A partially staggered discontinuous Galerkin method for transient electromagnetics

Conservation of energy, spurious-free, and optimal convergence are among the most favorite ingredients of a discontinuous Galerkin finite-element time-domain method (DG-FETD) for the analysis of transient electromagnetic problems. Unfortunately, due to the reliance on dissipative upwind flux to suppress spurious modes, most existing DG-FETDs possess only one or two of them. In this paper, we present a novel two-dimensional DG-FETD method, which combines all of the three advantages. The proposed method is based on the electric field E and magnetic field H, whose approximation spaces are composed of Whitney's edge functions. To inhibit the spurious modes while keeping the conservation of numerical energy, the numerical flux with dissipation is not adopted. Instead, a carefully designed interface condition along with the non-dissipative central flux is employed for this purpose. That is, across each face of an element except for those coinciding with boundaries of the computational domain, if E is strongly enforced to be tangential continuous then the continuity of H is weakly imposed, and vice versa. For the convenience of complying with this requirement and without loss of the inherent parallelism of the DG-FETD method, two partially staggered sets of subdomains are built for E and H, respectively. These subdomains are made up of sub-elements generated through a refinement of each cell on the initial mesh into four similar elements. The final discrete system is advanced with a second order leap-frog time-stepping scheme. A series of numerical examples demonstrate that the present method is robust and much more superior to the conventional DG-FETD methods.