Piecewise polynomial nonlinear model reduction

We present a novel, general approach towards model-order reduc-tion (MOR) of nonlinear systems that combines good global and lo-cal approximation properties. The nonlinear system is first approx-imated as piecewise polynomials over a number of regions, follow-ing which each region is reduced via polynomial model-reduction methods. Our approach, dubbed PWP, generalizes recent piece-wise linear approaches and ties them with polynomial-based MOR, thereby combining their advantages. In particular, reduced models obtained by our approach reproduce small-signal distortion and in-termodulation properties well, while at the same time retaining fi-delity in large-swing and large-signal analyses, e.g., transient sim-ulations. Thus our reduced models can be used as drop-in replace-ments for time-domain as well as frequency-domain simulations, with small or large excitations. By exploiting sparsity in system polynomial coefficients, we are able to make the polynomial reduc-tion procedure linear in the size of the original system. We provide implementation details and illustrate PWP with an example