An enlarged-partition based preconditioned iterative solver for parallel power grid simulation

This paper presents a novel parallel preconditioned iterative solver for VLSI power grid simulation. Although preconditioned iterative methods for power grid simulation have been proposed during the past years, parallelization of such methods is not well explored. Our algorithm divides the power grid into several disjoint partitions and computes an estimate of the global solution from solutions obtained on each partition. A key idea is to enlarge each partition by carefully selecting nodes and edges outside the partition such that the accuracy of the partition solution is increased significantly without much change in the computational cost. The global solution obtained by solving enlarged partition problems concurrently acts as a highly effective parallel preconditioner due to the spatial locality of power grids. A combination of effective preconditioning and efficient parallelization results in significant performance improvement [13.91X-34.35X] over a state-of-the-art direct solver on IBM power grid benchmarks.