Nanophotonic Applications of the Discontinuous Spectral Element Time-Domain (DG-SETD) Method

In time-domain computational electromagnetics, progress in spectral and high-order methods has significantly improved the simulation capability of large- scale electromagnetics modeling, for example, with the pseudospectral time-domain (PSTD) method and spectral element time-domain (SETD) method. Such methods can achieve much higher accuracy than the conventional finite difference time- domain method with much fewer grid points. In this work, we further combine the the discontinuous Galerkin method (DGM) with the spectral element time-domain method to improve the efficiency and mesh generation in the SETD and PSTD methods. The combined method is called the discontinuous Galerkin spectral element time-domain (DG-SETD) method. Specifically, this DG-SETD method allows the mesh to be discontinuous across interfaces between elements.