Improved polynomial chaos discretization schemes to integrate interconnects into design environments
Improved polynomial chaos discretization schemes to integrate interconnects into design environments
复制标题
改进的多项式混沌离散方案将互连集成到设计环境中
DOI：
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发表时间：
2013
影响因子：
3
通讯作者：
F. Canavero
中科院分区：
文献类型：
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作者：
Paolo Manfredi;D. Ginste;D. Zutter;F. Canavero
最近，提出了一种有效的随机建模方法的互连与固有的可变性，在其物理参数的基础上，应用所谓的多项式混沌（PC）的方法结合随机Galerkin方法（SGM）电报员的方程。虽然这种方法从数值的角度来看已经非常成功，但这种新技术不能方便地集成到SPICE类求解器中，限制了该方法的适用性。在这封信中，PC-SGM计划电报员的方程重新审视，查明这种不便的起源，并立即允许减轻问题。通过适应传统的离散化的随机电报员的方程的方法，一个增强的，但确定性的，一组常微分方程，原来是相同类型的电报员的方程，因此，互惠的物理属性被保存。因此，它可以直接和更有效地处理使用SPICE类求解器，通常假设矩阵对称。作为一个应用实例，一个国家的最先进的片上线毫米波应用的变异性分析是在SPICE求解器中进行的。
Recently, an efficient stochastic modeling method for interconnects with inherent variability in their physical parameters was proposed, based on applying the so-called polynomial chaos (PC) approach in conjunction with a Stochastic Galerkin Method (SGM) onto telegrapher's equations. Although this approach was already very successful from a numerical point of view, the novel technique could not be conveniently integrated into SPICE-like solvers, limiting the applicability of the method. In this letter, the PC-SGM scheme for telegrapher's equations is revisited, pinpointing the origin of this inconvenience and immediately allowing to mitigate the issue. By adapting the traditional discretization of the stochastic telegrapher's equations approach, an augmented, yet deterministic, set of ordinary differential equations is obtained that turns out to be of the same type as the telegrapher's equations, and hence, the physical property of reciprocity is preserved. Consequently, it can be directly and more efficiently handled using SPICE-like solvers, which usually assume matrix symmetries. As an application example, the variability analysis of a state-of-the-art on-chip line for millimeter-wave applications is performed in a SPICE solver.