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

Houssem Haddar (1) , Patrick Joly (1) , Hoai Minh Nguyen (1)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

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.

Keywords: GIBC; effective boundary conditions; highly conducting scatterers; electromagnetic scattering; Maxwell's equations; boundary layers; scaled asymptotic expansions; approximate models

Domains: Analysis of PDEs [math.AP]

Houssem Haddar, Patrick Joly, Hoai Minh Nguyen. Construction and analysis of approximate models for electromagnetic scattering from imperfectly conducting scatterers. [Research Report] RR-6302, 2007, pp.62. ⟨inria-00174345v2⟩