Fast Variational Analysis of On-Chip Power Grids by Stochastic Extended Krylov Subspace Method
Fast Variational Analysis of On-Chip Power Grids by Stochastic Extended Krylov Subspace Method
复制标题
随机扩展 Krylov 子空间方法对片上电网的快速变分分析
DOI：
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发表时间：
2008
影响因子：
2.9
通讯作者：
Xianlong Hong
中科院分区：
文献类型：
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作者：
N. Mi;S. Tan;Yici Cai;Xianlong Hong
本文提出了一种新颖的随机方法，用于分析片上电网的电压降变化，并考虑对数正态漏电流变化。这种新方法称为 StoEKS，应用 Hermite 多项式混沌来表示电网网络和输入泄漏电流中的随机变量。然而，与现有的基于正交多项式的随机模拟方法不同，扩展Krylov子空间（EKS）方法被用来计算由Hermite多项式系数组成的增广矩阵的变分响应。我们的贡献在于首次使用EKS方法加速谱随机方法快速求解变分电路方程。通过使用缩减技术，新方法部分缓解了与基于伽辽金谱随机方法的增广矩阵相关的电路尺寸增加问题。实验结果表明，该方法比现有的基于 Hermite PC 的仿真方法快约两个数量级，比带有边际误差的蒙特卡罗方法快多个数量级。与现有的基于 PC 的 Hermit 方法相比，StoEKS 具有可扩展性，可以分析更大的电路。
This paper proposes a novel stochastic method for analyzing the voltage drop variations of on-chip power grid networks, 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, extended 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 partially 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 scalable for analyzing much larger circuits than the existing Hermit PC-based methods.