Exploring the exponential integrators with Krylov subspace algorithms for nonlinear circuit simulation

Abstract

We explore Krylov subspace algorithms to calculate ϕ functions of exponential integrators for circuit simulation. Higham [1] pointed out the potential numerical stability risk of ϕ functions computation. However, for the applications to circuit analysis, the choice of methods remains open. This work inspects the accuracy of matrix exponential and vector product with Krylov subspace methods, and identifies the proper approach to achieving numerically stable solutions for nonlinear circuits. Empirial results verify the quality of the proposed methods using various orders of ϕ functions. Furthermore, instead of Newton-Raphson (NR) iterations in conventional methods, an iterative residue correction algorithm is devised for nonlinear system analysis. The stability and efficiency of our methods are illustrated with experiments.