Spectral filtering of the spatial green’s function

In the method-of-moments (MoM), applied to the electric field integral equation (EFIE), the solution (the unknown current) is approximated by a linear combination of a finite number of basis functions. The basic question addressed in this work is whether the use of the exact Green\´s function is the optimal choice once the (finite-dimensional) space of the approximate solution has been chosen. We approach to the above question introducing a new representation of the spatial Green\´s function obtained by an appropriate spectral filtering with a mesh-dependent spectral content. The first direct impact of this filtering is in the disappearance of the Green\´s function singularity; as a consequence, the spatial integration is easier, avoiding the extraction of the singular term in the integration process. In this paper, we consider both scattering and antenna problems in free space, proposing a "band limited" Green\´s function expressed in closed form in the spatial domain and obtained through an appropriate windowing in the spectral domain.