Dissipative terms and local time-stepping improvements in a spatial high order Discontinuous Galerkin scheme for the time-domain Maxwell’s equations

In this paper, we present some improvements, in terms of accuracy and speed-up, for a particular well adapted Discontinuous Galerkin method devoted to the time-domain Maxwell equations. First, to reduce spurious modes on very distorted meshes, the addition of dissipative terms as penalization in the numerical scheme is studied and compared on examples. Second, in order to increase the efficiency of the method, a multi-class local time-stepping strategy is presented and its validation and advantages are highlighted on different examples.