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arXiv · 2309.07777

Scattered wavefield in the stochastic homogenization regime

Josselin Garnier·Laure Giovangigli·Quentin Goepfert·Pierre Millien
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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 $L^2$- and $H^1$- error estimates for the asymptotic first-order expansion. The theoretical results are supported by numerical experiments.

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Josselin Garnier, Laure Giovangigli, Quentin Goepfert, Pierre Millien. 2023-09-14. Scattered wavefield in the stochastic homogenization regime. https://arxiv.org/abs/2309.07777

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