A Stable SBP-SAT FDTD Subgridding Method Without Region Split

Yuhui Wang; Langran Deng; Weibo Wu; Hanhong Liu; Xinyue Zhang; Xingqi Zhang; Jian Wang; Wei-Jie Wang; Zhizhang Chen; Shunchuan Yang

arXiv · 2604.14618

A Stable SBP-SAT FDTD Subgridding Method Without Region Split

Yuhui Wang·Langran Deng·Weibo Wu·Hanhong Liu·Xinyue Zhang·Xingqi Zhang·Jian Wang·Wei-Jie Wang·Zhizhang Chen·Shunchuan Yang

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Abstract

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.

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Yuhui Wang, Langran Deng, Weibo Wu, Hanhong Liu, Xinyue Zhang, Xingqi Zhang, Jian Wang, Wei-Jie Wang, Zhizhang Chen, Shunchuan Yang. 2026-04-16. A Stable SBP-SAT FDTD Subgridding Method Without Region Split. https://arxiv.org/abs/2604.14618

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