Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems

The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution of wave propagation problems required for the accurate transient modeling of systems involving electromagnetic waves in many emerging technologies. While Yees explicit, energy-conserving FDTD method is still prominent but restructed to structured grids and second-order accuracy, DGTD methods 1) are able to deal with unstructured, possibly locally-refined meshes around complex geometries, 2) remain fully explicit with easy parallelization, and 3) have extensions to high orders of accuracy. Non-dissipative versions exist, where some discrete electromagnetic energy is exactly conserved. However, the stability limit of the methods, related to the smallest elements in the mesh, calls for the construction of local-time stepping algorithms. These schemes have already been developed for N-body mechanical problems and are known as symplectic schemes. In this paper, they are transformed and applied to DGTD methods on wave propagation problems in order to obtain stable and accurate local time-stepping algorithms