A Stable SBP-SAT FDTD Subgridding Method Without Region Split

TL;DR

This paper introduces a stable SBP-SAT FDTD subgridding method that avoids region splitting, enabling direct coupling of refined and coarse regions with improved efficiency and accuracy.

Contribution

The proposed method achieves stability without region split by designing tailored projection SBP operators and SAT boundary conditions, simplifying implementation and enhancing topological flexibility.

Findings

Ensures long-time stability via discrete energy analysis.

Reduces computational complexity compared to multi-block methods.

Validates efficiency, accuracy, and flexibility through numerical results.

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.