A 3-D Hybrid Maxwell's Equations Finite-Difference Time-Domain (ME-FDTD)/Wave Equation Finite-Element Time-Domain (WE-FETD) Method

In this article, a 3-D hybrid Maxwell's equations finite-difference time-domain (ME-FDTD)/wave equation-based finite-element time-domain (WE-FETD) method is proposed. This method retains the nonconformal mesh and the implicit-explicit time integration scheme. The WE-FETD region is based on the wave equation rather than Maxwell's curl equations. This method needs to store all the electric fields in the entire region and only the magnetic fields on the interface, which can prominently reduce degrees of freedom (DoFs) and save calculation time. The ME-FDTD region follows Yee's scheme. A Maxwell's equations spectral element time-domain (ME-SETD) region and a virtual region are used to combine the ME-FDTD and WE-FETD regions. Consequently, a WE-FETD/ME-SETD/Virtual/ME-FDTD framework is formed. Hybrid Newmark-beta (NB) and Crank-Nicolson (CN) time stepping are employed for implicit WE-FETD and ME-SETD regions. The leapfrog (LF) time integration is used for the explicit virtual and FDTD regions. At the interface, it employs upwind flux in the discontinuous Galerkin (DG) method to couple neighboring regions. Numerical examples are included to demonstrate the accuracy of the proposed method. Several cases exhibit the improved efficiency compared with the hybrid FDTD/FETD method only based on Maxwell's equations and the pure FETD method.