Model Reduction by Proper Orthogonal Decomposition Coupled With Centroidal Voronoi Tessellations (Keynote)

Proper orthogonal decompositions (POD) have been used to define reduced bases for low-dimensional approximations of complex systems, including turbulent flows. Centroidal Voronoi tessellations (CVT) have been used in a variety of data compression and clustering settings. We review both strategies in the context of model reduction for complex systems and propose combining the ideas of CVT and POD into a hybrid method that inherets favorable characteristics from both its parents. The usefulness of such an approach and various practical implementation strategies are discussed.