Fast variational analysis of on-chip power grids by stochastic extended Krylov subspace method

Abstract—This paper proposes a novel stochastic method for analyzing the voltage drop variations of on-chip power grid net-works, considering lognormal leakage current variations. The new method, called StoEKS, applies Hermite polynomial chaos to represent the random variables in both power grid networks and input leakage currents. However, different from the existing orthogonal polynomial-based stochastic simulation method, ex-tended Krylov subspace (EKS) method is employed to compute variational responses from the augmented matrices consisting of the coefficients of Hermite polynomials. Our contribution lies in the acceleration of the spectral stochastic method using the EKS method to fast solve the variational circuit equations for the first time. By using the reduction technique, the new method par-tially mitigates increased circuit-size problem associated with the augmented matrices from the Galerkin-based spectral stochastic method. Experimental results show that the proposed method is about two-order magnitude faster than the existing Hermite PC-based simulation method and many order of magnitudes faster than Monte Carlo methods with marginal errors. StoEKS is scal-able for analyzing much larger circuits than the existing Hermit PC-based methods. Index Terms — Extended Krylov subspace method, on-chip power grids, statistic analysis