Evaluation of the discrete complex-image method for a NEC-like moment-method solution Page: 3 of 12
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EVALUATION OF THE DISCRETE COMPLEX-IMAGE METHOD
FOR A NEC-LIKE MOMENT-METHOD SOLUTION *
G. J. Burke
Lawrence Livermore National Laboratory
P.O. Box 5504, L-156, Livermore, CA 94550
The discrete image approximation for the field of a half-space is tested in the NEC antenna
modeling program as an alternative to the interpolation method presently used. The accuracy
and speed of the discrete image approximation are examined for varying number of images and
approximation contour, and the solution for current is obtained on a horizontal wire approaching
A common extension to frequency domain moment-method codes is to model structures in a
stratified medium or at least .near a homogeneous ground. The solution then requires the Green's
function for the stratified medium or half-space, which in its exact form involves an integral
over an infinite spectrum of waves [1, 2]. The moment-method solution generally requires many
evaluations of the Green's function for numerical integration over sources, so evaluation time and
accuracy become critical. A number of methods have been used in this evaluation, including
integration over the real radial wavenumber or on a contour deformed to the steepest descent
path . Linear filters have been very effective for lossy media . Lindell  has converted the
spectral integrals of Sommerfeld into integrals over an image distributed in complex space. While
this solution remains exact, it still requires numerical integration over the distributed images,
although the integrals may be more easily evaluated than the spectral form. The code NEC  uses
an interpolation method for a half-space . The Sommerfeld integrals are evaluated numerically
on contours deformed to accelerate convergence . The values are then transformed using the
approximate quasistatic or asymptotic behavior of the fields to remove rapid variations, and are
stored in tables from which the required values are obtained by interpolation. Alternatively,
a "model" containing functions from the asymptotic solution and variable parameters is fit to
the computed values in a technique known as model-based parameter estimation . These
interpolation methods are fast, accurate and reasonably simple when source and evaluation points
are in the same medium, but can get complicated for interactions across interfaces.
More recently a simple approximation of the Green's function for a stratified medium or
half-space has been developed in terms of a sum of discrete images in complex space . This
method has been applied to the solution of microstrip problems [11, 12] and to antennas over a
homogeneous ground  using the mixed-potential form of the integral equation. In this paper
results of using the discrete image method in a solution with continuous current expansion and
* Work performed under the auspices of the U. S. Department of Energy by the Lawrence Livermore
National Laboratory under Contract W-7405-Eng-48.
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Burke, G.J. Evaluation of the discrete complex-image method for a NEC-like moment-method solution, report, January 5, 1996; California. (digital.library.unt.edu/ark:/67531/metadc671246/m1/3/: accessed February 17, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.