Hierarchical Discretization of the Electric Field Integral Equation for the Scattering Analysis of Nonconformal Meshes

The scattering analysis with the Electric-Field Integral Equation of perfectly conducting objects by the Method of Moments has been traditionally carried out with Galerkin divergence-conforming schemes. These implementations are numerically convenient since the dominant Kernel contributions in near-field impedance computation become weakly singular. On the other hand, the divergence-conforming sets of basis functions enforce the continuity of the normal component of the expanded current or tested electric field through the edges arising from the discretization, which restricts the analysis to conformal meshes, where adjacent facets must have a single edge in common. In practice, this hampers the agile and versatile design of complex structures, which very often need to be modelled through the interconnection of independent meshes. In this paper, we introduce a new discretization of the Electric-Field Integral Equation that relies on the expansion of the current through a hierarchical rearrangement of the monopolar-RWG expansion of the current (discontinuous at edges) and the volumetric/surface testing of the tangential/normal electric-field components. We show with RCS-results the accuracy of the proposed scheme in the analysis of several perfectly conducting objects, either conformally or nonconformally meshed.