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Volume 7, Issue 2
Nonlinear Model Reduction Using Group Proper Orthogonal Decomposition

B. T. Dickinson & J. R. Singler

Int. J. Numer. Anal. Mod., 7 (2010), pp. 356-372.

Published online: 2010-07

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  • Abstract

We propose a new method to reduce the cost of computing nonlinear terms in projection based reduced order models with global basis functions. We develop this method by extending ideas from the group finite element (GFE) method to proper orthogonal decomposition (POD) and call it the group POD method. Here, a scalar two-dimensional Burgers' equation is used as a model problem for the group POD method. Numerical results show that group POD models of Burgers' equation are as accurate and are computationally more efficient than standard POD models of Burgers' equation.

  • Keywords

Model reduction, proper orthogonal decomposition, group finite element, nonlinear.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-356, author = {Dickinson , B. T. and Singler , J. R.}, title = {Nonlinear Model Reduction Using Group Proper Orthogonal Decomposition}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {2}, pages = {356--372}, abstract = {

We propose a new method to reduce the cost of computing nonlinear terms in projection based reduced order models with global basis functions. We develop this method by extending ideas from the group finite element (GFE) method to proper orthogonal decomposition (POD) and call it the group POD method. Here, a scalar two-dimensional Burgers' equation is used as a model problem for the group POD method. Numerical results show that group POD models of Burgers' equation are as accurate and are computationally more efficient than standard POD models of Burgers' equation.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/724.html} }
TY - JOUR T1 - Nonlinear Model Reduction Using Group Proper Orthogonal Decomposition AU - Dickinson , B. T. AU - Singler , J. R. JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 356 EP - 372 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/724.html KW - Model reduction, proper orthogonal decomposition, group finite element, nonlinear. AB -

We propose a new method to reduce the cost of computing nonlinear terms in projection based reduced order models with global basis functions. We develop this method by extending ideas from the group finite element (GFE) method to proper orthogonal decomposition (POD) and call it the group POD method. Here, a scalar two-dimensional Burgers' equation is used as a model problem for the group POD method. Numerical results show that group POD models of Burgers' equation are as accurate and are computationally more efficient than standard POD models of Burgers' equation.

Dickinson , B. T. and Singler , J. R.. (2010). Nonlinear Model Reduction Using Group Proper Orthogonal Decomposition. International Journal of Numerical Analysis and Modeling. 7 (2). 356-372. doi:
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