The development of a numerical impedance boundary condition for lossy dielectric interfaces

In considering scattering from the lossy surfaces, it is common practice to model the surface as a perfect electric conductor (PEC). To include the effects of finite conductivity in the model, an analytical impedance boundary condition (IBCs) is often used. Although these IBC models are adequate for many numerical simulations, the range of their validity is somewhat unclear and an accurate quantification of the error introduced is difficult. In order to address some of these concerns, a novel numerical implementation of the exact dielectric integral equations has been developed for scattering from a two-dimensional, lossy dielectric interface. In the standard approach, a coupled pair of integral equations or a single equation is formed. The formulation presented begins with the coupled integral equations and also combines them to form a single equation for two-dimensional surfaces. Next, this single equation is rearranged to recreate the magnetic field integral equation (MFIE) for a two-dimensional PEC surface with a perturbative term related to the finite conductivity of the surface. The advantage of this perturbation approach is that for ocean and other high loss surfaces, the solution is expected to be rapidly convergent with respect to other approaches.