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.

In this letter, a spatial modes filtering finite-element time-domain (SMF-FETD) method combined with dual-field domain decomposition (DFDD) is proposed for analyzing 2-D electromagnetic structures with fine features. The SMF-FETD method can obtain unconditional stability by removing unstable modes. Thus, a large time step is available in the SMF-FETD method though the fine features exist. However, the global eigenvalue solution is required in the SMF-FETD method, which brings a great burden on the computing memory and time. To solve this problem, the DFDD technique is introduced into the SMF-FETD method. The technique solves the SMF-FETD equations in each subdomain and relates the adjacent subdomains explicitly using the equivalent electromagnetic currents on the subdomain interfaces. It can greatly reduce the computing memory and time. Numerical examples are presented to verify the accuracy and effectiveness of the proposed DFDD-SMF-FETD method.

In this communication, an efficient finite difference time domain (FDTD) method is proposed by combining the leapfrog complying divergence implicit (LCDI) and split-field (SF) schemes to solve the oblique incidence problem of periodic structures. The conventional SF-FDTD is limited by the space discrete and the incident angles. If the incident angle is large, the computational efficiency is low. Thus, the LCDI scheme is introduced to obtain the unconditional stability, further improving computational efficiency. Besides, the formula and detailed implementation of LCDI-SF-FDTD method are presented. Two numerical examples are used to validate the accuracy and effectiveness of the proposed method. The proposed method offers substantial computational advantages in following two challenging scenarios: (1) periodic structures with fine features and (2) large-angle oblique incidence in periodic media.

A spatial modes filtering finite-element time-domain method with nonuniform subgridding mesh (NUSSMF-FETD) is proposed to enhance the modeling flexibility and computation efficiency of electromagnetic simulations with fine structures. Taking the nonuniform rectangular meshes as local refinement elements causes complex edge distributions in subgridding elements, the element and system matrices construction process of nonuniform subgridding FETD (NUS-FETD) is given in detail. Then the NUSSMF-FETD is obtained by introducing the spatial modes filtering (SMF) method. NUS-FETD effectively reduces the unknowns in local refinement regions compared to the uniform subgridding FETD (US-FETD). On this basis, NUSSMF-FETD can expand the time step and also keep computation accurate and efficient. The NUSSMF-FETD based on local eigenvalue solution (LES-NUSSMF-FETD) further reduces the time and memory consumption of system eigenvalue analysis. Numerical results present that the NUSSMF-FETD method has high spatial modeling flexibility and computation efficiency.