Tangential-normal line testing for a nonconforming discretization of the transversal-electric Electric-Field Integral Equation for 2D conductors

The Method-of-Moment (MoM) discretization of the Electric-Field Integral Equation (EFIE) for a transversal electric (TE) illuminating plane wave impinging on an infinitely long cylinder (2D-object) traditionally requires continuous piecewise linear basis functions. These basis functions are particularly convenient in the numerical implementation because they reduce the degree of the Kernel singularity. Recently, a nonconforming implementation of the TE-EFIE discretized with discontinuous piecewise linear basis functions has been successfully developed with the testing procedure done over small surface entities attached to the boundary of the object, inside the body under analysis. In this paper we present a novel nonconforming discretization of the TE-EFIE based on discontinuous piecewise linear basis functions with a testing procedure that relies only on line integrals. This allows for an easier and more efficient computation of the impedance matrix elements while preserving the improved far-field accuracy observed for sharp edged objects in the previous surface-tested TE-EFIE implementation.