CAJ | 학술논문

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.
위료제고수궤공예편차하문연시건모적계산정도화효솔,제출일충기우확전Gauss적분이론급감투식희소망격기술적수궤배치문연시건모방법.수선채용삼수공간중구유지수수렴특성적수궤정교다항식대수궤문연시진행핍근;연후침대현유적기우전통Gauss적분이론적희소망격수궤배치법소용적배치점불구유감투특성적문제,이용단변량확전Gauss적분이론급희소망격기술구조료일조감투식다변량Gauss적분점,장기작위수궤문연시건모적배치점.저조배치점기구유Gauss적분점적고정도,우만족감투성질,차재저계적분배치점상이경득도적문연시가이재고계적분시중복사용.여현유적기우비감투식배치점적수궤배치법상비,해방법적계산정도화효솔가이득도흔대적제승,수치실험결과야험증료해방법재계산정도화효솔상적우세.
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.