Couplage éléments finis-potentiels retardés pour la diffraction électromagnétique par un obstacle hétérogène

Abstract

On s'intéresse au calcul du champélectromagnétique diffracté par un obstacle conducteur recouvert d'un matériau hétérogène. Onétudie une méthode numérique consistantà coupler une approximation paŕ eléments finis de volumes avec des potentiels retardés de surface. Plusieurs formulations variationnelles espace-temps sont présentées. Onétablit des résultats de stabilité et de convergence pour la méthode proposée.

BEM‐FEM coupling for the 1D Klein–Gordon equation

“…The basic idea underlying the proposed numerical scheme is to preserve the symmetry properties and the energy estimates valid for the continuous weak formulation. Its essential elements are: (1) finite elements for space discretization and an implicit Newmark finite differences scheme for time discretization in the FEM interval 1 ; (2) collocation technique for the first integral equation in (5) and Galerkin method for the second one (which in this case plays the role of the hyper-singular equation).…”

Numerical solution of exterior Maxwell problems by Galerkin BEM and Runge–Kutta convolution quadrature

“…Important discretization techniques include Galerkin methods based on space-time variational formulations (cf. [3,30,36,2,1,16,33]) and methods based on bandlimited interpolation and extrapolation (cf. [41,39,40,42]).…”

Theoretical aspects of the application of convolution quadrature to scattering of acoustic waves

“…The papers [2,3] study the numerical approximation of the single-and double-layer retarded acoustic potentials in three dimensions. Extensions of these results are many (see [1,4,16] and the references in the review [15]), all of them dealing with Galerkin methods. For the collocation method applied to the single-layer retarded potential, see [14].…”