Model Reduction and Simulation of Nonlinear Circuits via Tensor Decomposition

Model order reduction of nonlinear circuits (especially highly nonlinear circuits), has always been a theoretically and numerically challenging task. In this paper we utilize tensors (namely, a higher order generalization of matrices) to develop a tensor-based nonlinear model order reduction (TNMOR) algorithm for the efficient simulation of nonlinear circuits. Unlike existing nonlinear model order reduction methods, in TNMOR high-order nonlinearities are captured using tensors, followed by decomposition and reduction to a compact tensor-based reducedorder model. Therefore, TNMOR completely avoids the dense reduced-order system matrices, which in turn allows faster simulation and a smaller memory requirement if relatively lowrank approximations of these tensors exist. Numerical experiments on transient and periodic steady-state analyses confirm the superior accuracy and efficiency of TNMOR, particularly in highly nonlinear scenarios.