Implementation of harmonic balance reduced model order equation

A model order reduction technique (MOR) for nonlinear circuit solution was recently proposed by E. Gad and M. Nakhla, that it can significantly reduce a system order while preserving the accuracy of the solution. This method presents however a bottleneck in constructing a pre-conditioner matrix which is ought to reduce the system size. Especially when the nonlinear device equations used are not explicitly defined. This paper will present a numerical differentiator method to try to overcome this limitation.