# Computational design of acoustic materials using an adaptive optimization algorithm

## TL;DR

This paper presents an adaptive optimization algorithm for designing acoustic materials with specific properties, utilizing local mesh refinement and symmetry considerations to improve efficiency and accuracy.

## Contribution

It introduces a novel adaptive mesh refinement strategy combined with interpolation for the efficient design of symmetric acoustic structures.

## Key findings

- Efficient construction of symmetric acoustic materials demonstrated in 2D.
- Adaptive refinement improves design accuracy and computational efficiency.
- Method can be extended to arbitrary geometries and higher dimensions.

## Abstract

We consider the problem of the construction of the acoustic structure of arbitrary geometry with prescribed desired properties. We use optimization approach for the solution of this problem and minimize the Tikhonov functional on adaptively refined meshes. These meshes are refined locally only in places where the acoustic structure should be designed. Our special symmetric mesh refinement strategy together with interpolation procedure allows the construction of the symmetric acoustic material with prescribed properties. Efficiency of the presented adaptive optimization algorithm is illustrated on the construction of the symmetric acoustic material in two dimensions.