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Article Dans Une Revue European Journal of Applied Mathematics Année : 2015

Scattering of a scalar time-harmonic wave by a penetrable obstacle with a thin layer

Résumé

This work looks at the asymptotic behaviour of the solution to the Helmholtz equation in a penetrable domain of $\mathbb{R}$ 3 with a thin layer of thickness δ which tends to 0. We use the method of multi-scale expansion to derive and justify an asymptotic expansion of the solution with respect to the thickness δ up to any order. We then provide approximate transmission conditions of order two defined on an interface located inside the thin layer, with accuracy up to O (δ 2 ), which allow one to take into account the influence of the thin layer.
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Dates et versions

hal-04518546 , version 1 (27-03-2024)

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K E Boutarene, P.-H. Cocquet. Scattering of a scalar time-harmonic wave by a penetrable obstacle with a thin layer. European Journal of Applied Mathematics, 2015, 27 (2), pp.264 - 310. ⟨10.1017/s095679251500056x⟩. ⟨hal-04518546⟩
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