An Integral Equation Method for the Scattering by Core-Shell Structures in a Layered Medium

Abstract

The core-shell structure design is an important subject in science and engineering, which also plays a key role in wave scattering and target reconstructions. This work aims to develop a novel boundary integral equation method for solving the acoustic scattering from a 3D core-shell structure in a two-layered lossy medium. The boundary integral equation contains continuous and weakly singular kernels. The well-posedness of the scattering problem is established by combining the integral equation, variational, and operator theory techniques. The study lays the groundwork for future numerical methods for layered obstacles and rough surfaces composite scattering and inverse scattering problems.