Efficient Representation and Analysis of Power Grids

Modern deep sub-micron ULSI designs with hundreds of millions of devices require huge grids for power distribution. Such grids, operating with increasingly low-power voltages, are a design limiting factor and accurate analysis of their behavior is of paramount importance as any voltage drops can seriously impact performance or functionality. As power grid models have millions of unknowns, highly optimized special purpose simulation tools are required to handle the time and memory complexity of solving for their dynamic behavior. In this work, we propose a hierarchical matrix representation of the power grid model that is both space and time efficient. With this representation, reduced storage matrix factors are efficiently computed and applied in the analysis at every time-step of the simulation. Results show an almost linear complexity growth, namely O(n log^a (n)), for some small constant a, in both space and time, when using this matrix representation. Comparisons of our academic implementation with production-quality code proves this method to be very efficient when dealing with the simulation of large power grid models.