Convergence of an Explicit Iterative Leap-frog Discontinuous Galerkin Method for Time-domain Maxwell's Equations in Anisotropic Materials

TL;DR

This paper introduces an explicit iterative leap-frog discontinuous Galerkin method for solving time-domain Maxwell's equations in anisotropic materials, with proven convergence and demonstrated effectiveness through numerical experiments and a practical application in modeling light scattering in the retina.

Contribution

It presents a novel explicit iterative leap-frog discontinuous Galerkin method with proven convergence for anisotropic Maxwell's equations, including numerical validation and a real-world application.

Findings

Convergence properties are rigorously derived.

Numerical experiments confirm the method's accuracy.

Application demonstrates modeling of light scattering in retinal tissues.

Abstract

We propose an explicit iterative leap-frog discontinuous Galerkin method for time-domain Maxwell's equations in anisotropic materials and derive its convergence properties. The a priori error estimates are illustrated by numerical means in some experiments. Motivated by a real application which encompasses modeling electromagnetic wave's propagation through the eye's structures, we simulate our model in a 2D domain aiming to represent a simple example of light scattering in the outer nuclear layer of the retina.