Abstract-We present new implementations in Method of Moments of two types of second kind integral equations: (i) the recently proposed Electric-Magnetic Field Integral Equation (EMFIE), for perfectly conducting objects, and (ii) the Müller formulation, for homogeneous or piecewise homogeneous dielectric objects. We adopt the Taylororthogonal basis functions, a recently presented set of facet-oriented basis functions, which, as we show in this paper, arise from the Taylor's expansion of the current at the centroid of the discretization triangles. We show that the Taylor-orthogonal discretization of the EMFIE mitigates the discrepancy in the computed Radar Cross Section observed in conventional divergence-conforming implementations for moderately small, perfectly conducting, sharp-edged objects. Furthermore, we show that the Taylor-discretization of the Müller-formulation represents a valid option for the analysis of sharpedged homogenous dielectrics, especially with low dielectric contrasts, when compared with other RWG-discretized implementations for dielectrics. Since the divergence-Taylor Orthogonal basis functions are facet-oriented, they appear better suited than other, edge-oriented, discretization schemes for the analysis of piecewise homogenous objects since they simplify notably the discretization at the junctions arising from the intersection of several dielectric regions.

The discretization of the Electric-Field Integral Equation (EFIE) by the Method of Moments (MoM) for a transversal electric (TE) illuminating wave impinging on an infinitely long cylinder (2D-object) is traditionally carried out with continuous piecewise linear basis functions. In this paper, we present a novel discretization of the TE-EFIE formulation for the scattering analysis of homogeneous, perfectly conducting 2D-objects based on the expansion of the currents around the line-boundary through discontinuous piecewise linear or piecewise constant basis functions. We show for several infinitely long cylinders, with smooth or sharp-edged sections, the good accuracy of the proposed approach in the computation of far-field and near-field quantities, such as RCS and currents, with respect to the observed accuracy in conventional continuous piecewise linear discretizations.Peer ReviewedPostprint (published version