Domain Transformation and Decomposition Method for Composable Thermal Modeling and Simulation of Chiplet-Based 2.5D Integrated System

Dynamic thermal analysis is imperative to ensure the reliability of chiplet-based 2.5D integrated systems. However, conventional simulation techniques typically incur high computational cost, especially in transient scenarios. In this paper, we propose a domain transformation and decomposition method (DTDM) to perform composable thermal modeling and simulation with high efficiency and accuracy. Temporally, the DTDM expands the time-variant temperature response into a sum of weighted Laguerre polynomials (WLPs). By leveraging Galerkin’s method and the orthogonality of WLPs, the heat conduction equation is transformed from the time domain to the Laguerre domain, thus breaking through the bottleneck of conventional marching-on-in-time approaches in terms of stability and efficiency. Spatially, the DTDM decomposes the system into multiple composable modules (CMs) according to the structural and functional characteristics. For each CM, a novel Laguerre-based macro-model is constructed to represent its internal heat transfer properties by mapping the relationship between the temperature and heat flux at the interface. Finally, the CMs are assembled together as a complete system by treating the macromodels as equivalent thermal boundary conditions, which reduces the computational complexity in both the temporal and spatial domains and thus facilitates efficient transient simulation. Moreover, since the resulting Laguerre-based macromodels are reusable in different system configurations, the DTDM is particularly suitable for composable thermal modeling and simulation. Numerical experiments on typical 2.5 D chiplet-based integrated systems show that the proposed method delivers a $485 \times$ speedup compared to the commercial software, while maintaining a maximum absolute error below 0.02 K.