TY - JOUR T1 - Reduced-Order Modeling of Burgers Equations Based on Centroidal Voronoi Tessellation AU - Lee , Hyung-Chun AU - Lee , Sung-Whan AU - Piao , Guang-Ri JO - International Journal of Numerical Analysis and Modeling VL - 3-4 SP - 559 EP - 583 PY - 2007 DA - 2007/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/878.html KW - reduced-order modeling, proper orthogonal decomposition, centroidal Voronoi tessellations, Burgers equations. AB -
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.