Efficient implicit-explict CN-LF time integration scheme for hybrid FDTD-FETD

Finite different time domain method (FDTD) is widely used for transient electromagnetic field modeling. It shows great computational efficiency by employing central differencing for spatial discretization based on the staggered Cartesian grid and Leap-frog time stepping for temporal discretization. This method avoids matrix operations and presents linear complexity. Thus it has robust adaptability in practical application. One drawback of FDTD is the staircasing error, due to the approximation of irregular structures with the Cartesian grid. Another popular time domain technique is finite element time domain method (FETD), which features great meshing flexibility for fine and complicated structures by employing unstructured tetrahedron element. This method, through a matrix assembly procedure, finally needs to solve a linear system, which involves matrix inversion and can thus become computationally costly, especially for large scale problems. An ideal attempt is to realize hybrid of FDTD and FETD in a way as follows: (1) for smoothly inhomogeneous regions and the perfectly matched layers (PML) in open problems, conventional FDTD is employed to reduce the overall number of unknowns for spatial discretization and improve the computational efficiency with explicit time integration scheme; (2) for fine and complicated structures, FETD is employed to eliminate the staircasing error and meanwhile implicit time integration scheme is used to overcome the CFL constraint. In this way, ideally we can take full advantages of both FDTD and FETD while effectively avoiding their limitations. This idea has attracted considerable attempts, which facilitated the mature of the hybrid method for practical application.