Computationally Efficient CN-PML for em Simulations

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.