Discontinuous Galerkin methods for dispersive and lossy Maxwellʹs equations and PML boundary conditions

In this paper, we will present a unified formulation of discontinuous Galerkin method (DGM) for Maxwellʹs equations in linear dispersive and lossy materials of Debye type and in the artificial perfectly matched layer (PML) regions. An auxiliary differential equation (ADE) method is used to handle the frequency-dependent constitutive relations with the help of auxiliary polarization currents in the computational and PML regions. The numerical flux for the dispersive lossy Maxwellʹs equations with the auxiliary polarization current variables is derived. Various numerical results are provided to validate the proposed formulation.