Unconditionally-stable Finite-difference Time-domain Method Research Articles

New hybrid FDTD algorithm for electromagnetic problem analysis**Project supported by the National Natural Science Foundation of China (Grant No. 61571348) and the Equipment Pre-Research Foundation of China (Grant No. 61405180202).

Since the time step of the traditional finite-difference time-domain (FDTD) method is limited by the small grid size, it is inefficient when dealing with the electromagnetic problems of multi-scale structures. Therefore, the explicit and unconditionally stable FDTD (US-FDTD) approach has been developed to break through the limitation of Courant–Friedrich–Levy (CFL) condition. However, the eigenvalues and eigenvectors of the system matrix must be calculated before the time iteration in the explicit US-FDTD. Moreover, the eigenvalue decomposition is also time consuming, especially for complex electromagnetic problems in practical application. In addition, compared with the traditional FDTD method, the explicit US-FDTD method is more difficult to introduce the absorbing boundary and plane wave. To solve the drawbacks of the traditional FDTD and the explicit US-FDTD, a new hybrid FDTD algorithm is proposed in this paper. This combines the explicit US-FDTD with the traditional FDTD, which not only overcomes the limitation of CFL condition but also reduces the system matrix dimension, and introduces the plane wave and the perfectly matched layer (PML) absorption boundary conveniently. With the hybrid algorithm, the calculation of the eigenvalues is only required in the fine mesh region and adjacent coarse mesh region. Therefore, the calculation efficiency is greatly enhanced. Furthermore, the plane wave and the absorption boundary introduction of the traditional FDTD method can be directly utilized. Numerical results demonstrate the effectiveness, accuracy, stability, and convenience of this hybrid algorithm.

A Compact Unconditionally Stable Method for Time-Domain Maxwell's Equations

Higher order unconditionally stable methods are effective ways for simulating field behaviors of electromagnetic problems since they are free of Courant-Friedrich-Levy conditions. The development of accurate schemes with less computational expenditure is desirable. A compact fourth-order split-step unconditionally-stable finite-difference time-domain method (C4OSS-FDTD) is proposed in this paper. This method is based on a four-step splitting form in time which is constructed by symmetric operator and uniform splitting. The introduction of spatial compact operator can further improve its performance. Analyses of stability and numerical dispersion are carried out. Compared with noncompact counterpart, the proposed method has reduced computational expenditure while keeping the same level of accuracy. Comparisons with other compact unconditionally-stable methods are provided. Numerical dispersion and anisotropy errors are shown to be lower than those of previous compact unconditionally-stable methods.

Analyses of bounces on power distribution networks using an unconditionally stable finite-difference time-domain method

An unconditionally stable finite-difference time-domain (US-FDTD) method is utilized for analyzing the bounces on structures of power distribution networks (PDNs), which is a critical issue in the electromagnetic compatibility analysis of mobile devices. The US-FDTD method does not utilize the explicit leapfrog time scheme of conventional FDTD method and can solve problems with fine structures well, such as via, thin material and so on. By using this full-wave method, electromagnetic fields between power/ground plane pairs are analyzed and discontinuities of through-hole vias are taken into account in the modeling of PDNs.

A Compact Unconditionally Stable FDTD Method

A novel compact unconditionally stable finite-difference time-domain (US-FDTD) method is introduced. This method utilizes proper intermediate field components to simplify the original unconditionally stable Crank-Nicolson (CN) scheme. The unconditionally stability of the proposed compact US-FDTD method is analytically proven. Numerical results are included to illustrate the stability, accuracy, and efficiency of the proposed compact US-FDTD

More accurate and efficient unconditionally stable FDTD method

A more accurate and efficient unconditionally stable finite-difference time-domain (US-FDTD) method is proposed. The two key points of the proposed US-FDTD method are: defining the field components at only n and (n+1) time steps; and arranging the left and right hands of the original updating equations to be as accurate (in respect of time) as possible. It is demonstrated that the US-FDTD method is more efficient (in both computer memory and CUP time) and more accurate than the recently developed ADI-FDTD method.