EI-MOR: A Hybrid Exponential Integrator and Model Order Reduction Approach for Transient Power/Ground Network Analysis

Exponential integrator (EI) method has been proved to be an effective technique to accelerate large-scale transient power/ground network analysis. However, EI requires the inputs to be piece-wise linear (PWL) in one step, which greatly limits the step size when the inputs are poorly aligned. To address this issue, in this work we first elucidate with mathematical proof that EI, when used together with the rational Krylov subspace, is equivalent to performing a moment-matching model order reduction (MOR) with single input in each time step, then advancing the reduced system using EI in the same step. Based on this equivalence, we next devise a hybrid method, EI-MOR, to combine the usage of EI and MOR in the same transient simulation. A majority group of well-aligned inputs are still treated by EI as usual, while a few misaligned inputs are selected to be handled by a MOR process producing a reduced model that works for arbitrary inputs. Therefore the step size limitation imposed by the misaligned inputs can be largely alleviated. Numerical experiments are conducted to demonstrate the efficacy of the proposed method.