The Heterogeneous Multiscale Method for dispersive Maxwell systems

TL;DR

This paper develops a finite element heterogeneous multiscale method for dispersive Maxwell systems, incorporating homogenization results and error analysis to improve understanding of multiscale dispersive electromagnetic phenomena.

Contribution

It introduces a novel multiscale finite element approach for dispersive Maxwell equations, including homogenization insights and error estimates for the micro problems.

Findings

Effective system includes additional dispersive effects

Error estimates for micro problems established

Semi-discrete error estimate proved

Abstract

In this work, we apply the finite element heterogeneous multiscale method to a class of dispersive first-order time-dependent Maxwell systems. For this purpose, we use an analytic homogenization result, which shows that the effective system contains additional dispersive effects. We provide a careful study of the (time-dependent) micro problems, including $\mathrm{H}^2$ and micro errors estimates. Eventually, we prove a semi-discrete error estimate for the method.