Nested Sparse-grid Stochastic Collocation Method and Its Application to Gate Delay Modeling under Process Variations

Abstract

In this paper,an extended Gaussian quadrature based nested sparse-grid stochastic collocation method(NSSCM) is proposed for further improving the computation accuracy and efficiency of stochastic gate delay modeling considering process variation.Firstly,the orthogonal polynomial bases in the stochastic space of gate parameters are employed in NSSCM to approximate the stochastic gate delay and exponential convergence rate is achieved.Secondly,the proposed NSSCM employs one-dimensional extended Gaussian quadrature points and sparse grid technique to construct the nested multidimensional collocation points.Compared with the existing non-nested sparse-grid stochastic collocation method(SSCM),the nested collocation points used in NSSCM not only maintain the high computation precision of Gaussian quadrature,but also have the nested property to guarantee that gate delays obtained at low order collocation points can be reused in high order quadrature.The reuse of collocation points can remarkably improve the computation accuracy and efficiency of gate delay modeling.Experimental results demonstrated the merits of the proposed method.