Cooling and related thermal problems are the principal challenges facing 3D integrated circuits (3D-ICs). Active cooling techniques such as integrated inter-tier liquid cooling are promising alternatives for traditional fan-based cooling, which is insufficient for 3D-ICs. In this regard, fast full-chip transient thermal modeling and simulation techniques are required to design efficient and cost-effective cooling solutions for optimal performance, cost and reliability of packages and 3D ICs. In this paper, we propose an efficient finite difference based full-chip simulation algorithm for 3D-ICs using the GMRES method based on CPU platforms. Unlike existing fast thermal analysis methods, the new method starts from the physics-based heat equations to model 3D-ICs with inter-tier liquid cooling microchannels and directly solves the resulting partial differential equations using GMRES. To speedup the simulation, we further develop a preconditioned GPU-accelerated GMRES solver, GPU-GMRES, to solve the resulting thermal equations on top of some published sparse numerical routines. Experimental results show the proposed GPU-GMRES solver is up to 4.3× faster than parallel CPU-GMRES for DC analysis and 2.3× faster than parallel LU decomposition and one or two orders of magnitude faster than the single-thread CPU-GMRES for transient analysis on a number of thermal circuits and other published problems.
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