Analysis and Improvement of the Stability of a 3-D FDTD Subgridding Method by Applying an LECT-Based Technique

Abstract

This article studies and improves the stability of a finite-difference time-domain (FDTD) subgridding method based on the orthogonalized-integral-based methodology. First, we identify the electric and magnetic field components of the FDTD lattices used at the interface between different mesh regions playing a critical role in its stability. Then, we use them to find a closed criterion for the Courant–Friedrichs–Lewy number (CFLN). Next, we analyze the stability by the classical spectral method and validate it with numerical heuristic simulations, proving the methodology used in the analytical approach. This information is used to devise a locally enlarged cell technique (LECT) to modify locally the scheme used to update the field components identified as most critical for stability so that an increased time step can be used. Finally, we analyze the effect of these modifications on the accuracy of the method for typical transmission and scattering problems.