A quadratic method for nonlinear model order reduction

In order to simulate and optimize efficiently systems which include micromachined devices, designers need dynamically accurate macromodels for the those devices. Although it is possible to develop such macromodels by hand, it would be vastly more efficient if it were possible to automatically derive such macromodels directly from physical coupled-domain simulation. Although such automatic techniques exist if the problem is linear, most micromachined devices are at least mildly nonlinear and new techniques must be developed. In this paper we present a quadratic reduction method which makes use of the Krylov subspace generated from linearized analysis. The result is a reduced-order model with a quadratic nonlinearity. Results on using the method for a nonlinear resistor network show that the nonlinear approach is much more accurate than using a linearized approach alone.