Physics-aware domain decomposition for high-speed PCB signal integrity analysis using spectral clustering

This paper proposes an efficient domain decomposition method based on spectral clustering to address the challenge of signal integrity (SI) analysis for large-scale high-speed multilayer printed circuit boards (PCBs). Traditional full-wave electromagnetic simulation methods have excessively high computational costs for complex entire PCBs, while existing geometric segmentation methods easily damage strong coupling regions, reducing simulation accuracy. A physics-based broadband analytical coupling model for vias and striplines is established to quickly evaluate electromagnetic coupling strength between interconnect structures. A weighted adjacency matrix constructs the PCB’s coupling topology, and an adaptive spectral clustering algorithm intelligently identifies weak coupling boundaries for automatic region division. Each subdomain is solved via a finite element solver. Numerical experiments demonstrate that for a 42-layer high-speed complex PCB, the proposed method achieves good agreement with full-board full-wave simulation in the 0–40 GHz frequency band while reducing computational time by up to 96%, showing a significant acceleration effect and providing an effective approach for signal integrity analysis of large-scale complex PCB systems.