Reduced-order modeling of complex systems with multiple system parameters

Abstract

The computational approximation of solutions of complex systems such as the Navier-Stokes equations is often a formidable task. For example, in feedback control settings where one often needs solutions of the complex systems in real time, it would be impossible to use large-scale finite element or finite-volume or spectral codes. For this reason, there has been much interest in the development of low-dimensional models that can accurately be used to simulate and control complex systems. Reduced-order modeling approaches based on proper orthogonal decompositions and centroidal Voronoi tessellations are discussed. The important implementation issue of how boundary conditions containing multiple parameters are handled in the reduced-order modeling context is highlighted. © Springer-Verlag Berlin Heidelberg 2006.