Analysis of the time domain acoustic scattering from open cavities

TL;DR

This paper develops a mathematical framework for analyzing how sound waves scatter in the time domain from open cavities, using boundary conditions and integral equations to ensure well-posedness.

Contribution

It introduces a transparent boundary condition and boundary integral equations for the first time in this context, enabling better analysis of acoustic scattering from open cavities.

Findings

Established well-posedness of the reduced scattering problem.

Derived time domain boundary integral equations.

Provided a new approach for analyzing acoustic scattering.

Abstract

This paper is concerned with the analysis of the time domain acoustic scattering from two-dimensional open cavities. A transparent boundary condition is developed to reformulate the scattering problem into an equivalent initial boundary value problem in the interior domain of the open cavity. The well-posedness, that is, the existence, uniqueness and stability of the solution to the reduced problem are studied via a "Laplace domain" to time domain analysis. Moreover, time domain boundary integral equations for the reduced problem are established.