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.

翻译：本文提出了一种无需区域分割、可证明稳定的求和-分部-同时逼近项（SBP-SAT）时域有限差分（FDTD）子网格方法。通过设计适用于嵌入拓扑特征的投影SBP算子，并推导相应的SAT边界条件，本方法通过离散能量分析保证了长时间稳定性。与传统依赖对齐或多块配置的SBP-SAT FDTD子网格技术不同，所提方法能够实现内部细化区域与单一外部粗网格域之间的直接耦合，无需引入辅助块或造成区域碎片化。数值结果验证了所提方法的效率、精度和拓扑灵活性。与现有多块SBP-SAT方法相比，本方法通过最小化SAT边界条件有效降低了计算复杂度，并提高了网格界面附近的计算精度。