Power grid analysis with hierarchical support graphs

It is increasingly challenging to analyze present day large-scale power delivery networks (PDNs) due to the drastically growing complexity in power grid design. To achieve greater runtime and memory efficiencies, a variety of preconditioned iterative algorithms has been investigated in the past few decades with promising performance, while incremental power grid analysis also becomes popular to facilitate fast re-simulations of corrected designs. Although existing preconditioned solvers, such as incomplete matrix factor-based preconditioners, usually exhibit high efficiency in memory usage, their convergence behaviors are not always satisfactory. In this work, we present a novel hierarchical support-graph preconditioned iterative algorithm that constructs preconditioners by generating spanning trees in power supply networks for fast power grid analysis. The support-graph preconditioner is efficient for handling complex power grid structures (regular or irregular grids), and can facilitate very fast incremental analysis. Our experimental results on IBM power grid benchmarks show that compared with the best direct or iterative solvers, the proposed support-graph preconditioned iterative solver achieves up to 3.6X speedups for DC analysis, and up to 22X speedups for incremental analysis, while reducing the memory consumption by a factor of four.