Nonlinear Model Reduction: Methods and Applications
by
Jeff Borggaard
Virginia Tech

Model reduction is the process of generating low dimensional systems that approximate behavior of large or infinite dimensional systems. These reduced-order models can then be used in a variety of applications where full-order (or high fidelity numerical simulations) would be prohibitive, such as control, optimization, or gaining better understanding of the underlying dynamics in the system. We begin by discussing the most common method for performing this reduction, proper orthogonal decomposition followed by Galerkin projection. We then present a number of extensions and applications.

Date received: September 11, 2007