On stable subcell modeling in time-domain finite-element simulations

The ability to model features that are small relative to the cell size is often important in electromagnetic simulations. In principle, an unstructured grid could be used to resolve these small features. However, the increase in number of unknowns can be prohibitive. Thus, the development of accurate models that characterize the physics of the feature without the need for a highly resolved grid is essential. Practical systems possess narrow cracks and gaps that can be challenging to include in an analysis. Therefore, subcell modeling techniques have been proposed for thin slots. It has been shown that a unified approach for modeling thin wires and thin slots is possible. We show how to generalize the thin wire algorithm previously presented (Edelvik, F. et al., IEEE Trans. Antennas Propag., vol.51, no.8, p.1797-1805, 2003) to model arbitrary thin slots. Our interpolation technique used for arbitrarily located and oriented wires is successfully applied to thin slots. Allowing the slots to run arbitrarily in the grid and not aligned with the edges gives considerable modeling flexibility when including these subcellular structures in the simulations. A symmetric coupling between field and slot, and between field and wire, makes it possible to prove that the fully discrete field-wire-slot system is unconditionally stable.