A provably stable summation-by-parts simultaneous approximation term (SBP-SAT) finite-difference time-domain (FDTD) subgridding method without region split is proposed. By designing projection SBP operators tailored for embedded topological features and deriving the corresponding SAT boundary conditions, this approach guarantees long-time stability through discrete energy analysis. Unlike conventional SBP-SAT FDTD subgridding techniques that rely on aligned or multi-block configurations, the proposed method enables a direct coupling between an internal refined region and a single surrounding coarse-grid domain without introducing auxiliary blocks or causing domain fragmentation. Numerical results validate the efficiency, accuracy, and topological flexibility of the proposed method. Compared with existing multi-block SBP-SAT methods, this method effectively reduces computational complexity by minimizing SAT boundary conditions and improves calculation accuracy near grid interfaces.
@article{arxiv.2604.14618,
title = {A Stable SBP-SAT FDTD Subgridding Method Without Region Split},
author = {Yuhui Wang and Langran Deng and Weibo Wu and Hanhong Liu and Xinyue Zhang and Xingqi Zhang and Jian Wang and Wei-Jie Wang and Zhizhang Chen and Shunchuan Yang},
journal= {arXiv preprint arXiv:2604.14618},
year = {2026}
}