A parallel fast transform-based preconditioning approach for electrical-thermal co-simulation of power delivery networks

Efficient analysis of massive on-chip power delivery networks is among the most challenging problems facing the EDA industry today. Due to Joule heating effect and the temperature dependence of resistivity, temperature is one of the most important factors that affect IR drop and must be taken into account in power grid analysis. However, the sheer size of modern power delivery networks (comprising several thousands or millions of nodes) usually forces designers to neglect thermal effects during IR drop analysis in order to simplify and accelerate simulation. As a result, the absence of accurate estimates of Joule heating effect on IR drop analysis introduces significant uncertainty in the evaluation of circuit functionality. This work presents a new approach for fast electrical-thermal co-simulation of large-scale power grids found in contemporary nanometer-scale ICs. A state-of-the-art iterative method is combined with an efficient and extremely parallel preconditioning mechanism, which enables harnessing the computational resources of massively parallel architectures, such as graphics processing units (GPUs). Experimental results demonstrate that the proposed method achieves a speedup of 66.1X for a 3.1M-node design over a state-of-the-art direct method and a speedup of 22.2X for a 20.9M-node design over a state-of-the-art iterative method when GPUs are utilized.