Boundary element method with high order impedance boundary condition for Maxwell’s equations

Abstract

A boundary-element method is introduced for solving electromagnetic scattering problems for coated objects. We develop a new approximate impedance boundary condition with Hodge operator and propose a variationnal formulation for the physical problem. The existence and uniqueness of the solution are studied and we propose a discretization of the unknowns which are magnetic and electric currents with Rao-Wilton-Glisson basis functions to lead to the correct field continuity properties at the interface of different media. And the unknowns are the fluxes of the magnetic and electric currents across the edges of the mesh. Numerical results from the formulation is presented and measurements are compared in order to obtain test cases for the development and validation of numerical method. In the first time, we compare standard impedance boundary condition and high order impedance boundary condition on bodies of revolution with simple topology and we show the increased accuracy of the high order impedance boundary condition solution relative to the standard impedance boundary condition solution. Finally, a benchmark test is treated to show the interest of our method.