This work is about the numerical solution of the time-domain Maxwell's equations in dispersive propagation media by a discontinuous Galerkin time-domain method. The Debye model is used to describe the dispersive behaviour of the media. The resulting system of differential equations is solved using a centred-flux discontinuous Galerkin formulation for the discretization in space and a second-order leapfrog scheme for the integration in time. The numerical treatment of the dispersive model relies on an auxiliary differential equation approach similar to that which is adopted in the finite difference time-domain method. Stability estimates are derived through energy considerations and convergence is proved for both the semidiscrete and the fully discrete schemes.

This paper is concerned with the design of a reduced-order discontinuous Galerkin (DG) method based on proper orthogonal decomposition (POD) method for electromagnetic simulation. A centered flux approximation for surface integral and a second order leap-frog (LF2) scheme for advancing in time are applied in the classical DG method. The POD basis is created by the eigensytem of the correlation matrix, which is generated by the snapshot matrix whose columns are the snapshot vectors extracted from the high fidelity DG simulation. The POD-DGTD formulation with lower dimension and sufficiently high accuracy is established by applying a Galerkin projection for the semi-discrete DG scheme. The overall goal is to reduce the computational cost while maintaining an acceptable level of accuracy. Numerical experiments for electromagnetic problems illustrate the performance of the proposed reduction method.