Recent Developments to the Discontinuous Galerkin Time-Domain Method for 3-D Multiscale Problems

Recent developments to the discontinuous Galerkin time-domain (DGTD) method for 3-D multiscale problems are reported in this paper. Although the DGTD method is very popular to electromagnetic problems at present, realistic electromagnetic wave propagation problems are often multiscale due to complex geometries or heterogeneous media, which leads to many restrictions of the traditional DGTD methods. Therefore, this paper reports on some significant advances about the DGTD method. First of all, in order to overcome the severe stability restrictions caused by the locally refined meshes, we propose a time integration strategy by combining excellent stability properties with a new explicit time scheme. Second, we apply this strategy into the inhomogeneous media to solve the multiscale dispersive problems. Considering some multiscale meshes with very small size, an unconditional stable hybridizable discontinuous Galerkin time method is proposed to increase time step so that greatly reducing computational time. Particularly, from meshes point of view, a new strategy is proposed by combining the DGTD with Multiscale Hybrid Method (MHM), and the parallel technologies can be greatly performed. By using the above methods, accurate numerical results can be obtained as well as a higher computational performance in the time-domain multiscale problems.