Implementation of High-Order Impedance Boundary Conditions in Some Integral Equation Formulations

The scattering problem from an object coated with materials is solved in the frequency domain. The coating is modeled by an impedance boundary condition (IBC) implemented in an integral equation (IE) prescribed on its outer surface. The Leontovich IBC (IBC0) is local and constitutes a poor approximation for low index coatings. A possible remedy is to employ higher order IBCs. These, as well as the IBC0, are implemented in two IE formulations: 1) CFIE with the electric current as sole unknown and 2) EFIE+MFIE where the unknowns are both the electric and magnetic currents. The problems raised by the discretization of the surface div and surface curl operators involved in the IE and IBC formulations are solved by employing a simple and computationally cheap technique, the accuracy of which is numerically assessed. The performances of the various IBC and IE formulations are evaluated by calculating the radar cross section (RCS) of some axisymmetric objects.