Daniel S. Katz*
Cray Research, Inc.
c/o Jet Propulsion Laboratory
MS 301-455, 4800 Oak Grove Drive
Pasadena, CA 91109-8099
Eric T. Thiele
McCormick School of Engineering
Evanston, IL 60208
Berenger has recently published a novel absorbing boundary condition (ABC) for FD-TD meshes in two dimensions, with substantially improved performance relative to any earlier technique (J. P. Berenger, Jour. Comp. Phys., in press). This method, which he calls the "perfectly matched layer for the absorption of electromagnetic waves," is based on a decomposition of electric or magnetic fields components in the absorbing boundary region with the possibility of assigning losses to the the individual split field components. The net effect of this is to create a non-physical absorbing medium adjacent to the outer FD-TD mesh boundary that has a wave impedance independent of the angle of incidence and frequency of outgoing scattered waves. Berenger reported effective reflection coefficients for his ABC 1/3000th that of the standard 2nd and 3rd order ABCs (i.e., Mur). Furthermore, he reported total grid noise energies reduced to 10-7th the level produced by conventional ABCs.
In this paper we report confirmation of these remarkable claims, and two extensions of the Berenger ABC. First, we reproduced his claimed reflection coefficients and total grid noise reductions for the two-dimensional TE and TM grid cases. Furthermore, we found that the Berenger ABC can be easily adapted to provide a reflection-less grid boundary when the interior is filled with a uniform dielectric with non-unity relative permittivity
In the major contribution of this paper, we have extended the Berenger ABC to three-dimensional Cartesian FD-TD meshes. We will show results for measurements of grid noise due to imperfect ABCs that are on the order of 1/100th that of the standard second-order Mur ABC. The implication of these findings is that the effective dynamic range of FD-TD modeling (as limited by imperfect ABCs) is increased by 40 dB by the implementation. This will allow modeling antennas and scattering objects have pattern dynamic ranges of 80dB or more.