Scattered wavefield in the stochastic homogenization regime
Abstract
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 - and - error estimates for the asymptotic first-order expansion. The theoretical results are supported by numerical experiments.
Cite
@article{arxiv.2309.07777,
title = {Scattered wavefield in the stochastic homogenization regime},
author = {Josselin Garnier and Laure Giovangigli and Quentin Goepfert and Pierre Millien},
journal= {arXiv preprint arXiv:2309.07777},
year = {2023}
}