Electromagnetics-Based Co-Simulation of Linear Network and Nonlinear Circuits Accelerated by Time-Domain Orthogonal Finite-Element Reduction-Recovery Method

摘要

The co-simulation of electromagnetic structures and nonlinear circuits has been explored in the framework of the finite-difference time-domain method, the time-domain finiteelement method [1], and the time-domain integral equation method. However, they often have been found not amenable for on-chip VLSI design because of unique on-chip modeling challenges and large number of nonlinear devices. Recently, a time-domain layered finite-element reduction-recovery (LAFE-RR) based nonlinear-linear cosimulation algorithm was developed for solving large-scale integrated circuits and package problems [2-3]. This method can reduce the system matrix of 0(N) rigorously to that of 0(M) for any multilayered structure, with N being the number of unknowns in the entire 3-D structure, and M the number of unknowns on a single surface. Furthermore, the reduction from O(N) to O(M) was achieved analytically. The reduced linear-nonlinear coupled system is solved and the rest of the unknowns are then recovered in linear complexity. However, the reduced single-surface linear-nonlinear system is a strongly coupled system which either introduces a dense submatrix in the Jacobian matrix of the Newton's method or introduces extra iterations in the solution procedure. When the number of devices is large, the large dense submatrix or the large number of iterations will limit the capacity of this algorithm.