Efficient multidimensional statistical modeling of high speed interconnects in SPICE via stochastic collocation using stroud cubature

In this paper, a novel stochastic collocation approach for the efficient statistical analysis of high-speed interconnect networks within a SPICE environment is proposed. This approach employs the Stroud cubature rules to locate the sparse grid of collocation nodes within the random space where the deterministic SPICE simulations of the network are performed. The major advantage of this approach lies in the fact that the number of collocation nodes scales optimally (i.e. linearly) with the number of random dimensions unlike the exponential or polynomial scaling exhibited by the conventional tensor product grids or the Smolyak sparse grids respectively. This enables the quantification of the statistical moments for interconnect networks involving large random spaces at only a fraction of the typical CPU cost. The validity of this methodology is demonstrated using a numerical example.