Iteration-Based Temporal Subgridding Method for the Finite-Difference Time-Domain Algorithm

A novel temporal subgridding technique is proposed for the finite-difference time-domain (FDTD) method to solve two-dimensional Maxwell's equations of electrodynamics in the TEz mode. Based on the subgridding FDTD algorithm with a separated spatial and temporal interface, our method focuses on the temporal subgridding region, as it is the main source of late-time instability. Different from other subgridding algorithms that work on the interpolation between coarse and fine meshes, our method stabilizes the solution by using iterative updating equations on the temporal coarse-fine mesh interface. This new method presents an alternative approach aimed at improving the stability of the subgridding technique without modifying the interpolation formulas. We numerically study the stability of the proposed algorithm via eigenvalue tests and by performing long-term simulations. We employ a refinement ratio of 2:1 in our study. Our findings indicate the stability of the conventional temporal subgridding FDTD algorithm with a magnetic field (Hz) interpolation. However, when electric fields (Ex and Ey) are utilized in interpolation, late-time instability occurs. In contrast, the proposed iteration-based method with an electric field interpolation appears to be stable. We further employ our method as the forward problem solver in the Through-the-Wall Radar (TWR) imaging application.