Scattered wavefield in the stochastic homogenization regime

Josselin Garnier, Laure Giovangigli, Quentin Goepfert and 
Pierre Millien
septembre, 2023
Publication type:
Preprint
arXiv:
assets/images/icons/icon_arxiv.png 2309.07777
Keywords :
Helmholtz equation; Quantitative stochastic homogenization; Transmission problem; Boundary layer;
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 𝐿2- and 𝐻1- error estimates for the asymptotic first-order expansion. The theoretical results are supported by numerical experiments.
BibTeX:
@preprint{Gar-Gio-Goe-Mil-2023,
    title={Scattered wavefield in the stochastic homogenization regime },
    year={2023 },
    month={9},
    comment={{umatype:'preprint'}},
}