Time Domain Finite Element Modeling of Thin Sheets and Coatings using Shell Elements

F. Edelvik, E. Abenius. In EMB07, Lund, Sweden, pp. 35-41, October 2007.


Transient finite-element methods based on Whitney elements represent powerful techniques for solution of the Maxwell equations. These methods are normally used on unstructured, body conforming grids, and therefore do not suffer from the staircasing errors present in e.g. the finite-difference time-domain (FDTD) method. In principle, a tetrahedral grid could be used to resolve fine system details. However, in practice, the number of unknowns can be prohibitive and may lead to worse conditioning of the system. Thus the development of accurate models the characterice the physics of small features without the need for a highly resolved grid is essential. In recent publications accurate and stable subcell models for the FETD method have been developed for thin wires and thin slots. In this paper we focus on modeling of thin material sheets and coatings. Important applications include among others: complex antennas etched on thin dielectric substrates, structures coated with thin layers of radar absorbing material (RAM) and radomes used to enclose antennas. A drawback with previously published methods based on first-order, Leontovich, impedance boundary conditions (IBCs) is that only the tangential electric field component at the sheet is affected by these boundary conditions and the fact that the normal electric field component is discontinuous across a dielectric sheet is not taken into account. In this paper we follow a different approach where thin structures are modeled through the use of degenerated prism elements, so-called shell elements. The use of shell elements makes it possible to take the discontinuous normal electric field component into account by introducing additional degrees of freedom. The underlying assumptions are that for a dielectric sheet the thickness is small compared to the wavelength for all frequencies of interest and for conducting sheets that the thickness is small compared to the skin depth for all frequencies of interest. The details of the method and some validation cases will be included in the final paper. An extension of the method to thin sheets with frequency dispersive materials will be considered.


Authors and Affiliations

  • F. Edelvik, Fraunhofer-Chalmers Centre
  • E. Abenius, Efield AB

Photo credits: Nic McPhee