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

Abstract

The discretization by the method of moments (MoM) of integral equations in the electromagnetic scattering analysis most often relies on divergence-conforming basis functions, such as the Rao-Wilton-Glisson (RWG) set, which preserve the normal continuity of the expanded currents across the edges arising from the discretization of the target boundary. Although for such schemes the boundary integrals become free from hypersingular kernel-contributions, which is numerically advantageous, their practical implementation in real-life scenarios becomes particularly cumbersome. Indeed, the application of the normal continuity condition on composite objects becomes elaborate and convoluted at junction-edges, where several regions intersect. Also, such edge-based schemes cannot even be applied to nonconformal meshes, where adjacent facets may not share single matching edges. In this paper, we present nonconforming schemes of discretization for the scattering analysis of complex objects based on the expansion of the boundary unknowns, electric or magnetic currents, with the facet-based monopolar-RWG set. We show with examples how these schemes exhibit great flexibility when handling composite piecewise homogeneous objects with junctions or targets modelled with nonconformal meshes. Furthermore, these schemes offer improved near-and far-field accuracy in the scattering analysis of electrically small single sharp-edged dielectric targets with moderate or high dielectric contrasts.

Enhanced discretization of surface integral equations for resonant scattering analysis of sharp-edged plasmonic nanoparticles

“…3). In this work we define their geometry conformal to the boundary [40] taking into account the angles formed by the corresponding field triangle originating from the surface tessellation and the three neighboring triangles. The accuracy of this implementation can be fine-tuned by adjusting the height of the testing tetrahedral elements (H p ) which in turn is defined with the same value in both regions as a fraction of the length of the pth edge, h p , shared by the corresponding field triangles where the volumetric elements are constructed.…”

“…The results of the previous section indicate that faster convergence in the far-field region can be obtained with the scattering spectra of a plasmonic cube with edge length a = 50 nm. For this purpose, we define the root-mean-square (rms) near-field relative error e near as follows [40]:…”

“…These basis functions are identified with facets originating from the surface tessellation and the corresponding discretization scheme is nonconforming to the natural divergence function spaces. Despite that, it has been shown by several examples that the monopolar-RWG discretization of PMCHWT equations produces more accurate results in the near field and far field than the standard RWG approach for the cases of dielectric objects that exhibit singular or near-singular field distribution near sharp edges [40]. Unfortunately, the improved performance of the monopolar-RWG PMCHWT approach was observed for a restricted range of heights of the tetrahedral-testing elements [40,41].…”

“…Despite that, it has been shown by several examples that the monopolar-RWG discretization of PMCHWT equations produces more accurate results in the near field and far field than the standard RWG approach for the cases of dielectric objects that exhibit singular or near-singular field distribution near sharp edges [40]. Unfortunately, the improved performance of the monopolar-RWG PMCHWT approach was observed for a restricted range of heights of the tetrahedral-testing elements [40,41]. A remedy to this problem was given in [41] where a hierarchical decomposition of the monopolar-RWG space is proposed.…”

A Multitrace Surface Integral Equation Method for PEC/Dielectric Composite Objects

“…Upon discretization, multi-trace formulations result in a larger matrix system but the easier meshing process and the improved matrix conditioning are often worth the increase in the matrix dimension. Note that the junction basis functions can also be avoided without requiring two sets of unknowns on the same surface through the use of a monopolar RWG based discretization [19]. DDM utilizes CFIE or JMCFIE as the governing equation to ensure a well-conditioned matrix system [12]- [18].…”