Volumetric testing with wedges for a nonconforming discretization of the PMCHWT formulation

Abstract

The monopolar-Rao-Wilton-Glisson (RWG) discretization of the Poggio-Miller-Chan-Harrington-Wu-Tsai (PM-CHWT) integral equation imposes no continuity constraints in the current expansion across the edges arising from the discretization of the boundary surface. The numerical evaluation of the hypersingular kernel contributions can be carried out through the volumetric testing of the fields over a set of tetrahedral elements attached to the boundary surface of the target. This facet-based implementation becomes well-suited for the scattering analysis of composite objects or nonconformal meshes. Furthermore, improved accuracy has been observed in the analysis of moderately small sharp-edged dielectric objects and high contrasts with the proper choice of the height of the testing tetrahedral elements. In this paper, we introduce a novel monopolar-RWG discretization of the PMCHWT formulation where wedge testing elements are adopted. We show with radar cross section results that this scheme offers improved accuracy for a wider range of heights of the testing elements than the approach with tetrahedral testing.