Advanced Discontinuous Galerkin Time-Domain Methods for Challenging Engineering Problems

The unique properties of the discontinuous Galerkin time-domain (DGTD) method make it a very powerful numerical solver for engineering problems from different disciplines. The use of discontinuous basis functions and numerical fluxes enables many advanced techniques to be developed and implemented for the DGTD method. In this paper, our effort towards a flexible numerical solver based on the DGTD method is reviewed. The development of advanced techniques, such as dynamic h-adaptation based on adaptive Cartesian meshes, dynamic p-adaptation based on tetrahedral meshes, and multirate time integration, makes the DGTD method widely applicable to different problems.