Face Centered Anisotropic Surface Impedance Boundary Conditions in FDTD

Thin sheet models are essential to allow shielding effectiveness of composite enclosures and vehicles to be modelled. Thin dispersive sheets are often modeled using surface impedance models in finite-difference time-domain (FDTD) codes in order to deal efficiently with the multi-scale nature of the overall structure. Such boundary conditions must be applied to collocated tangential electric and magnetic fields on either side of the surface; this is usually done on the edges of the FDTD mesh cells at the electric field sampling points. However, these edge based schemes are difficult to implement accurately on stair-cased surfaces. Here we present a novel face centered approach to the collocation of the fields for the application of the boundary condition. This approach naturally deals with the ambiguities in the surface normal that arise at the edges on stair-cased surfaces, allowing a simpler implementation. The accuracy of the new scheme is compared to edge based and conformal approaches using both planar sheet and spherical shell canonical test cases. Stair-casing effects are quantified and the new face-centered scheme is shown have up to 3 dB lower error than the edge based approach in the cases considered, without the complexity and computational cost of conformal techniques.