Higher Order CPML for Leapfrog Complying-Divergence Implicit FDTD Method and Its Numerical Properties

The leapfrog complying-divergence implicit finite-difference time-domain (CDI-FDTD) method is an implicit scheme that is unconditionally stable involving the simplest and most efficient leapfrog update procedures with minimum floating-point operations (flops). Moreover, the method possesses complying divergence satisfying Gauss's law, while other methods, including the leapfrog alternating direction implicit (ADI)-FDTD counterpart, do not. These desirable features make the leapfrog CDI-FDTD useful for electromagnetic simulations when the unconditional stability is to be exploited. In this article, a higher order convolutional perfectly matched layer (CPML) for leapfrog CDI-FDTD is developed and implemented for simulating open space problems. To formulate the CPML for leapfrog CDI-FDTD, we have carefully considered the order of CPML update along with proper use of main and auxiliary fields to retain the unconditional stability and complying divergence. The proposed CPML for leapfrog CDI-FDTD remains stable beyond the Courant time step as ascertained through von Neumann analysis. By comparing the flops and computation time, the leapfrog CDI-FDTD is shown to be most efficient among common implicit FDTD methods with CPML. The formulation of numerical divergence for higher order CPML is also presented. Simulation results show that the proposed higher order CPML has many advantages of simplicity, complying divergence, and high absorption efficiency.