A Stable SBP-SAT FDTD Subgridding Method Without Region Split
For computational electromagnetics practitioners, this method simplifies subgridding implementation while ensuring long-time stability, offering a more efficient and accurate alternative to existing multi-block techniques.
This paper introduces a provably stable SBP-SAT FDTD subgridding method that eliminates the need for region split, enabling direct coupling between refined and coarse grids without auxiliary blocks. Numerical results demonstrate reduced computational complexity and improved accuracy near grid interfaces compared to multi-block approaches.
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.