THERMEXP: An Efficient Thermal Analysis Method via Matrix Exponential

Nowadays, thermal management of integrated circuits (ICs) has become a critical challenge due to increasing power densities and miniaturization. Efficient thermal analysis methodologies are essential to prevent overheating and ensure the reliability and longevity of electronic components. While the problem formulation using a thermal equivalent circuit can be easily constructed, solving the corresponding 3D equations network involves time-consuming numerical simulations. While Dynamic Compact Thermal Models (DCTMs) can reduce computational complexity, there are several cases where they cannot capture all the heat transfer interactions, leading to less accurate results. To this end, we propose a fast semi-analytical approach, based on the matrix exponential, for the solution of large-scale thermal models. The proposed method incorporates the extended Krylov subspace (EKS) technique to effectively simulate large thermal models and speed up the computation of the final solution. Experimental results on several benchmarks demonstrate that our methodology can achieve speedups of up to 139.52× compared to an established arithmetic method and 29.65× compared to DCTMs, while maintaining negligible error.