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Based upon the higher order (HO) concept and the convolution perfectly matched layer (CPML) formulation, the efficient and tight HO-CPML implementation is proposed for electromagnetic (EM) simulation. The proposed formulation has the advantages of the higher order concept and the CPML in terms of enhancing absorbing performance and improving computational efficiency. Numerical examples including the half-space soil/metal plate structure and the patch antenna radiation model are carried out in the finite-difference time-domain lattice to validate the effectiveness and efficiency. It can be demonstrated that the proposed HO-CPML can further enhance the absorbing performance compared with the CPML and enjoy considerable computational efficiency compared with the other HO-perfectly matched layers (HO-PMLs). Meanwhile, the proposal can terminate arbitrary mediums without changing the update equations in the PML regions.

Based on iterated Crank–Nicolson (CN) procedure, an alternative algorithm with perfectly matched layer (PML) formulation is proposed in the body‐of‐revolution (BOR) finite‐difference time‐domain (FDTD) lattice for the simulation of rotational symmetric geometrics. For the nonuniform domain simulation, an alternative subgridding method is employed to during the simulation. The iterated CN procedure improves the efficiency through preventing the calculation of tri‐diagonal matrices. The alternative subgridding method enhances the accuracy in nonuniform domains by the calculation of subregions. Numerical example is carried out for the demonstration of effectiveness including efficiency, accuracy and absorption. Through the results, the proposed scheme shows considerable absorption and accuracy improvement in nonuniform domains. Compared with the other CN schemes, the iterated CN procedure can significantly increase the efficiency with small time steps. In conclusion, the advantages and novelty of the proposed algorithm can be described as follows: (1) The iterated CN procedure is proposed for rotational symmetric geometrics. (2) Absorption boundary condition for iterated CN is proposed in BOR‐FDTD. (3) An alternative subgridding method for iterated CN procedure is proposed in BOR‐FDTD lattice. Thus, the proposed algorithm shows potential in nonuniform rotational symmetric geometrics open region simulation.

Unconditionally stable approximate Crank-Nicolson (CN) perfectly matched layer (PML) implementation is proposed to treat open region problems for a bandpass rotational symmetric structure. To be more specific, this implementation is based upon the CN Douglas-Gunn (DG) procedure and the complex envelope (CE) method in body of revolution (BOR) finite-difference time-domain (FDTD) lattice. The proposed scheme inherits the advantages of the CNDG procedure, CE method, and BOR-FDTD algorithm which can improve the efficiency, enhance the absorption, and maintain the calculation accuracy. The effectiveness which includes accuracy, efficiency, occupied resources, and absorption is illustrated through a numerical example. The numerical results reveal that the proposed scheme provides considerable accuracy, creditable absorption, and outstanding efficiency. Meanwhile, it can also verify that the proposed scheme is stable without the limitation of Courant-Friedrich-Levy (CFL) condition.

To efficient simulate symmetric rotationally geophysical problems, implicit Crank–Nicolson (CN) scheme incorporated with approximate decoupling procedure is proposed in the body of revolution (BOR) finite‐difference time‐domain (FDTD) algorithm. For further absorption of large number of low‐frequency waves in bandpass simulation, complex envelope method is incorporated with the perfectly matched layer implementation. To be more specific, the proposed implementation shows advantages in terms of improved efficiency, considerable accuracy, and remarkable absorption. To demonstrate effectiveness and efficiency of the proposed implementation, geophysical numerical examples are carried out in the BOR‐FDTD domain. Through different numerical examples, it can be concluded from simulation results that the proposed implementation can obtain admirable entire performance in bandpass geophysical simulation. In addition, it can also be illustrated that it can keep stable when time step surpasses far beyond the Courant–Friedrichs‐ Levy condition.

The original Factorization‐Splitting (FS) algorithm solves large number of coefficients and components in each iteration cycle which significantly affects the computational resources and calculation efficiency. Meanwhile, it can merely solve problems in uniform domains due to the limitation of discretized mesh sizes. In order alleviate these drawbacks, system incorporated factorization‐splitting algorithm is proposed to efficiently solve problems in nonuniform domains. The finite‐difference time‐domain (FDTD) domain is terminated by the higher order perfectly matched layer (PML) formulation which shows advantages in improving the absorbing performance. As the employment of the original domain decomposition method results in the algorithm unstable, an alternative domain decomposition method is proposed which can split the entire nonuniform domain into several sub‐regions. Metamaterial structure is introduced to demonstrate the performance of the proposed algorithms. Through results, the proposed algorithm can decrease memory consumption and simulation duration due to the calculation prevention of repeated components and coefficients. The absorption can be further improved especially in the low‐frequency band due to the enhanced absorption of propagation waves. In addition, the alternative domain decomposition method shows considerable advantages in the simulation of nonuniform domains.

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Based upon the approximate Crank–Nicolson (CN) finite-difference time-domain method implementation, the unconditionally stable algorithm is proposed to investigate the wave propagation and transmission through extremely thin graphene layers. More precisely, by incorporating the CN Douglas–Gunn algorithm, the piecewise linear recursive convolution method and the auxiliary differential equation method, the analytical model is proposed for Drude-like graphene model. To obtain the solution of the governing equations, the perfectly matched layer and the periodic boundary condition are applied to the graphene structure with two dimensional nano-materials. Numerical examples are carried out for further investigation. During the simulation, the influences of the parameters such as the grating slit and its thickness on the wave transmission are investigated and discussed. The result shows that not only the graphene grating has high transmission performance but also the proposed methods have considerable performance and accuracy.