F. Edelvik

Stable modeling of arbitrarily oriented thin slots in the FDTD method

A subcell model for thin wires in the finite-difference time-domain (FDTD) method using modified telegraphers equations has been developed by Holland et al. Edelvik has previously presented an extension of their algorithm, which allows for arbitrarily located and oriented wires with respect to the Cartesian grid. This is important to be able to accurately model wires that cannot be aligned to the Cartesian grid, e.g., tilted wires and circular loop wires. Recently, a dual set of equations has been proposed for modeling of thin slots. In this paper, we show that using a similar algorithm as for thin wires we can also handle slots of arbitrary location in Cartesian planes. Previous thin slot models have been susceptible for instabilities. We show that a symmetric coupling between field and slot yields a stable time-continuous field-slot system and that the fully discrete field-slot system is stable under a generalized Courant-Friedrich-Lewy (CFL) condition. The proposed method is demonstrated for scattering from a finite-length slot in an infinite conducting wall and a shielding enclosure including a slot. The results are in good agreement with published experimental data.

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.