On the use of Fourier series/FFT's as global basis functions in the solution of boundary integral equations for EM scattering

Current methods for the solution of the surface integral equations of interest to practical electromagnetic scattering appear to have reached an impasse. Plagued by disputes concerning the suitability and performance of various competing choices for piecewise basis functions and facing horribly complicated piecewise quadratures for the construction of influence matrix elements, it has become quite commonplace for these methods to be matrix-build-time limited rather than matrix-solve-time limited. An extremely simple alternative to all this is described below and demonstrated, in an introductory sense, on some 2-D problems. In this procedure, the FFT method, the basis functions are all global Fourier series in a suitably chosen parameter, and one attempts to estimate the coefficients describing the unknown surface current directly from the integral equation. This format circumvents all of the shortcomings discussed above-there are no singular integrals to evaluate. Furthermore, since the FFT algorithm is used throughout, the computation is extremely efficient. The results shown below suggest that, so far, this approach is very effective.<
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