Back-Scaling Based Exponential Integrator Method with Multi-Process Parallel Processing for Transient Power/Ground Network Analysis

The exponential integrator (EI) method has proven to be an effective technique for accelerating transient circuit simulation. Owing to its higher accuracy order, EI can use larger step sizes to speed up the simulation without compromising accuracy. However, leaping with large steps may sometimes omit some fine-grained variations of the waveforms, especially for power/ground network analysis where over/under-shoots are important. We propose a back-scaling technique to address this issue to complete the detailed waveform between two consecutive time points in EI simulation without extra LU factorizations or triangular solves. The key is to re-use the Krylov subspace generated at the starting time point and scale the step size to obtain solutions at any place between the two endpoints, exploiting the special scaling invariant property of the Krylov subspace in EI. In addition, we also develop a multi-process parallelization based on MPI to accelerate the back-scaling process. Numerical experiments are conducted to demonstrate the accuracy and efficacy of the proposed method.