Numerical Modeling of Very Thin Dielectric Materials

Abstract

In this work, a Method of Moments (MoM) formulation is presented for the numerical solution of very thin dielectric materials in the frequency domain. The dielectric material is represented by a triangular mesh and a parameter controlling the thickness of the dielectric. The triangular mesh can represent bodies with arbitrary curvature and results in significantly fewer unknowns than volume formulations.

The dielectric material is first replaced with an equivalent set of currents. An integral equation is then developed to relate the currents in the dielectric material to an incident excitation wave. Currents flowing tangentially to the surface of the dielectric are represented by a set of RWG functions and half-RWG functions at the boundary edges in order to account for charges at the edge of the dielectric. Currents normal to the surface are modeled by pulse functions which also account for surface charges on the dielectric sheet. The MoM procedure is then applied resulting in a linear system which can be easily solved by matrix inversion. Finally, the dielectric is coupled with a perfect electrical conductor solution al- lowing us to solve systems involving both conducting and thin dielectric materials.

Furthermore, the similarity between the dielectric and conductor basis functions al- lows one to easily add support for conductors once the dielectric code has been im- plemented or vice versa.