A Stable SBP-SAT FDTD Subgridding Method Without Region Split

2026-04-16

AI Summary

This work proposes a stable subgridding method for SBP-SAT FDTD that eliminates the need for domain decomposition or multi-block structures, which traditionally lead to high computational complexity and domain fragmentation. By designing embedding-aware projection SBP operators together with compatible SAT boundary conditions, the approach enables direct coupling between fine and coarse grids within a single computational domain. This strategy avoids auxiliary blocks or explicit domain partitioning, substantially reducing the number of SAT interfaces while preserving long-term numerical stability and enhancing interfacial accuracy. Numerical experiments demonstrate that the proposed method outperforms existing approaches in terms of computational efficiency, solution accuracy, and topological flexibility.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Application Domains: Humanities & Computational Social Science
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

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.

Problem

• FDTD subgridding
• SBP-SAT
• region split
• grid refinement
• numerical stability

Innovation

• SBP-SAT
• FDTD subgridding
• projection operators
• discrete energy stability
• topological flexibility