Nonlinear model reduction using group proper orthogonal decomposition
Benjamin T. Dickinson 1, John R. Singler 21 School of Mechanical, Industrial, and Manufacturing Engineering, Oregon State University, Corvallis, OR 97331, USA.
2 Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409, USA.
Received by the editors September 5, 2008 and, in revised form, August 3, 2009.
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.AMS subject classifications: 35R35, 49J40, 60G40
Key words: Model reduction, proper orthogonal decomposition, group finite element, nonlinear.
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