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

Abstract

Abstract-The Method-of-Moment (MoM) discretization of boundary integral equations in the scattering analysis of closed infinitely long (2D) objects, perfectly conducting or penetrable, is traditionally carried out with continuous piecewise linear basis functions, which embrace pairs of adjacent segments. This is numerically advantageous because the discretization of the transversal component of the scattered fields, electric (TE) or magnetic (TM), becomes free from hypersingular Kernel contributions. In the analysis of composite objects, though, the imposition of the continuity requirement around junction nodes, where the boundaries of several regions intersect, becomes especially awkward. In this paper, we present, for the scattering analysis of composite objects, a new combined discretization of the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) integral equation, for homogeneous dielectric regions, and the Electric-Field Integral Equation (EFIE), for perfectly conducting regions, such that the basis functions are defined strictly on each segment, with no continuity constraint between adjacent segments. We show the improved observed accuracy with the proposed TE-PMCHWT implementation on several dielectric objects with sharp edges and corners and moderate or high contrasts. Furthermore, we illustrate the versatility of these schemes in the analysis of 2D composite piecewise homogeneous objects without sacrificing accuracy with respect to the conventional implementations.

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

“…In the scattering analysis of dielectric targets with smooth boundaries and/or low relative permittivities, where singular field behavior does not occur [41], our schemes offer for a given meshing similar accuracy as the conventional RWG approaches but doubling the number of unknowns. Analogous observations have been reported in the scattering analysis of conductors [27] or 2D dielectrics [32] with the nonconforming discretization of, respectively, the EFIE and the TE-PMCHWT formulations.…”

“…Also, the proposed implementations can handle nonconformal meshes when applied to piecewise (or fully) homogeneous arbitrarily shaped objects. This represents significant progress with respect to previous schemes, mainly addressing nonconformal meshes of homogeneous 3D targets, PEC [27]- [30] or dielectric [33], [34], or 2D composite objects [32]. Our schemes become also well suited for the enhancement of integralequation domain decomposition methods [34]- [36], since the transmission conditions between contiguous subdomains may be satisfied through the off-boundary testing and the discontinuous monopolar-RWG expansion.…”

“…The volumetrically tested monopolar-RWG discretization of the PMCHWT leads to the following matrix system [32]…”

“…3) . The monopolar-RWG discretization of the PMCHWT formulation with tangential-normal testing gives rise to the following matrix system [32]       , (20) where the testing of the gradients of the scalar potentials can be simplified through , S (see Fig. 3).…”

“…These implementations are nonconforming since the finite-dimensional spaces spanned by the monopolar-RWG functions belong to the space of square-integrable functions   2 L  [30]. Interestingly, they exhibit similar or better accuracy than the conventional RWG-schemes in the scattering analysis of targets with sharp edges and corners, PEC [27]- [29], [31] or 2D TE-dielectric [32], especially if moderately small. Note that for a given discretization the monopolar-RWG space includes the space spanned by the RWG basis functions [27].…”