High-order impedance boundary conditions for multilayer coated 3-D objects

The scattering problem by a multilayer coated three-dimensional (3-D) object where the coating is modeled by an impedance boundary condition (IBC) is considered. First, the exact boundary condition is obtained for an infinite planar coating with an arbitrary number of layers. Then, various approximations for the pseudodifferential operators involved in this exact condition are proposed. In the expressions of the resulting IBCs, all tangential derivatives of the fields of order higher than two are suppressed. These IBCs are compared, in terms of numerical efficiency, by computing either the reflection coefficients on an infinite planar metal-backed coating or the radar cross section (RCS) of a perfectly conducting coated sphere using the tangent plane approximation. In both cases, it is found that the highest order IBC models the coating with a good accuracy. Finally, some guidance is given on how this IBC may be numerically implemented in an integral equation or a finite-element formulation for an arbitrarily shaped object