Abstract
Electromagnetic scattering for various geometrical constructs is often modeled with the aid of specialized electromagnetic simulation software. Currently, the Method of Moments is one of the most used methods for analysis of scattering. However, this method has a more computationally efficient alternative known as the Spectral Projection Model (SPM). The SPM takes the kernel for the Electric Field Integral Equation and decomposes it into a projection of the spectral signature of a source point onto an observation point. This is possible using Graf’s Addition Theorem (GAT) for the Bessel and Hankel functions. Showing that GAT can be represented as a Hadamard product in the Fourier domain requires the computation of the inverse of the Circular/Hankel Hadamard Product for elliptical cross sections. In MATLAB, an algorithmic approach is employed to compute the inverse of each submatrix and construct the inverse based on these submatrices. This approach yields an inversion time complexity of O(N2.75) as an alternative to the O(N3) time complexity of a standard matrix inversion.