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Scattering at Coated Dielectric Objects

Researcher(s): Prof. Dr. R. Hiptmair
  Bogdan Cranganu-Cretu. ABB Corporate Research, Baden-Dättwil
Funding: no external funding
Duration: 10/2003-10/2004

Description. We developed a new variational direct boundary integral equation approach for solving the scattering and transmission problem for dielectric objects partially coated with a PEC layer. The main idea is to use the electromagnetic Calderón projector along with transmission conditions for the electromagnetic fields. This leads to a symmetric variational formulation which lends itself to Galerkin discretization by means of divergence-conforming discrete surface currents. A wide array of numerical experiments confirms the efficacy of the new method.

Figure 1: Sketch of the geometry for the metallic container filled with sea water.


Figure: Container: modulus of inner tangential magnetic field (A/m). Wave number $ \kappa=4.5\mathrm{m}^{-1}$.

Figure: Container: modulus of outer tangential magnetic field (A/m). Wave number $ \kappa=4.5\mathrm{m}^{-1}$.

Figure: Container: modulus of transmitted electric field (A/m). Wave number $ \kappa=4.5\mathrm{m}^{-1}$.

The geometry considered in an numerical experiment [CCH04] was a metallic rectangular container filled with sea water. The upper part is partially covered with a metallic lid as can be seen in figure Fig. 1. The dielectric constant of the water was assumed to equal $ \epsilon_{s} = 80\epsilon_{0}$. This leads to a situation beyond the scope of the EFIE.

A convergence study on four meshes ranging from very coarse (471 unknowns) to fine (4858 unknowns) is reported in Fig. [*] ( $ \kappa=1\mathrm{m}^{-1}$). Obviously, away from any resonance frequencies, the solution on the coarse meshes is satisfactory already, whereas on a resonance frequency fine meshes yield significantly better results.

Plots of the electromagnetic field on the surface of the cube are presented in Figs. [*]-[*]. Field singularities at edges are conspicuous. A section of the transmitted field is shown in (Fig. [*] for a wave number $ \kappa=4.5\mathrm{m}^{-1}$.

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Prof. Ralf Hiptmair 2004-11-11