The preceding works introduced the leapfrog complying divergence implicit finite-difference time-domain (CDI-FDTD) method, which exhibits high accuracy and unconditional stability. In this study, the method is reformulated to simulate general electrically anisotropic and dispersive media. The auxiliary differential equation (ADE) method is employed to solve the equivalent polarization currents, which are then integrated into the CDI-FDTD method. The iterative formulae are presented, and the calculation method is similar to that of the traditional CDI-FDTD method. Additionally, the Von Neumann method is utilized to analyze the unconditional stability of the proposed method. To evaluate the performance of the proposed method, three numerical cases are conducted. These include calculating the transmission and reflection coefficients of a monolayer graphene sheet and a monolayer magnetized plasma, as well as the scattering properties of a cubic block plasma. The numerical results obtained by the proposed method demonstrate its accuracy and efficiency in simulating general anisotropic dispersive media, compared to both the analytical method and the traditional FDTD method.

In this letter, a 3-D subgridding finite-difference time-domain (FDTD) approach is proposed. The calculation domain is divided into regions with dense meshes and regions with coarse meshes. By applying the proposed subgridding technique to dense grid regions, memory and computation resources can be significantly reduced. Furthermore, the Courant–Friedrich–Levy (CFL) limitation of dense mesh regions is broken by the one-step leapfrog alternately direction-implicit (ADI)-FDTD. Coarse and dense regions can adopt a uniform time step, which is limited only by the standard FDTD CFL condition for coarse meshes. In comparison with the standard FDTD approach and the subgridding FDTD approach, numerical results demonstrate the efficiency and accuracy of the proposed method.

This study introduces a novel, unified arbitrary-order matrix exponential-symplectic FDTD^(p,q) (ME-SFDTD^(p,q)) method tailored for simulating anisotropic time-varying plasma medium. The governing equations, comprising both current density and Maxwell’s equations, are reformulated into a compact first-order differential matrix form and then discretized in the temporal domain using a multistage p-order symplectic integrator. Meanwhile, the matrix exponential (ME) coefficients arising from the symplectic discretization are efficiently computed utilizing the ME method, while spatial derivatives are approximated by a q-order central-difference scheme. These processes yield a complete numerical iteration framework specific to the ME-SFDTD^(p,q) format, optimized for field components calculations in an anisotropic time-varying plasma medium. To effectively truncate the simulation space modeled by the ME-SFDTD^(p,q) method, a high-performance complex frequency-shifted perfectly matched layer (CFS-PML) technique is proposed, which shares the same primary iteration formulas as the ME-SFDTD^(p,q) method, exhibiting excellent absorption performance and high compatibility. In addition, a comprehensive numerical stability and dispersion analysis is conducted to confirm the feasibility of the proposed method. Finally, several numerical examples are presented to thoroughly validate the accuracy and efficiency of the approach.

The face-centered cube (FCC) grid has more sampling points than the traditional Yee cell (as it contains a total of 14 grid points, of which six are center points and eight are vertices, and each grid point has three field components). Thus, FCC is better than the former in dealing with the dispersion error of anisotropic media. On the basis of this feature, this article first derived the FCC-finite-difference time-domain (FDTD) iterative formula for nonuniform plasma on the basis of FCC grid and verifies the accuracy of the algorithm. This algorithm is combined with the nonuniform plasma flow field model of hypersonic vehicles, and the backward single-station radar cross sections (RCSs) of vertical polarization (VV) and horizontal polarization (HH) are calculated under different flight altitudes, flight velocities, and external conditions. Results showed that as flying height increased or flying speed decreased, it results in an increase in RCS. Different external magnetic fields and incident angles also had an obvious impact on the electromagnetic scattering characteristics. From the perspective of electromagnetic wave polarization, both VV polarization and HH polarization have a great impact on RCS. These results provide a theoretical basis for studying the electromagnetic scattering characteristics of nonuniform plasma targets.

A dispersive finite-difference time-domain (FDTD) method based on the recursive integration (RI) technique for the modeling of the lossy multipole Debye dispersive media is described in this article. The interaction between the electromagnetic (EM) field and the human tissues is simulated by means of the RI method, and the frequency-dependent formulations which possess good compatibility with the main FDTD algorithm are achieved. Next, the expression of the multipole Debye dispersion model is similar to the multipole complex frequency shift (CFS) stretching function which is utilized to build the multipole perfectly matched layer (MPML). Therefore, a significant feature of using the RI method is its overall modeling of both multipole Debye dispersive media and MPML boundary conditions. Furthermore, the stability analysis of the RI method in solving the lossy multipole Debye dispersive model indicates that the Courant–Friedrich–Levy (CFL) stability limit of the regular FDTD can be maintained. At last, the numerical cases performed in this work demonstrate the correctness of the RI method in modeling dispersive media.