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Volume 4, Issue 3-4
Reduced-Order Modeling of Burgers Equations Based on Centroidal Voronoi Tessellation

Hyung-Chun Lee, Sung-Whan Lee & Guang-Ri Piao

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

Published online: 2007-04

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  • 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

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@Article{IJNAM-4-559, author = {Lee , Hyung-ChunLee , Sung-Whan and Piao , Guang-Ri}, title = {Reduced-Order Modeling of Burgers 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 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.

Lee , Hyung-ChunLee , Sung-Whan and Piao , Guang-Ri. (2007). Reduced-Order Modeling of Burgers Equations Based on Centroidal Voronoi Tessellation. International Journal of Numerical Analysis and Modeling. 4 (3-4). 559-583. doi:
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