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Since nearly all studies concerning the approximate Crank–Nicolson perfectly matched layer (CN-PML) are limited to 2-D cases, a computationally efficient implementation that can be used to truncate 3-D finite-difference time-domain (FDTD) lattices is presented in this article. More precisely, it is based on the CN direct-splitting (DS) scheme and the bilinear transform (BT) method. This article can fully exploit the unconditional stability of the standard CN-FDTD method and can be free from the Courant–Friedrich–Lewy (CFL) limit; hence, it is especially suitable for situations where space discretization step is much smaller than 1/10th or 1/20th of the smallest wavelength of interest. Aiming at further reducing the requirement of the computer resources, this new implementation can be reformulated in more simple forms if proper auxiliary variables are introduced. It therefore shows a higher iteration speed than other published unconditionally stable PMLs as fewer numbers of arithmetic operations are involved. Finally, three numerical examples, including scatting, transmission, and radiation, are also provided to validate its running time, unconditional stability, and absorption characteristic. [ABSTRACT FROM AUTHOR]

Through the digital signal processing (DSP) techniques, two simple implementations of the stretched coordinate perfectly matched layer (SC-PML) are proposed in this letter. Specially, they are based on the bilinear Z-transform and matched Z-transform methods, respectively. In addition, incorporating the concept of generalized material independent PML into these formulations enable them to be completely independent of material properties. Thus, these new implementations can be used to terminate the finite-difference time-domain lattices composed of arbitrary media. As for resource utilization, the proposals can guarantee that only one auxiliary variable is needed for each field component in the whole PML regions. A brief comparison of the number of floating-point operations and constant coefficients successfully shows that they can achieve a bit higher efficiency compared with other published efficient SC-PML implementations. Finally, two numerical examples of electromagnetic waves radiating in vacuum and soil half-space are provided to validate these DSP-based algorithms. [ABSTRACT FROM AUTHOR]