Recently, CVT(centroidal Voronoi tessellation) is applied reduced order models for dynamical systems. In this thiesis, we have studied for distributed and boundary feedback control of Burgers equation with reduced order models based on CVT.
First, review of the CVT schematic approaches to reduced-order bases are provided. In CVT-reduced order modelling, we start with a snapshot set just as is done in a POD(proper orthogonal decomposition)-based setting.
Secondly, we develop the reduced-order feedback control for spatially distributed Burgers equation via CVT method. In this method, the density is taken to be uniform(constant) and we call this case as the ``CVT-uniform" algorithm.
Finally, we shall introduce a new algorithm of CVT as a procedure to determine the basis elements for the approximating subspaces. In the CVT new algorithm, the focus is choice of nonuniform (variable) density and we call this case as the ``CVT-nonuniform" algorithm. We describe some numerical experiments including comparison of CVT(CVT-uniform, CVT-nonuniform)-based algorithm with numerical results obtained from FEM(finite element method) and POD-based algorithm. We apply CVT-nonuniform-based reduced-order modelling technique to a boundary feedback control problem for Burgers equation.
