On Model Order Reduction and Exponential Integrator for Transient Circuit Simulation

Model order reduction (MOR) has long been a mainstream strategy to accelerate large scale transient circuit simulation. Exponential integrator (EI) based on Krylov subspace approximation methods, on the other hand, are more recently developed for a similar goal. This article aims to examine in-depth the underlying relationship between model order reduction (MOR) and exponential integrator (EI) that are commonly seen as two separate methods. The main finding is that EI can be viewed as a moment-matching MOR in the time-domain. Specifically, EI, under certain conditions, is equivalent to performing moment-matching MOR based on rational Krylov subspace projection at each time step with a single input vector and a selected expansion point, then advancing the reduced system one step in the time-domain. The equivalence is mathematically proved under different settings and numerically verified in the experiments. Their differences in the transient circuit analysis context are also elaborated from various perspectives. It is hoped that these new insights would benefit the future development of this classical EDA topic.