Bryn Davies

Discrete approximations for elliptic PDE models: a framework for metamaterials and waveguides

Many modern wave control devices, such as metamaterials and waveguides, feature complex small-scale structures. This allows for exceptional feats to be achieved but presents a challenging design problem, wherein the simplicity and accuracy of a model need to be balanced. In this work, we present a framework for modelling the challenging case of high-contrast metamaterials with subwavelength resonant material inclusions. Starting from a PDE model, we obtain a discrete approximation for the subwavelength part of the spectrum. This can be generalised to a variety of metamaterial settings, including robust topological waveguides, cochlea-inspired metamaterials, active metamaterials for sensing, non-Hermitian skin effect arrays and localisation in random systems. Some of these applications will be surveyed in this talk.