Construction and analysis of approximate models for electromagnetic scattering from imperfectly conducting scatterers

TL;DR

This paper develops higher order approximate models called GIBCs for electromagnetic scattering from imperfect conductors, using asymptotic expansions based on skin depth, with explicit formulas and error estimates.

Contribution

It introduces a systematic construction of GIBCs for 3-D Maxwell problems, providing explicit formulas up to third order and rigorous error analysis.

Findings

Explicit third-order GIBC formulas derived

Error estimates related to skin depth established

Theoretical justification for asymptotic expansion at all orders

Abstract

This report is dedicated to the construction and analysis of so-called Generalized Impedance Boundary Conditions (GIBCs) used in electromagnetic scattering problems from imperfect conductors as higher order approximations of a perfect conductor condition. We consider here the 3-D case with Maxwell equations in a harmonic regime. The construction of GIBCs is based on a scaled asymptotic expansion with respect to the skin depth. The asymptotic expansion is theoretically justified at any order and we give explicit expressions till the third order. These expressions are used to derive the GIBCs. The associated boundary value problem is analyzed and error estimates are obtained in terms of the skin depth.