A New Explicit-Implicit Hybridizable Discontinuous Galerkin Time-Domain Method for Electromagnetics

For time-domain electromagnetics, the choice of time scheme is very pivotal. Usually, an explicit time scheme has the stability constraint on small grid size. Though the implicit time scheme is unconditionally stable, it has a necessary expense of computing the global system at each time iteration. To alleviate the expensive computational cost, a new explicit-implicit hybridizable discontinuous Galerkin time-domain method that combines the explicit DGTD (exDGTD) method and our former imHDGTD method will be proposed for the first time. Here let's call it exDGTD-imHDGTD (ex-imHDGTD). This letter gives its implementation, including a new transmission condition. Unlike the traditional explicit-implicit methods, imHDGTD is used to replace traditional implicit algorithms for the refined region, which leads to a remarkable reduction of degrees of freedom (DOFs) and a better matrix solving ability. Numerical results show that the proposed ex-imHDGTD is very effective both on accuracy and performance.