嵌套式稀疏网格随机配置法及其在随机门延时建模中的应用

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

为了提高随机工艺偏差下门延时建模的计算精度和效率,提出一种基于扩展Gauss积分理论及嵌套式稀疏网格技术的随机配置门延时建模方法.首先采用参数空间中具有指数收敛特性的随机正交多项式对随机门延时进行逼近;然后针对现有的基于传统Gauss积分理论的稀疏网格随机配置法所用的配置点不具有嵌套特性的问题,利用单变量扩展Gauss积分理论及稀疏网格技术构造了一组嵌套式多变量Gauss积分点,将其作为随机门延时建模的配置点.这组配置点既具有Gauss积分点的高精度,又满足嵌套性质,且在低阶积分配置点上已经得到的门延时可以在高阶积分时重复使用.与现有的基于非嵌套式配置点的随机配置法相比,该方法的计算精度和效率可以得到很大的提升,数值实验结果也验证了该方法在计算精度和效率上的优势.

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.