The Hybridizable Discontinuous Galerkin Time Domain Method to Solve the 3D Maxwell's Equations

摘要

The hybridizable discontinuous Galerkin (HDG) method is very popular at present because of its lower number of globally coupled degrees of freedom compared with the discontinuous Galerkin (DG) method. However there is pretty few research about HDG in time domain computational electromagnetics. Considering the time domain methods can contain more the transient information and reflect directly the electromagnetic response characteristics compared the frequency domain, we propose a new hybridizable discontinuous Galerkin time domain (HDGTD) method to solve the Three-Dimensional (3D) time domain Maxwell's equations in this paper. We use the implicit time intergration to achieve unconditional stability compared with the explicit DGTD, which obtains bigger time step and fewer the freedom of unknown. Applying the HDGTD method to numerical example, we further verify its Feasibility and accuracy compared with the DGTD method and the analytical solutions.