# Computational high frequency scattering from high contrast heterogeneous media

## TL;DR

This paper develops a multiscale computational method for simulating high-frequency acoustic wave scattering in strongly heterogeneous media with high contrast, capturing complex physical phenomena efficiently.

## Contribution

It introduces a novel multiscale approach with rigorous error analysis for high contrast, high frequency wave propagation in non-periodic heterogeneous structures.

## Key findings

- Method accurately captures wave scattering in high contrast media.
- Numerical experiments confirm theoretical error estimates.
- Approach effectively models physical phenomena in complex materials.

## Abstract

This article considers the computational (acoustic) wave propagation in strongly heterogeneous structures beyond the assumption of periodicity. A high contrast between the constituents of microstructured multiphase materials can lead to unusual wave scattering and absorption, which are interesting and relevant from a physical viewpoint, for instance, in the case of crystals with defects. We present a computational multiscale method in the spirit of the Localized Orthogonal Decomposition and provide its rigorous a priori error analysis for two-phase diffusion coefficients that vary between $1$ and very small values. Special attention is paid to the extreme regimes of high frequency, high contrast, and their previously unexplored coexistence. A series of numerical experiments confirms the theoretical results and demonstrates the ability of the multiscale approach to efficiently capture relevant physical phenomena.