Publications

Titre : Scattered wavefield in the stochastic homogenization regime
Année : 2023
Type : prépublication
Auteurs : J. Garnier, L. Giovangigli, Q. Goepfert, P. Millien
Résumé : In the context of providing a mathematical framework for the propagation of ultrasound waves in a random multiscale medium, we consider the scattering of classical waves (modeled by a divergence form scalar Helmholtz equation) by a bounded object with a random composite micro-structure embedded in an unbounded homogeneous background medium. Using quantitative stochastic homogenization techniques, we provide asymptotic expansions of the scattered field in the background medium with respect to a scaling parameter describing the spatial random oscillations of the micro-structure. Introducing a boundary layer corrector to compensate the breakdown of stationarity assumptions at the boundary of the scattering medium, we prove quantitative 𝐿2- and 𝐻1- error estimates for the asymptotic first-order expansion. The theoretical results are supported by numerical experiments.
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