Graduate Thesis Or Dissertation
 

Nonlinear model reduction using the group proper orthogonal decomposition method

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/g732dc61m

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  • Proper orthogonal decomposition (POD) in conjunction with the Galerkin projection has been used as a model reduction technique for the tractable real-time control of high-dimensional systems. While POD based model reduction may improve the tractability of high-dimensional models, the nonlinear POD based model may be impractical for control due to the cost of computing its nonlinear terms. In this work, a new technique designed to reduce the computational cost of nonlinear POD models is introduced. This technique extends ideas from the group finite element method to POD and is called the group POD method. A forced, single variable, two dimensional Burgers’ equation is used as a model problem to assess group POD method. Simulations of group POD models for Burgers’ equation are shown to accurately converge to analytically known benchmark solutions. For Burgers’ equation, a preliminary mathematical investigation shows the group POD method may reduce the computational cost of the nonlinear terms as compared to the standard POD method.
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