Work

On Asymptotic Behaviors of Acoustic Waves Due to High‐Contrast Material Inclusions

Year: 2025

Type: article

Abstract: ABSTRACT This paper investigates the asymptotic behaviors of time‐harmonic acoustic waves generated by an incident wave illuminating inhomogeneous medium inclusions with high‐contrast material parameters. We derive sharp asymptotic estimates and obtain several effective acoustic obstacle scattering models when the material parameters take extreme values. The results clarify the connection between inhomogeneous medium scattering and obstacle scattering for acoustic waves, providing a clear criterion for identifying the boundary conditions of acoustic obstacles in practice. The contributions of this paper are twofold. First, we provide a rigorous mathematical characterization of the classical sound‐hard and sound‐soft obstacle scattering models. We demonstrate that a sound‐hard obstacle can be viewed as an inhomogeneous medium inclusion with infinite mass density, while a sound‐soft obstacle corresponds to an inclusion with zero mass density and zero bulk modulus. Second, we introduce two novel acoustic obstacle scattering models when the mass density of the inclusion degenerates to zero. These new models offer a fresh perspective on considering inhomogeneous medium inclusions with high‐contrast material parameters.

Source: Studies in Applied Mathematics

DOI: 10.1111/sapm.70048

Authors: Yueguang Hu, Hongyu Liu

Institution: City University of Hong Kong

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,550

Funders: City University of Hong Kong, Agence Nationale de la Recherche, National Natural Science Foundation of China