On the edge element boundary element method/finite element method coupling for time harmonic electromagnetic scattering problems

Abstract

Over recent decades coupled MoM/FEM formulation emerged as dominant method for solving EM scattering problems over inhomogeneous domains. Initial efforts on coupling of edge element BEM with edge element FEM have lost momentum and somehow disappeared from recent literature, possibly because of mathematical and other issues. This article, however, presents correct coupling of edge element BEM with edge element FEM. Such coupling is convenient because edge basis functions are used for modeling both the surface and the interior of the problem. We show that singularity extraction is simpler when compared with singularity extraction in MoM/FEM. Because BEM part of edge element BEM/FEM formulation uses simpler Green's function, the method is easier to implement than MoM/FEM which uses Dyadic Green's functions. The accuracy of the method is demonstrated by comparison with Mie series and with MoM/FEM and MoM/VSIE methods. Convergence of the method with respect to number of surface and interior edges was investigated by comparing 20 computational models with Mie series. Computational results suggest that edge‐element BEM/FEM performs well for scattering problems involving objects with sharp corners. Finally, the ability of the method to cope with relatively large number of elements was demonstrated on the example of human head illuminated by 3.5 GHz EM plane wave.

On some computational aspects for electromagnetic-thermal dosimetry of mm waves

“…The human head exposed to EM wave is treated as a classical scattering problem. The unbounded domain exterior to human head can be treated via the Stratton-Chu equation [12]:…”

“…The details on the coupling between interior and exterior region and numerical treatment of the above hybrid formulation can be found elsewhere, e.g. [9,12].…”

A Method for Determining the Envelope of Induced Electric Field on a Simple Human Head Model by Peaks Detection

“…In case of a time-harmonic field, the problem can be specified using the following integro-differential expressions. The exterior domain is treated by the Stratton-Chu integral equation facilitating the rephrasing of both electric and magnetic fields in terms of their tangential components [17]:…”

“…where R is the distance from the observation point to the source point, ⃗ r and ⃗ r ′ , respectively, and k is the wave number. The interior domain of the problem (human head) is governed by the following equation [17]:…”

“…The expressions (1) and ( 3) can be coupled and numerically solved using a hybrid BEM/FEM method. The interested reader could find details on the applied BEM/FEM procedure in [8], [17].…”