Tangential-Normal Surface Testing for the Nonconforming Discretization of the Electric-Field Integral Equation

Abstract

Abstract-Nonconforming implementations of the ElectricField Integral Equation (EFIE), based on the facet-oriented monopolar-RWG set, impose no continuity constraints in the expansion of the current between adjacent facets. These schemes become more versatile than the traditional edge-oriented schemes, based on the RWG set, because they simplify the management of junctions in composite objects and allow the analysis of nonconformal triangulations. Moreover, for closed moderately small conductors with edges and corners, they show improved accuracy with respect to the conventional RWGdiscretization. However, they lead to elaborate numerical schemes because the fields are tested inside the body, near the boundary surface, over volumetric subdomains attached to the surface meshing. In this paper, we present a new nonconforming discretization of the EFIE that results from testing with RWG functions over pairs of triangles such that one triangle matches one facet of the surface triangulation and the other one is oriented perpendicularly, inside the body. This "tangentialnormal" testing scheme, based on surface integrals, simplifies considerably the matrix generation when compared with the volumetrically tested approaches. Index Terms-Basis functions, electric field integral equation (EFIE), integral equations, moment method

Versatile and Accurate Schemes of Discretization in the Scattering Analysis of 2-D Composite Objects With Penetrable or Perfectly Conducting Regions

“…where the limiting values of the singular Kernel contributions in (25), at both sides of the boundary line, are cancelled out so that such integrals can be taken as Cauchy principal values. In this paper, we present two nonconforming MoM-discretizations of the TE-PMCHWT.…”

“…Content may change prior to final publication. MoM-implementations of the (TE-)EFIE, based on the discontinuous cell-based expansion of the current − monopolar-RWG (3D) or discontinuous piecewise linear (2D) − exhibit faster converging solutions than the conventional conforming schemes [22]- [25]. On the other hand, the point-based Locally Corrected Nyström (LCN) method, another nonconforming scheme with discontinuous current expansion [26]- [29], shows for low-order expansions less accurate solutions than continuous implementations for sharp-edged conductors [27][30].…”

Versatile and accurate schemes of discretization for the electromagnetic scattering analysis of arbitrarily shaped piecewise homogeneous objects

“…For this, we employ the EFIE-PMCHWT integral-equation formulation [21], which follows from the application of the EFIE or PMCHWT formulations over boundary surfaces, respectively, enclosing PEC regions or separating penetrable regions. The proposed schemes rely on the expansion of the currents with the facetbased, discontinuous-across-edges, monopolar-RWG set [26]- [29]. This choice gives rise to boundary integrals with hypersingular kernels, which we handle by testing the equations with wellsuited testing functions defined off the boundary tessellation, inside the region where, in light of the surface equivalence principle, the fields must be zero.…”

Nonconforming discretization of the PMCHWT integral equation applied to arbitrarily shaped dielectric objects

“…However, in the analysis of a composite object, made up of several regions with different electromagnetic properties, the definition of the RWG set around junctions, edges where several regions intersect, becomes a cumbersome task [5]. Recently, new nonconforming schemes, based on the facetoriented monopolar-RWG set, with no interelement continuity constraints, have been developed for the scattering analysis of conductors with the Electric Field Integral Equation (EFIE) [6][7] [8]. In these schemes, the hypersingular Kernel contributions are properly evaluated by testing the fields off the boundary surface, in the inner region of the body, through two different non-Galerkin testing strategies.…”

“…In these schemes, the hypersingular Kernel contributions are properly evaluated by testing the fields off the boundary surface, in the inner region of the body, through two different non-Galerkin testing strategies. The fields are either tested over small volumetric entities (tetrahedral elements or wedges) attached to the boundary elements [6] [7] or with RWG functions defined over pairs of connected triangles, one matching a surface facet and the other one oriented normally inside the conductor [8]. The latter testing scheme, "tangentialnormal", cancels out the hypersingular scalar potential contributions and leads to an easier matrix generation than the former "volumetric" approach.…”