Deflated Restarting of Exponential Integrator Method for Efficient Transient Circuit Simulation

Abstract

Exponential integrator (EI) method based on Krylov subspace approximation is a promising method for large-scale transient circuit simulation, which however suffers from large subspace dimension required to achieve convergence when the circuit is stiff. Restarting is commonly applied to alleviate the storage issues associated with the large subspace dimension, but it also slow down the convergence and degrading the overall computational efficiency. In this work, we develop a deflated restarting technique to accelerate the convergence of restarted Krylov subspace approximation for EI methods for transient simulation of stiff circuits. The technique deflates a specific invariant subspace of the matrix that impedes the convergence of the restarted approximation process. Numerical experiments demonstrate that proposed method largely accelerates the convergence of restarted Krylov subspace approximation compared to the non-deflated version.