High‐frequency asymptotic analysis of a dissipative transmission problem resulting in generalized impedance boundary conditions

Article type: Research Article

Authors: Antoine, X. | Barucq, H. | Vernhet, L.

Affiliations: Laboratoire de Mathématiques pour l'Industrie et la Physique, UMR 5640, Université P. Sabatier, Toulouse III, UFR MIG, 118, route de Narbonne, 31062 Toulouse cedex 4, France E‐mail: [email protected]‐tlse.fr | Laboratoire de Mathématiques Appliquées pour l'Industrie & CNRS ERS 2055, Université de Pau et des Pays de l'Adour, avenue de l'Université, 64000 Pau, France E‐mail: {helene.barucq,laurent.vernhet}@univ‐pau.fr

Abstract: The present work investigates boundary conditions that modelize the penetration of a time‐harmonic wave into a dissipative obstacle. The exact model is given through a transmission problem that couples the propagations into an absorbing domain and an exterior domain. The conditions arise from an asymptotic analysis of the interior solution whose propagation is studied by using pseudodifferential technics classically involved for the construction of radiation boundary conditions. Herein, first and second‐order conditions are analyzed and some numerical experiments illustrate their validity domain.

Keywords: acoustics, Helmholtz equation, dissipation, pseudodifferential operators, asymptotic expansion, approximate boundary condition

Journal: Asymptotic Analysis, vol. 26, no. 3-4, pp. 257-283, 2001