Computational method for acoustic wave focusing

TL;DR

This paper presents a computational approach to design materials with specific acoustic wave focusing properties by solving an inverse scattering problem involving small particles.

Contribution

It introduces a novel algorithm for inverse design of acoustic materials with desired focusing characteristics, linking particle density to scattering behavior.

Findings

Algorithm effectively designs materials with targeted focusing properties.

Theoretical analysis confirms the relationship between particle density and scattering behavior.

Numerical simulations demonstrate the practical applicability of the method.

Abstract

Scattering properties of a material are changed when the material is injected with small acoustically soft particles. It is shown that its new scattering behavior can be understood as a solution of a potential scattering problem with the potential $q$ explicitly related to the density of the small particles. In this paper we examine the inverse problem of designing a material with the desired focusing properties. An algorithm for such a problem is examined from the theoretical as well as from the numerical perspective.