An Improved Vector Wave Equation-Based Discontinuous Galerkin Time Domain Method and Its Hybridization With Maxwell’s Equation-Based Discontinuous Galerkin Time Domain Method

Abstract

An improved vector wave equation-based discontinuous Galerkin time domain (IDGTD-WE) is proposed to efficiently solve electromagnetic problems for the first time. The electric field is solved using the primal form of discontinuous Galerkin time domain (DGTD) method based on vector WE, while the magnetic field can be obtained with the help of a weak form auxiliary equation related to the electric fields. Considering that governing equation of the electric fields does not directly depend on the magnetic fields, the solution of the magnetic fields can be obtained in the desirable region. With the proposed IDGTD-WE method, the electric and magnetic fields can achieve the optimal convergence rate of $\textrm {O}(h^{p+1})$ simultaneously. The comparison between the presented method and the conventional DGTD method based on Maxwell’s equations (DGTD-ME) is made to demonstrate advantages of the proposed method in memory requirement and CPU time. Furthermore, a stable upwind flux-based hybrid scheme composed of the IDGTD-WE and DGTD-ME methods has been developed to flexibly model the complex electromagnetic problems. Numerical examples are conducted to demonstrate validity, versatility, and efficiency of the proposed method.