A discontinuous Galerkin scheme for solving 2D wave propagation in anisotropic materials

Abstract

Optical Coherence Tomography, OCT, is a relatively recent imaging technique that allows high-resolution imaging of the retina. It relies in certain optical characteristics of light to provide information of the eye fundus, facilitating the diagnosis of some eye pathologies [13]. In order to better understand the information carried in an OCT, we must model in detail the behavior of the electromagnetic wave as it travels through the sample with Maxwell's equations. In this work we discuss the numerical discretization of the time-dependent Maxwell's equations using a leap-frog type discontinuous Galerkin (DG) method. Nodal DG method [4] was chosen for the integration in space due to its high-order of accuracy and its ability to handle complex geometries. We focus on numerically illustrate the convergence properties of fully discrete schemes. In the model we consider anisotropic permittivity tensors which arise naturally in our application of interest [1].