ICN‐FDTD scheme with absorption boundary condition for nonuniform rotational symmetric geometrics

Abstract

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.

Numerical Dispersion Analysis of the One-Dimensional Iterated Crank-Nicolson-Based FDTD Method

“…Note that the ICN-FDTD method is constrained by the CFL condition as the explicit FDTD method [10]. Recently, the ICN-FDTD method has been extended with the domain decomposition [12], body-of-revolution technique [13] and frequency-dependent formulation [14]. Although the validity of the ICN-FDTD method has been demonstrated, its numerical dispersion property has not yet been discussed.…”

Frequency‐dependent finite‐difference time‐domain method based on iterated Crank–Nicolson scheme

“…To alleviate this difficulty of the CN‐FDTD, we have proposed an iterated CN (ICN)‐based FDTD [10], in which an implicit CN procedure can be replaced with an explicit iteration process [11]. Very recently, the ICN‐FDTD has been applied to the domain decomposition [12] and body‐of‐revolution techniques [13]. Although the effectiveness of the ICN‐FDTD has been demonstrated, its application has been limited only to the analysis of non‐dispersive media.…”

“…As can be seen, the result from the present method is in perfect agreement with that from the explicit FDTD, showing the band-stop properties of the filter.Finally, we mention the memory requirement and the computation time in comparison with the traditional explicit FDTDs. The required memory is about twice that of the explicit counterpart and without ingenuity the computation time is not fast due to the iteration calculations (the recently-developed ICN-FDTD techniques in[12,13] show efficiency improvement compared with the explicit FDTD). Although the advantage of the present method has not been fully demonstrated here, the method even with the CFL condition is expected to be faster than the original implicit dispersive CN-FDTD for not only 2D but also 3D problems[9].…”