Quasi-Analytical Wiener-Hopf Solutions of Electromagnetic Problems to Benchmark Full Numerical Computational Electromagnetics Programs

Abstract

Since a long time, exact and semi-analytical solutions of canonical electromagnetic scattering problems have received great interest from mathematical, physics and engineering communities. Solutions of new complex canonical problems are important by themselves but in this abstract we highlight the utility to benchmark full numerical codes like Finite Element Method (FEM), the Method of Moments (MoM) with surface/volume integral equation formulations, Finite Difference (FD) method… All full numerical methods suffer of loss of precision and ill-conditioning in particular circumstances. For example loss of precision is experienced when impenetrable/penetrable structures are sharp in term of wavelength: wedges, edges, knife, tips, cones‥. In this cases the loss of precision is commonly produced by wrong or unsuitable modelling in numerical methods. The presence of sharp structures requires the modelling of expansion functions that follows the true physics of the problems, i.e. singular basis functions with proper quadrature techniques [1]–[3]. To know the true local physics of problems, exact and semi-analytical solutions of novel complex canonical structures are required. Another example of loss of precision in full numerical codes is the case of thin layer/multilayer structures. The tiny thickness of penetrable materials eventually coating impenetrable surfaces creates loss of precision in numerical codes due to the discretization procedure (mesh generation and its quality), near-self interactions among structures in particular in integral formulations and the incorrect modelling of sharp singularity effects. For these reasons, the study of novel complex canonical problems with semi analytical techniques is of great impact.