Decoupled Polynomial Chaos and Its Applications to Statistical Analysis of High-Speed Interconnects

This paper presents a new Hermite-based approach to circuit variability analysis using the polynomial-chaos (PC) paradigm. The new approach is aimed at limiting the growth of the computational cost with the increase in the number of random variables and the number of Hermite coefficients used to represent the circuit response in each random variable. The proposed method is based on deriving a closed form for the structure of the augmented matrices generated by the PC approach. It then develops an algorithm to decouple the large augmented matrices into independent matrices that can be factorized in parallel. Several numerical examples are presented to demonstrate the computational efficiency of the proposed method and its ability to handle the increasing dimension of random space.