Reduced-order modeling of Burger equations based on centroidal Voronoi Tessellation
Hyung-Chun Lee 1*, Sung-Whan Lee 1, Guang-Ri Piao 11 Department of Mathematics, Ajou University, Suwon, Korea 443-749
Received by the editors February 15, 2006 and, in revised form, February 23, 2006.
In this paper, we study a reduced-order modeling for Burgers equations. Review of the CVT (centroidal Voronoi tessellation) 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. We shall investigate the technique of CVT as a procedure to determine the basis elements for the approximating subspaces. Some numerical experiments including comparison of CVT-based algorithm with numerical results obtained from FEM (finite element method) and POD- based algorithm are reported. Finally, we apply CVT-based reduced order modeling technique to a feedback control problem for Burgers equation.
AMS subject classifications: 35B40, 35B37, 35Q30, 65M60
Key words: reduced-order modeling; proper orthogonal decomposition; centroidal Voronoi tessellations; Burgers equations