Higher order generalized impedance boundary conditions in electromagnetic scattering problems

Abstract

RésuméNous effectuons une revue succincte de l'obtention et l'utilisation des conditions d'impédances généralisées (GIBC) dans le cas de revêtements diélectriques minces et dans le cas d'objets fortement conducteurs. Nous nous plaçons dans le cadre des probèmes de diffraction d'ondesélectromagnétiques en régime harmonique. Nous testons numériquement la validité et la précision de ces conditions aux limites pour le cas de forte conductivité. En présence de géométries comportant des coins, nous proposons un traitement numérique astucieux afin de garder la même précision que dans le cas de géométries régulières. AbstractWe briefly review the use and the derivation of Generalized Impedance Boundary Conditions (GIBC) in the case of thin dielectric coatings and in the case of strongly absorbing media, within the context of electromagnetic scattering problem at a fixed frequency. We then numerically test the validity and accuracy of these boundary conditions in the case of high absorption. A numerical treatment of the corner singularity is proposed to recover the accuracy of the GIBC for singular geometries.

Generalized Impedance Boundary Conditions for Scattering Problems From Strongly Absorbing Obstacles: The Case of Maxwell's Equations

“…The numerical pertinence of obtained conditions have already been demonstrated in Ref. 6 where, in particular, the interest of using a third-order condition rather than a first or a second order condition is clearly shown.…”

High order transmission conditions for thin conductive sheets in magneto-quasistatics

“…Impedance boundary conditions (IBC), have been originally proposed for solid conductors by Shchukin [27] and Leontovich [17], for which recently IBCs of higher orders [1,10,12,26] as for perfect conductors with thin coatings [2,3,8] located at the boundary of the physical domain have been derived.…”

Generalized impedance boundary conditions for thin dielectric coatings with variable thickness

“…It is well known that a possible approach to overcome the numerical difficulties caused by the small thickness of the coating is the use of so-called Generalized Impedance Boundary Conditions (gibc) [5,2,1]. These conditions lead to approximate models that are close to the original one up to an O(δ k+1 ) error, where k denotes the order of the gibc.…”