A Tutorial on Nonlinear Model Order Reduction

This tutorial introduces nonlinear methods for model order reduction of structures discretised with finite elements, with a particular emphasis on the case of geometric nonlinear structures. The aim of model order reduction (MOR) is to reduce the dimensionality of a large system of nonlinear ordinary differential equations by performing a change of coordinates from the original ones to new reduced ones. The two main ingredients of each (MOR) method are (i) the change of coordinates and (ii) the reduced dynamics in the new coordinate system. Specifically, nonlinear methods differ from linear-based techniques, as they rely on a nonlinear change of coordinates rather than the addition of new vectors to enlarge the linear projection basis.