L'objectif de cette thèse est de proposer une nouvelle formulation variationnelle du problème de diffusion électromagnétique avec des conditions au bord 'impédance approximatives. On étudie un conducteur parfait recouvert d'une couche mince diélectrique. L'operator d'impedance est approximé par un rapport de polynômes d'opérateurs différentiels, de sorte que les conditions sur la bord sont présentées comme une équation des polynômes. Nous appelons cette condition d'ordre supérieur IBC (HOIBC). Nous proposons la formulation de ce problème, la discrétisation et les résultats numériques dans le cas bidimensionnel. Aussi, nous élaborons la formulation et différentes méthodes de discrétisation pour le cas tridimensionnel. / The main subject of this thesis is to propose a new variational formulation of electromagnetic scattering problem with approximate impedance boundary conditions. We consider a perfect conductor coated with a thin dielectric layer. The impedance operator is approximated as a ratio of polynomials of differential operators, so that the boundary conditions are presented as an equation of these polynomials. We call this condition as higher order IBC (HOIBC). We propose the formulation of the problem, the discretization and the numerical results in two dimensional case. Also we elaborate the formulation and some different methods of discretization for three dimensional case.

The main subject of this thesis is to propose a new variational formulation of electromagnetic scattering problem with approximate impedance boundary conditions. We consider a perfect conductor coated with a thin dielectric layer. The impedance operator is approximated as a ratio of polynomials of differential operators, so that the boundary conditions are presented as an equation of these polynomials. We call this condition as higher order IBC (HOIBC). We propose the formulation of the problem, the discretization and the numerical results in two dimensional case. Also we elaborate the formulation and some different methods of discretization for three dimensional case.