IntroductionThe Numerical Electromagnetics Code, NEC as it is commonly known, continues to be one of the more widely used antenna modeling codes in existence. With several versions in use that reflect different levels of capability and availability, there are now 450 copies of NEC4 and 250 copies of NEC3 that have been distributed by Lawrence Livermore National Laboratory to a limited class of qualified recipients, and several hundred copies of NEC2 that had a recorded distribution by LLNL. These numbers do not account for numerous copies (perhaps 1000s) that were acquired through other means capitalizing on the open source code, the absence of distribution controls prior to NEC3 and the availability of versions on the Internet. In this paper we briefly review the history of the code that is concisely displayed in Figure 1. We will show how it capitalized on the research of prominent contributors in the early days of computational electromagnetics, how a combination of events led to the tri-service-supported code development program that ultimately led to NEC and how it evolved to the present day product. The authors apologize that space limitations do not allow us to provide a list of references or to acknowledge the numerous contributors to the code both of which can be found in the code documents.

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0 , the percentage difference between the SEFS approach and mixed-potential approach is less than 3%. The percentage difference (in complex value sense) tends to get smaller as gets larger. The oscillation in the mixed-potential method results is attributed to (a) higher numerical requirements for smooth G V () in the near field, and (b) in (22), for rooftop basis function, Ѩb (i) ( xЈ, yЈ)/Ѩ xЈ is actually a doublet. This is equivalent to taking a finite difference (or derivative) so that G V has to be calculated with fine spacing and the curve has to be smooth. For Figure 6, the physical parameters and the numerical parameters are identical, as before. For impedance matrix elements, each patch has dimensions of ⌬x by ⌬y where ⌬x ϭ ⌬y ϭ 0.000915 m. In (21), Z xx ji of the SEFS formulation can be calculated easily by quadrature with a tabulated value of W () and W () for G xx (). In (22), G A () and G V () are first tabulated as function of and then applied in the calculation of Z xx ji . CONCLUSIONIn this Letter the surface electric field and impedance matrix elements are calculated with the use of (a) an electric field spatial domain Green's function without using potentials or the SEFS method, and (b) the electric field spatial domain Green's function based on mixed-potential (MP) formulation, respectively. In the first approach, convergence of the Sommerfeld integral is facilitated by the half-space extraction technique with exponential decay of the Sommerfeld integrand and two-orders-of-magnitude reduction on the Sommerfeld integration domain. Because potentials are not used in this formulation, it is not necessary to take derivatives in this approach. In the second approach, the integrand of the Sommerfeld integral decays algebraically (inverse power law dependence). It is also necessary to take the first and second derivative of G V () in the surface electric field calculation because potentials are used here. For an illustrated distance between 0.1 0 and 10 0 , the numerical results of both surface electric field and impedance matrix elements of the first approach maintain good accuracy. On the other hand, numerical oscillation is observed from the second approach in near field due to the need of taking the derivative of G V (). This implies that the second approach is more sensitive to the numerical noise, and more numerical effort (greater kЈ max and more sample points on SIP) is needed for better accuracy.