An Adaptive High-Order Transient Algorithm to Solve Large-Scale Anisotropic Maxwell's Equations

This article presents a stabilized nodal discontinuous Galerkin pseudospectral time-domain (DG-PSTD) algorithm for fully anisotropic electromagnetic waves. This solver permits arbitrary high-order basis functions and adaptive hexahedral elements, thus very efficient for large-scale wave propagation in complex media. Maxwell's equations are reformulated in a unified hyperbolic form, where a localized anisotropic Riemann solver is derived to serve as a numerical flux to exchange information across adjacent elements in the DG-PSTD scheme. This local analysis method also helps impose the time-domain anisotropic plane wave incidence in the total/scattering field framework. Numerical validations and applications demonstrate the efficiency, accuracy, and capability of this new high-order solver for 3-D large-scale generally anisotropic electromagnetic media.