Volumetric testing for the nonconforming discretization of integral equations in scattering problems

Abstract

The traditional discretizations of the electric-field integral equation (EFIE) impose the continuity of the normal component current across the edges in the meshing. These edgeoriented schemes become awkward in the analysis of composite objects or of closed conductors meshed with nonconformal meshes. In this context, the nonconforming expansion of the current with facet-oriented schemes, like the monopolar-RWG set, with no imposed interelement continuity, leads to EFIEimplementations with enhanced versatility. However, the traditional Galerkin method-of-moment implementation gives rise to hypersingular Kernel contributions, which cannot be evaluated numerically. Recently, we have proposed a nonconforming monopolar-RWG discretization of the EFIE where the testing is carried out over volumetric elements attached to the surface triangulation inside the object under analysis. In this paper, we review the so-called volumetric monopolar-RWG discretization of the EFIE with testing over tetrahedral or wedge elements. These schemes show improved accuracy, when compared with the RWG-discretization, for a particular range of heights of the testing elements. As we show in this paper, this range becomes wider for the wedge testing choice than with the tetrahedral choice.