We propose a new method to reduce the cost of computing nonlinear terms in projec- tion based reduced order models with global basis functions. We develop this method by extending ideas from the group nite 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 e cient than standard POD models of Burgers' equation.
B. T. Dickinson and J. R. Singler, "Nonlinear Model Reduction Using Group Proper Orthogonal Decomposition," International Journal of Numerical Analysis and Modeling, vol. 7, no. 2, pp. 356 - 372, Institute for Scientific Computing and Information, Jan 2010.
Mathematics and Statistics
Article - Journal
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01 Jan 2010