” Journal of Infrared, Millimeter, and Terahertz Waves, 2010.
D. Sullivan, “Nonlinear FDTD formulations using Z transforms,” IEEE Transactions on Microwave Theory and Techniques, vol. 43, no. 3, pp. 676-682, 1995.
D. B. Miron, “Z-transform frameworks for FDTD,” Antennas and Propagation Magazine IEEE, vol. 54, pp. 131-144, 2012, ISSN 1045-9243.
R. Luebbers and F. Hunsberger, “FDTD for Nthorder dispersive media,” IEEE Trans. Antennas Propagat., vol. 40, no. 11, pp. 1297-1301, 1992.
D. F. Kelley and R. J. Luebbers, “Piecewise linear recursive convolution for dispersive media using FDTD,” IEEE Trans. Antennas Propagat., vol. 44, no. 6, pp. 792-797, June 1996.
I. Giannakis and A. Giannopoulos, “A novel piecewise linear recursive convolution approach for dispersive media using the finite-difference time-domain Method,” IEEE Trans. Antennas Propagat., vol. 62, no. 5, pp. 2669-2678, 2014.
M. Okoniewaki, M. Mrozowski, and M. Stuchly, “Simple treatment of multi-term dispersion in FDTD,” IEEE Microwave and Guided Wave Letters, vol. 7, no. 5, pp. 121-123, 1997.
M. Alsunaidi and A. Al-Jabr, “A general ADEFDTD algorithm for the simulation of dispersive structures,” IEEE Photonics Technology Letters, vol. 21, no. 12, pp. 817-819, 2009.
M. Okoniewski and E. Okoniewska, “Drude dispersion in ADE FDTD revisited,” Electronics Letters, vol. 42, no. 9, p. 503, 2006.
S. Garcia, R. Rubio, A. Bretones, and R. Martin, “Extension of the ADI-FDTD method to Debye media,” IEEE Trans. Antennas Propagat., vol. 51, no. 11, pp. 3183-3186, 2003.
H.-L. Chen, B. Chen, D.-G. Fang, and H. Liu, “Extension of the ADI-BOR-FDTD method to Debye dispersive media,” IEEE Microwave and Wireless Components Letters, vol. 19, no. 6, pp. 344-346, 2009.
T. Hirono, Wayne Lui, S. Seki, and Y. Yoshikuni, “A three-dimensional fourth-order finite-difference time-domain scheme using a symplectic integrator propagator,” IEEE Transactions on Microwave Theory and Techniques, vol. 49, no. 9, pp. 1640- 1648, 2001.
W. Sha, Z. Huang, M. Chen, and X. Wu, “Survey on symplectic finite-difference time-domain schemes for Maxwell's equations,” IEEE Trans. Antennas Propagat., vol. 56, no. 2, pp. 493-500, 2008.
X. Ren, Z. Huang, X. Wu, S. Lu, H. Wang, L. Wu, and S. Li, “High-order unified symplectic FDTD scheme for the metamaterials,” Computer Physics Communications, vol. 183, no. 6, pp. 1192-1200, 2012.
J. Fang, “Time domain finite difference computation for Maxwell’s equations,” Ph.D. dissertation, Univ. California, Berkeley, CA, 1989.
I. Jung, I. Oh, Y. Hong, and J. Yook, “Optimized higher order 3-D (2,4) FDTD scheme for isotropic dispersion in plasma,” in Asia-Pacific Microwave Conference Proceedings, Seoul, South Korea, pp. 815-817, 2013.
Q. Wu and A. Guellab, “Accuracy and stability analysis of a 3D high-order staggered FDTD for Maxwell's equations,” in Applied Computational Electromagnetics Society Symposium (ACES), 2017 International, pp. 1-2, 2017.
L. Trefethen, Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations. Chap. 4: Stability, and Convergence, Ithaca, N.Y.: Cornell University-Department of Computer Science and Center for Applied Mathematics, 1996.
O. Ramadan, “On the stability of the FDTD implementation of high order rational constitutive relations,” IEEE Microwave and Wireless Components Letters, vol. 27, no. 1, pp. 4-6, 2017.
X. Fei and T. Xiaohong, “Stability and numerical dispersion analysis of a fourth-order accurate FDTD method,” IEEE Trans. Antennas Propagat., vol. 54, no. 9, pp. 2525-2530, 2006.
K. Abdijalilov and J. Schneider, “Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: Lossy material and evanescent fields,” Antennas and Wireless Propagation Letters, vol. 5, no. 1, pp. 454-458, 2006.
C. A. Balanis, Antenna Theory Analysis and Design. 3rd ed., Chap 4: Linear Wire Antennas, WileyInterscience, 2005.
F. Costen, J. Berenger, and A. Brown, “Comparison of FDTD hard source with FDTD soft source and accuracy assessment in Debye media,” IEEE Trans. Antennas Propagat., vol. 57, no. 7, pp. 2014-2022, 2009.
