An Efficient Hybrid FDTD-PITD Formulation for Solving Multiscale Electromagnetic Wave Problems

A novel hybrid sub-gridding algorithm based on both the finite-difference time-domain (FDTD) method and the precise-integration time-domain (PITD) method is proposed for efficient numerical simulations of the multiscale electromagnetic wave problems. The fundamental idea of the proposed hybrid method consists of discretizing the computational domain by the local refined sub-grids containing the fine structures and the coarse grids for other domain, solving the field components on the coarse grids and the sub-grids by FDTD method and PITD method, respectively. Meanwhile, a stable interpolation strategy is proposed to exchange the computational information through the interface between the coarse and fine grids. This method can reduce the number of meshes for electromagnetic multiscale problems and significantly reduce the memory requirements. On the other hand, because the PITD method can break through the limit of the Courant-Friedrich-Levy (CFL) numerical stability condition, the proposed hybrid method can use a larger time step depending on the coarse grid to finish the simulation. The numerical results demonstrate the stability, feasibility and high efficiency of the proposed hybrid algorithm.