Asymptotic modelling of an acoustic scattering problem involving very small obstacles: mathematical justification

Hélène Barucq 1 Vanessa Mattesi 1, 2 Sébastien Tordeux 1
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : Within the context of an acoustic scattering problem involving small heterogeneities, ones can use the matched asymptotic expansion method to build an approximate model. The key step of this method is the matching procedure between the near-field expansion and the far-field one. We control this step by estimating the difference between these two expansions and a so-called matching function in the intermediate zone. These estimates are based on the valuation of the rest of the radial expansion of the regular solution to wave equation which is, up to our knowledge, not given in the literature. We thus provide a proof of convergence which uses Mellin transform and the fundamental theorem on singularities for the wave equation.
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Hélène Barucq, Vanessa Mattesi, Sébastien Tordeux. Asymptotic modelling of an acoustic scattering problem involving very small obstacles: mathematical justification. [Research Report] RR-8829, INRIA Bordeaux. 2015. ⟨hal-01250654⟩

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