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Three-Dimensional Finite Element Analysis
Published in Özlem Özgün, Mustafa Kuzuoğlu, ®-based Finite Element Programming in Electromagnetic Modeling, 2018
The far-zone scattered field can be obtained by Huygens’ surface equivalence principle, as explained in Sec. 5.6.1. The equivalent surface electric and magnetic currents are determined by J=n^×H and M=E×n^, respectively. The far-zone scattered fields are calculated by using the same equations given in (5.111). The details of the calculation are given below. A Huygens’ surface is chosen outside the object and the surface integral is evaluated on each face of the element adjacent to this boundary. First, unit normal vector (n^), position vector of the observation point (r), and electric field intensity (which is total electric field computed by FEM) are expressed in terms of the Cartesian components as follows:
Fundamentals of Method of Moments for Artificial Materials
Published in Filippo Capolino, Theory and Phenomena of Metamaterials, 2017
Christophe Craeye, Xavier Radu, Filippo Capolino, Alex G. Schuchinsky
A contrast magnetic current MV = jω (μin(r) − μout)H(r) can be defined similarly, based on the variation of permeability μin(r) versus position. An example of metamaterial analysis based on the volume IE can be found in [8]. In Section 5.3, we discuss the MoM for the solution of surface IEs. However, before proceeding further we illustrate the equivalence principle for two important particular cases. In Figure 5.2 the surface equivalence principle is illustrated for the case of a scatterer made by a perfect electric conductor (PEC). In this case, only the equivalent current on the boundary S is necessary to restore the original field outside the scatterer, since the total tangential electric field vanishes because of the PEC boundary condition, which implies M=E×n^=0 = 0. This special case is particularly important in the RF/microwave range because metals are well approximated by PECs. In Figure 5.3 the surface equivalence principle is illustrated for the case of a scatterer made by a PEC surface with an aperture in it. The equivalent problem consists of two regions separated by a closed PEC surface. Radiation by the equivalent magnetic current M=E×n^, located just outside the scatterer at the location of the original aperture, restores the exterior field. Radiation by the equivalent magnetic current −M, located just inside the scatterer at the location of the original aperture, restores the interior field. The opposite signs of the exterior and interior magnetic currents establish the continuity of the tangential electric field across the aperture. The continuity of the tangential magnetic field across the aperture is enforced by the IE (Section 5.3). The latter version of the equivalence principle is also used to model apertures (and periodic sets of apertures) in PEC screens of infinite extent, shown in Figure 5.3c and d.
Low frequency scattering simulation of homogeneous objects in layered medium by Muller formed SIE
Published in Electromagnetics, 2023
As shown in Figure 1, a homogeneous dielectric object with the parameters is immersed in LM and is under the illumination of an electromagnetic field. According to the surface equivalence principle, an equivalent surface electric current and magnetic current on the surface will be generated. The scattered fields and by and can be represented by the electric field integral equation (EFIE) and magnetic field integral equation (MFIE) as (Chew 1995)