High-Order ME-CFS-PML Implementations for Terminating the FDTD Domain Composed of Arbitrary Media

An arbitrary high-order matrix exponential (ME) complex frequency-shift (CFS) perfect matched layer (PML) algorithm is proposed for truncating the simulation space in the finite-difference time-domain (FDTD) method. The algorithm introduces a frequency-domain splitting generalization of high-order PML stretching function to construct a high-order format of the ME algorithm. Update formulations for the electromagnetic fields and auxiliary variables are derived accordingly. Moreover, the algorithm allows for simple modifications to obtain a regularized form of arbitrary higher order PML with improved accuracy and better expansion characteristics. This regularized form removes the convolution operation and can be used for arbitrary media and the stability of the algorithm is verified by the Fourier method. To evaluate the performance and efficiency, several numerical examples involving a perfectly electrically conducting (PEC) plate, printed F antenna, and small metamaterial antenna are analyzed. The results demonstrate improved absorption effects, reduced memory consumption, and shorter simulation times compared to the ME-PML and traditional CFS-PML algorithms. In addition, the proposed algorithm effectively addresses the issue of data inaccuracy in the early stages of antenna and device simulations due to its reliable absorption capabilities. The proposed algorithm offers strong technical support and potential applications in the simulation and design of antennas and microwave devices.