Higher-Order Matrix Exponential Perfectly Matched Layer Scheme With Sub-Gridding Technique Based on the Factorization Approximate Crank-Nicolson Algorithm

Although finite difference time-domain (FDTD) algorithms are potentially applicable to broadband wave propagation and radiation problems, various problems related to the absorbing boundary condition and complex structural meshing limit the accuracy of FDTD calculations. This paper develops an unconditionally stable Crank-Nicolson factorization-splitting (CNFS) algorithm with a higher-order perfectly matched layer (PML) scheme. The higher-order PML is formulated through the matrix exponential (ME) method, which requires fewer operators and less manipulation than the existing implementation. To analyze the fine details and curves, the sub-gridding technique is modified through the unconditionally stable CNFS algorithm. Introducing nonuniform mesh sizes inside the computational domains improves the efficiency without degrading the computational accuracy. The effectiveness of the algorithm is evaluated in wave radiation and propagation problems, including radar cross-section evaluation and antenna design. The numerical and experimental results favorably agree, confirming the effectiveness of the sub-gridding technique and ME-PML based on the CNFS algorithm.