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