A non-conforming discontinuous Galerkin method for solving Maxwell's equations

A Discontinuous Galerkin Method for the Time-Domain Solution of 3D Maxwell's Equations on Non-Conforming Locally Refined Grids

A discontinuous Galerkin method is proposed for the numerical solution of the three-dimensional time-domain Maxwell's equations. A leap frog scheme is used for advancing in time. The scheme resulting can handle highly heterogeneous material, non diffusive and highly adaptable (it has been implemented on tetrahedral or hexahedral grids, including non-conforming). In some cases, some divergence c...

Optimized Schwarz method for solving time-harmonic Maxwell's equations discretized by a discontinuous Galerkin method

Development of a hp-like discontinuous Galerkin time-domain method on non-conforming simplicial meshes for electromagnetic wave propagation

This work is concerned with the design of a hp-like discontinuous Galerkin (DG) method for solving the two-dimensional time-domain Maxwell equations on non-conforming locally refined triangular meshes. The proposed DG method allows non-conforming meshes with arbitrary-level hanging nodes. This method combines a centered approximation for the evaluation of fluxes at the interface between neighbo...

A high-order non-conforming discontinuous Galerkin method for time-domain electromagnetics

In this paper, we discuss the formulation, stability and validation of a high-order non-dissipative discontinuous Galerkin (DG) method for solving Maxwell’s equations on non-conforming simplex meshes. The proposed method combines a centered approximation for the numerical fluxes at inter element boundaries, with either a second-order or a fourth-order leap-frog time integration scheme. Moreover...

Optimal non-dissipative discontinuous Galerkin methods for Maxwell's equations in Drude metamaterials

Abstract. Simulation of electromagnetic wave propagation in metamaterials leads to more complicated time domain Maxwell’s equations than the standard Maxwell’s equations in free space. In this paper, we develop and analyze a non-dissipative discontinuous Galerkin (DG) method for solving the Maxwell’s equations in Drude metamaterials. Previous discontinuous Galerkin methods in the literature for...