Scattering by a highly oscillating surface

Abstract

International audienc

Improved impedance conditions for a thin layer problem in a nonsmooth domain

“…The subject still generates active research activities. Let us mention Abdelkader and Moussa, Bellieud et al, and Bonnet et al for mechanical applications; Perrussel and Poignard, Bendali and Poirier, and Schmidt and Chernov for electromagnetic problems; Zhao and Yao for the Stokes system; Li et al for the heat equation; and Cai and Xu and Diaz and Péron for general purposes. On the other hand, the case of a random thickness has been investigated; see Basson and Gérard‐Varet in the context of rough surfaces, and Dambrine et al for a practical application of approximate boundary conditions to compute moments of solutions of boundary value problems inside random domains.…”

“…21 The subject still generates active research activities. Let us mention Abdelkader and Moussa, 22 Bellieud et al, 23 and Bonnet et al 24 for mechanical applications; Perrussel and Poignard, 6 Bendali and Poirier, 25 32 for a practical application of approximate boundary conditions to compute moments of solutions of boundary value problems inside random domains. Let us mention the works [33][34][35] on polarization tensor for thin inclusions of rough layers.…”

Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers

“…The subject still generates active research activities. Let us mention [1,10,15] for mechanical applications, [12,48,54] for electromagnetic problems, [59] for the Stokes system, [46] for the heat equation, [17,29] for general purposes. On the other hand, the case of a random thickness has been investigated, see [9] in the context of rough surfaces, and [23] for a practical application of approximate boundary conditions to compute moments of solutions of boundary value problems inside random domains.…”