A Comparison of Two Conformal Methods for FDTD Modeling

Two conformal Finite-Di erence Time-Domain (FDTD) methods are considered, which eliminate the e ects of the stair-step approximation inherent at low points per wavelength (PPW). The rst, proposed by Jurgens et al. [IEEE Trans. Antennas Propagat., 40, 357{366, 1992], uses the contour path method. The second, proposed by Yee et al. [IEEE Trans. Antennas Propagat., 40, 1068{1075, 1992], uses overlapping grids. Both TE and TM electromagnetic scattering from a two-dimensional (2-D), perfectlyconducting circular cylinder are used to test the accuracy of modeling curved surfaces. Radar cross section results are presented for a circular cylinder with a radius of half a wavelength. Also, TE and TM electromagnetic scattering from a 2-D, perfectlyconducting rotated square cylinder are used to test the accuracy of modeling corners and edges. Radar cross section results are presented for a rotated square cylinder with the length of one side equal to a wavelength. It is shown that the conformal method proposed by Yee et al. provides signi cant improvement in accuracy over the original FDTD algorithm at low PPW for all geometries studied in this paper. Implementation of this method was not di cult for the geometries studied in this paper, but implementation becomes more di cult as geometries become more complex. The conformal method proposed by Jurgens et al. provides signi cant improvement in accuracy over the original FDTD algorithm at low PPW for most of the geometries studied in this paper. However, improvement did not occur for the TM case when the positioning of the rectangular cylinder was such that its corners could not be modeled accurately. Implementation of this method was not di cult and should not increase as the geometries become more complex. In general, the results for the conformal method proposed by Yee et al. are more accurate than those for the conformal method proposed by Jurgens et al. 1