A Numerical Study of Efficient Leapfrog CD-HIE-FDTD Method With CFS-PML Technique

The recently proposed complying-divergence implicit finite-difference time-domain (CDI-FDTD) method was demonstrated with relatively superior numerical performance, especially with the unconditional stability of implicit methods and the complying-divergence property. In addition, the complying-divergence property was also extended to and successful utilized in semi-implicit FDTD methods for significantly more efficient and accurate electromagnetic (EM) computations with models containing fine structures in one or two directions. This work offers an effective implementation of the complex frequency-shifted perfectly matched layer (CFS-PML) based on a one-step leapfrog complying-divergence-hybrid implicit-explicit FDTD (CD-HIE-FDTD) method with more robust simulations to address more complicated open-domain EM challenges. The stretching factors are initially introduced into Maxwell’s equations to derive a compact 1st-order differential matrix form. Subsequently, the matrix is subjected to space-time operator splitting to establish a complying-divergence framework with a two-step iterative solution. For more numerical efficiency, we utilize the leapfrog time-stepping strategy to eliminate intermediate variables and get a one-step iterative solution. Moreover, for the aforementioned computational framework, we offer an analysis for the terms of numerical stability and complying-divergence property. Meanwhile, the various examples given in this work also verify the correctness and efficacy of the proposed method.