We address the electromagnetic problem involving small structures, and put forward an improved, explicit finite difference time domain (FDTD) algorithm based on the Newmark discretization with subgridding technique. This algorithm achieves a stable, low-reflection, and straightforward subgridding with an arbitrary grid refinement ratio by adopting hanging variables. The Newmark method is employed to discretize the numerical system generated by the subgridding method. Besides, the Neumann series is used to obtain the inverse of the coefficient matrix. It makes the time-marching explicit and stable with a uniform large time step only determined by the coarse grid size in the whole computational domain. The series expansion avoids the matrix inversion operation, which largely enhances the calculation efficiency compared to the traditional Newmark-FDTD method. Numerical results prove the reliability and robustness of the proposed method.

A novel hybrid finite-element time-domain (FETD) algorithm is proposed to solve electromagnetic modeling with fine structures. This algorithm is based on the unconditionally stable finite-element time-domain (US-FETD) and the traditional FETD methods. The US-FETD is used in one subdomain containing all fine grids and parts of coarse grids adjacent to the fine grids. The traditional FETD is applied in the other one subdomain. A compensation and correction scheme is used to update the fields on the subdomain boundary. The hybrid FETD can make the explicit time marching unconditionally stable with a uniform time step determined by the coarse grids in the entire computational domain. In addition, the unstable modes of the entire system in the hybrid FETD can be effectively obtained by solving the partial solutions of the eigenvalue problem in the US-FETD subdomain. In comparison with the US-FETD in the entire computational domain, the eigenvalue analysis costs less memory and time. Numerical results certify the high efficiency of the hybrid FETD.

A subgridding unconditionally stable finite-element time-domain method based on local eigenvalue solution (SUSL-FETD) is proposed to solve multiscale modeling. In this method, subgridding elements are used to discrete a multiscale computational domain, and the explicit central-difference method is applied for temporal discretization. Compared with traditional elements, the subgridding elements have a more complex distribution of edges and nodes. Therefore, an efficient subgridding scheme is given to form the element matrix for each subgridding element. Such system matrices assembled by all element matrices are symmetric. The subgridding FETD (S-FETD) is then further developed into the subgridding unconditionally stable FETD (SUS-FETD) by filtering spatial unstable modes. It is time-consuming to obtain the unstable modes by global eigenvalue decomposition. In this article, the local eigenvalue decomposition is proposed to get the unstable modes, which further reduces the memory storage and computing time. Numerical examples certify that the proposed SUSL-FETD has high accuracy and efficiency.

A nuclear electromagnetic pulse (NEMP) is the fourth effect of a nuclear explosion, characterized by a strong electromagnetic field that can instantly damage electronic devices. To investigate the spatial field value distribution characteristics of the source region of low-altitude NEMPs, this study employed a finite-difference time-domain (FDTD) method based on a rotating ellipsoidal hyperbolic coordinate system. Due to intense field variations near the explosion center, non-uniform grids were employed for both spatial and temporal steps, and an OpenMP parallel algorithm was utilized to enhance computational efficiency. Analysis focused on the following two scenarios: varying angles at a constant distance and varying distances at a constant angle, considering both transverse magnetic (TM) and transverse electric (TE) waves. The results indicate that the spatial field value distribution characteristics differ between the two wave types. For TM waves, the electric and magnetic fields share the same polarity, but their waveform polarities are opposite above and below the explosion center. A TE wave is exactly the opposite. Compared with a TM wave, a TE wave has stronger peak electromagnetic fields but narrower pulse widths and lower overall energy. This research provides significant support for the development of nuclear explosion detection technology and offers theoretical foundations for the protection of surrounding environmental facilities.

A 2-D hybrid method combining cylindrical explicit and unconditionally stable finite-difference time-domain (CEUS-FDTD) with traditional cylindrical FDTD (C-FDTD) methods is proposed to analyze the electromagnetic cylindrical structures efficiently. The unconditional stability of the proposed method is achieved by eliminating the unstable modes which are obtained by solving the eigenvalue problem of the system matrix. However, solving global eigenvalue is time-consuming. To solve this, the domain is divided into the CEUS-FDTD region and C-FDTD region by analyzing the spectral radius of one single grid. All unstable modes can be found only in the CEUS-FDTD region. The electric fields on the boundary of the two regions are corrected without any approximation. The proposed method saves iteration time compared to C-FDTD and costs less time than CEUS-FDTD for the eigenvalue solution. Results show validity and efficiency.

An improved finite difference time domain (FDTD) method is proposed to calculate the transient coupling of a dielectric-coated wire above the rough soil surface under the high power electromagnetic (HPEM) pulse. The improved method is based on the domain decomposition technique, in which the dielectric-coated wire and the rough surface are allocated into the target subdomain and the rough surface subdomain, respectively. The reflected waveform from the rough surface is computed by applying the FDTD method combined with the time-domain Huygen's technique. The incident field on the target subdomain is calculated through the superposition of the excitation fields generated with the directly incident wave and the reflected wave from the rough surface. The near-field distribution and the energy-flux density (EFD) inside the dielectric-coated wire are simulated by running the FDTD in the target subdomain. The accuracy and high efficiency of the improved method are validated and demonstrated by comparing with the conventional FDTD method. Finally, the influences of some parameters related to the rough soil surface and dielectric-coated wire on the EFD are analyzed through the typical examples.