Fast Transient Simulation of System-Level Power Delivery Networks via Parallel Waveform Relaxation

This application paper addresses the problem of transient simulation of system-level power distribution networks (PDNs) of multicore processing systems. In particular, we consider a postlayout power integrity (PI) verification problem where all system parts are finalized and a highly accurate transient verification is performed to ensure that voltage supply signals remain within prescribed bounds when the PDN is loaded by realistic current stimuli. Systems with tens of even hundreds of cores are considered, equipped with per-core local voltage stabilization, attained through integrated voltage regulators (IVRs) suitably controlled by sensing and feedback loops. Transient simulation of such system-level PDNs becomes particularly challenging when interconnect models or macromodels computed by electromagnetic solvers are embedded. In order to break system complexity, we propose a set of algorithms based on an ad hoc system partitioning strategy, combined with multilevel waveform relaxation (WR) schemes. The main advantage of this approach is a straightforward parallelization, aimed at solving concurrently by parallel computing threads only small and well-defined circuit partitions. Several partitioning and associated WR schemes are discussed and tested, showing excellent scalability with up to 60 computing threads, with significant speedup in runtime with respect to a standard SPICE-based approach.