A coupled iterative/direct method for efficient time-domain simulation of nonlinear circuits with power/ground networks

A coupled iterative/direct circuit analysis method is proposed for efficient SPICE-accurate time-domain simulation of nonlinear circuits with large-scale power/ground networks. The system under study is partitioned into a linear part including power/ground networks, a nonlinear part, and an interface between them. The part of power/ground networks is formulated by nodal analysis based on RCLK elements, and solved by an efficient conjugate gradient iterative method with an incomplete Cholesky decomposition preconditioner. The nonlinear circuit part is formulated by modified nodal analysis, and solved by the direct method as in SPICE. The iterative method and the direct method are coupled by a Gauss-Seidel like relaxation scheme with SPICE built-in varying time step-size numerical integration. How the condition number of a circuit matrix changes with time step-sizes is further studied. Experimental results on digital circuits with power/ground networks demonstrate that the proposed coupled iterative/direct method yields SPICE-like accuracy with orders of magnitude speedup for circuits with tens of thousands of elements.