Based on the alternating direction implicit finite-difference time-domain (ADI-FDTD) algorithm, a higher order perfectly matched layer (HO-PML) is proposed to solve the problems in a three-dimensional computational domain. The proposed scheme can not only take advantage of the HO-PML for improving the absorbing performance but also has the advantage of the ADI-FDTD algorithm in terms of the unconditional stability. A dielectric resonator antenna example is carried out to validate its effectiveness. The results show that the Courant-Friedrich-Levy limit can be eliminated and the absorbing performance can be further enhanced.

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.

Based upon the approximate Crank-Nicolson (CN) algorithms and the higher order concept, unconditionally stable perfectly matched layer (PML) implementations are proposed for electromagnetic problems in the finite-difference time-domain (FDTD) lattice. The approximate CN algorithms include the CN direct-splitting (CNDS) and CN approximate-factorizationsplitting (CNAFS). The proposed schemes take advantages of the approximate CN algorithms in terms of eliminating the Courant-Friedrichs-Levy stability condition and maintaining the computational accuracy. By introducing the higher order concept to the PML formulation, the absorbing performance can be enhanced during the simulation. Furthermore, to cope with the existence of half time step problems in simulating the anisotropic magnetized plasma, a modified ADE method is proposed at the integer time step. Thus, the modified ADE method can be directly employed to the approximate CN algorithms. Numerical examples and experiments are carried out to demonstrate the effectiveness, efficiency and performance. Through the results, it can be observed that the computational efficiency and the absorbing performance can be significantly improved. Meanwhile, it can be concluded that the CNAFS-PML and CNDS-PML algorithms show higher accuracy and considerable efficiency, respectively, when the time step surpasses far beyond the CFL condition.

Instead of applying the standard Crank–Nicolson (CN) method, an efficient perfectly matched layer (PML) based on the CN approximate-factorization-splitting (CNAFS) scheme is proposed to terminate three-dimensional (3-D) finite-difference time-domain lattices. It can not only be free from the Courant– Friedrich–Levy limit, but also has higher efficiency than the standard CN-PML. Considering that its iteration form based on the original CNAFS scheme is still complicated, its calculation speed is further improved via introducing a series of intermediate variables. All mathematical derivations are based on the bilinear transform method to guarantee the accuracy. Finally, the absorption performance, computational efficiency, and unconditional stability of our work are verified through two 3-D numerical examples of electromagnetic waves radiating in homogeneous spaces.

An efficient implementation of the complex frequency-shifted perfectly matched layer (PML) is proposed to terminate the finite-difference time domain (FDTD) lattices. The proposal is based on the matrix exponential algorithm originally used for modeling frequency dispersive media. As the equations of describing E (D) fields, H (B) fields, and auxiliary variables associated with PML are formulated as a compact first-order differential matrix form, no convolution operations, variable substitutions, or equations rearrangements are needed in its mathematical derivations. Via the concept of generalized material-independent PML, this new implementation can also be used to truncate arbitrary media. Furthermore, since its iteration forms are similar to those of the convolutional PML (CPML) that has been widely used in FDTD simulations, the proposal can be directly applied to existing codes with only minor changes. Meanwhile, it can achieve better absorption effect than CPML. Through a numerical example in terms of the printed F antenna and corresponding analyses of performance and efficiency, we find that the proposal works well as absorbing boundary condition.