Non-intrusive Variability Analysis of Large Circuits with Parallelism in the Stochastic Space and Time-Domain

We propose an efficient method for time-domain variability analysis of circuits described by large systems of equations. An embarrassingly parallel technique is proposed in both the stochastic space and the time-domain, which is not possible if standard time-domain integration techniques are used in the analysis. The proposed method is based on stochastic collocation and numerical inversion of Laplace transform. The stochastic collocation algorithm selects the nodes (samples) in the space of the stochastic parameters in a parsimonious way by means of sparse grids. This is a non-intrusive sampling-based approach. Numerical inversion of Laplace transform is used to compute the time-domain response of the model at each node. This technique allows the computation of the response at different time instances independently, making the transient simulation amenable to parallel computation, which is not possible with standard time-marching techniques commonly used for circuit simulation. Next, the time-domain responses obtained at each node are used by the stochastic collocation scheme to compute stochastic information (e.g., mean and standard deviation). Pertinent numerical results are presented to validate the efficiency, accuracy, and parallelism feature of the proposed method.