Numerical dispersion and numerical loss in explicit finite-difference time-domain methods in lossy media

The numerical dispersion relations of finite-difference time-domain (FDTD) methods have been analyzed extensively in lossless media. This paper investigates numerical dispersion and loss for Yee's FDTD in lossy media. It is shown that: the numerical velocity can be smaller or larger than the physical velocity; there is no "magic time step size" in lossy media; and the numerical loss is smallest at the Courant limit. It is shown that the numerical loss is always larger than its physical value, and so Yee's FDTD overestimates the absorption of electromagnetic energy in lossy media. The numerical velocity anisotropy can be positive or negative, but the numerical loss anisotropy is always positive. The anisotropies in the three-dimensional (3-D) case are usually larger than those in the 2-D case. Numerical experiments in 1-D are shown to agree with the theoretical prediction.

[1]  Philippe Ferrari,et al.  Comparison of FDTD and SPICE simulations for lossy and dispersive nonlinear transmission lines , 2000 .

[2]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[3]  José A. Pereda,et al.  FDTD modeling of wave propagation in dispersive media by using the Mobius transformation technique , 2002 .

[4]  FDTD Algorithm for Microstrip Antennas with Lossy Substrates Using Higher Order Schemes , 2004 .

[5]  M. Celuch-Marcysiak,et al.  Extended theory of FDTD S- and P-eigenmodes in lossy media and its application to the analysis of coupled problems , 2004, 2004 IEEE MTT-S International Microwave Symposium Digest (IEEE Cat. No.04CH37535).

[6]  Propiedades numéricas de distintas formulaciones para la incorporación de dieléctricos con pérdidas en simuladores FDTD , 2003 .

[7]  C. Balanis.  Advanced Engineering Electromagnetics , 1989 .

[8]  J. Strikwerda.  Finite Difference Schemes and Partial Differential Equations , 1989 .

[9]  José A. Pereda,et al.  Numerical dispersion and stability analysis of the FDTD technique in lossy dielectrics , 1998 .

[10]  Generalized analysis of stability and numerical dispersion in the discrete-convolution FDTD method , 2000 .

[11]  W. Thiel.  A surface impedance approach for modeling transmission line losses in FDTD , 2000 .

[12]  Theodoros D. Tsiboukis,et al.  Higher-order FDTD(2,4) scheme for accurate simulations in lossy dielectrics , 2003 .

[13]  A weighted-average scheme for accurate FDTD modeling of electromagnetic wave propagation in conductive media , 2004, IEEE Antennas and Wireless Propagation Letters.

[14]  J.E. Schutt-Aine,et al.  Analysis of lossy systems via 2D-FDTD and ESPRIT , 2001, IEEE Antennas and Propagation Society International Symposium. 2001 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.01CH37229).

[15]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[16]  R. J. Kruhlak,et al.  Dispersion of homogeneous and inhomogeneous waves in the Yee finite-difference time-domain grid , 2001 .