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The details of a Galerkin discretization scheme for a modified form of the electric field integral equation are outlined for smooth, three-dimensional, perfectly conducting scatterers. Limitations of the divergence conforming finite-element bases in preserving the self-stabilizing properties of the electric field integral equation operator are indicated. A numerically efficient alternative is outlined which relies on an operator-based Helmholtz decomposition. The condition number of the resulting matrix equation is demonstrated to be frequency independent for scattering from a perfectly conducting sphere at various frequencies. Index Terms--Electric field integral equation (EFIE), preconditioner.

Modeling wire structures with a high degree of curvature generally requires a large number of piecewise linear segments to accurately represent rapid geometrical variations. In order to reduce the number of segments required to model curved wire structures, a method of moments formulation using curved wire segments is presented. Specifically, piecewise quadratic wire segments are used to discretize the wire geometry. This algorithm is used to analyze a small wire loop antenna and a multiple-arm Archimedian spiral antenna. For each example, a comparison is made between results obtained using this quadratic segment algorithm and a linear segment algorithm. These examples demonstrate that the memory required is significantly reduced and a reduction in the solution time is achieved when quadratic segments are used.

A mathematical analysis of the current in Archimedian spiral antennas led to a general algorithm based on the moment method solution of a mixed voltage electric field integral equation. Taking into account radiation and scattering problems, the formulation made use of impedance loading along the arms for the model, a four-arm Archimedian spiral. Results obtained with and without impedance loading demonstrated its effect on current distribution and far-field patterns. Matrix memory storage was also lessened for structures with discrete rotational summetry.