Homogenizing metamaterials, three times

TL;DR

This paper explores three different approaches to homogenizing periodic metamaterials, integrating multiple scattering theory, functional analysis, differential geometry, and optimization, with detailed numerical results and connections between methods.

Contribution

It introduces a comprehensive framework combining three perspectives for metamaterial homogenization, enhancing understanding and computational techniques.

Findings

Connections between different homogenization approaches are clarified.

Numerical results demonstrate the effectiveness of the combined methods.

The framework improves accuracy and insight into metamaterial properties.

Abstract

The homogenization of a metamaterial made of a collection of scatterers periodically disposed is studied from three different points of view. Specifically tools for multiple scattering theory, functional analysis, differential geometry and optimization are used. Detailed numerical results are given and the connections between the different approaches are enlightened.