Volume 4, Issue 3-4
Reduced-order Modeling of Burger Equations Based on Centroidal Voronoi Tessellation

A Kunoth, M. Schlichtenmayer & C. Schneider

DOI:

Int. J. Numer. Anal. Mod., 4 (2007), pp. 559-583

Published online: 2007-04

Preview Purchase PDF 0 826
Export citation
  • Abstract

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.

  • Keywords

reduced-order modeling proper orthogonal decomposition centroidal Voronoi tessellations Burgers equations

  • AMS Subject Headings

35B40 35B37 35Q30 65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{IJNAM-4-559, author = {A Kunoth, M. Schlichtenmayer and C. Schneider}, title = {Reduced-order Modeling of Burger Equations Based on Centroidal Voronoi Tessellation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2007}, volume = {4}, number = {3-4}, pages = {559--583}, abstract = {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. }, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/878.html} }
TY - JOUR T1 - Reduced-order Modeling of Burger Equations Based on Centroidal Voronoi Tessellation AU - A Kunoth, M. Schlichtenmayer & C. Schneider JO - International Journal of Numerical Analysis and Modeling VL - 3-4 SP - 559 EP - 583 PY - 2007 DA - 2007/04 SN - 4 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/ijnam/878.html KW - reduced-order modeling KW - proper orthogonal decomposition KW - centroidal Voronoi tessellations KW - 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.
A Kunoth, M. Schlichtenmayer & C. Schneider. (1970). Reduced-order Modeling of Burger Equations Based on Centroidal Voronoi Tessellation. International Journal of Numerical Analysis and Modeling. 4 (3-4). 559-583. doi:
Copy to clipboard
The citation has been copied to your clipboard