Hierarchical Grid-Robust Discretization of the Electric-Field Integral Equation by the Method of Moments

Traditionally, the scattering analysis with the Electric-Field Integral Equation of perfectly conducting objects has been carried out through divergence-conforming schemes of discretization, which are numerically convenient because the dominant Kernel contributions are weakly singular. Since the divergence-conforming sets enforce by definition the continuity of the normal component of the expanded magnitudes through the edges arising from the discretization, the analysis can only be applied to objects conformally meshed, with adjacent facets sharing a single edge. In practice, this hampers the flexible analysis of complex structures, which very often need to be modelled through the interconnection of independent meshes. In this paper, we introduce two novel schemes of discretization of the Electric-Field Integral Equation that are based on the expansion of the current through a hierarchical rearrangement of the monopolar-RWG expansion of the current (fully discontinuous at edges). Both schemes manage the zeroth-order scheme of testing in the same manner. The first-order testing scheme, though, is implemented differently in both cases, either through volumetric or through surface testing integrals. We show with RCS-results the accuracy of the proposed schemes in the analysis of a sharp-edged perfectly conducting object.