A Parallel Floating Random Walk Solver for Reproducible and Reliable Capacitance Extraction

The floating random walk (FRW) method is a popular and promising tool for capacitance extraction, but its stochastic nature leads to critical limitations in reproducibility and physics-related reliability. In this work, we present FRW- RR, a parallel FRW solver with enhancements for Reproducible and Reliable capacitance extraction. First, we propose a novel parallel FRW scheme that ensures reproducible results, regardless of the degree of parallelism (DOP) or machine used. We further optimize its parallel efficiency and enhance the numerical stability. Then, to guarantee the physical properties of capacitances and reliability for downstream tasks, we propose a regularization technique based on constrained multi-parameter estimation to postprocess FRW's results. Experiments on actual IC structures demonstrate that, FRW-RR ensures DOP-independent reproducibility (with at least 12 decimal significant digits) and physics-related reliability with negligible overhead. It has remarkable advantages over existing FRW solvers, including the one in [1].