New approximation method for high order impedance boundary condition with surface integral equations for the scattering problem

Abstract

In this paper, we propose a new method to approximate operators resulted from solving the scattering Problem in electromagnetism by dielectrically coated conducting bodies, using integral equations and high order impedance boundary condition. We introduce the variational Problem and we prove its well‐posedness. After discretization, we find that operators arising from the high‐order impedance boundary conditions are not well‐defined. We present the new theoretical approach and highlight its potential through numerical experiments.