ADAPTIVE CVT-BASED REDUCED-ORDER MODELING OF BURGERS EQUATION

  • Piao, Guang-Ri (DEPARTMENT OF MATHEMATICS, YANBIAN UNIVERSITY) ;
  • Du, Qiang (DEPARTMENT OF MATHEMATICS, PENNSYLVANIA STATE UNIV., UNIVERSITY PARK) ;
  • Lee, Hyung-Chun (DEPARTMENT OF MATHEMATICS, AJOU UNIVERSITY)
  • Received : 2009.05.12
  • Accepted : 2009.05.30
  • Published : 2009.06.25

Abstract

In this article, we consider a weighted CVT-based reduced-order modelling for Burgers equation. Brief 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. So far, the CVT was researched with uniform density ($\rho$(y) = 1) to determine the basis elements for the approximatin subspaces. Here, we shall investigate the technique of CVT with nonuniform density as a procedure to determine the basis elements for the approximating subspaces. Some numerical experiments including comparison of two CVT (CVT-uniform and CVT-nonuniform)-based algorithm with numerical results obtained from FEM(finite element method) and POD-based algorithm are reported.

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