Hybrid DGTD method with FDTD/SETD/FETD

The proposed hybrid DGTD method aims to realize hybridization of finite difference method with Cartesian grid, spectral element method with hexahedron elements, and finite element method with tetrahedron elements in time domain based on the DG framework. For homogeneous, smoothly inhomogeneous areas and the perfectly matched layer (PML), finite difference method is employed to improve the computational efficiency, as the staircasing approximation in these areas causes negligible errors and moreover Cartesian grid discretization results in fewer numbers of unknowns with respect to a tetrahedron mesh. For irregular geometries, spectral element or finite element method is utilized by employing unstructured mesh to eliminate the staircasing errors. The proposed hybrid DGTD method divide the original model into FDTD, buffer and SETD/FETD regions. When the buffer and SETD/FETD regions are with large DoFs, they can be further split into multiple subdomains to reduce computational complexity. To improve the time-marching efficiency, the explicit leapfrog (LF) time integration is employed for the FDTD and buffer regions, and an implicit Crank-Nicolson (CN) based time integration is used for the FETD region. For the SETD region both explicit and implicit time integration can apply. Thus, a global implicit-explicit time integration is given for the hybrid method. Numerical results are shown to demonstrate the accuracy and long-time stability of the proposed hybrid method.