Discontinuous Galerkin methods for dispersive and lossy Maxwell's equations and PML boundary conditions

Authors:
Tiao Lu;Pingwen Zhang;Wei Cai
Affiliations:
LMAM and School of Mathematical Science, Peking University, Beijing, 100871, PR China;LMAM and School of Mathematical Science, Peking University, Beijing, 100871, PR China;Department of Mathematics, University of North Carolina at Charlotte, Charlotte, NC
Venue:
Journal of Computational Physics
Year:
2004

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Abstract

In this paper, we will present a unified formulation of discontinuous Galerkin method (DGM) for Maxwell's 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 Maxwell's equations with the auxiliary polarization current variables is derived. Various numerical results are provided to validate the proposed formulation.