Proper orthogonal decomposition for reduced order modeling: 2D heat flow
Efe, M. Ö.
Proceedings of 2003 IEEE Conference on Control Applications, CCA 2003
1273 - 1277
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Modeling issues of infinite dimensional systems is studied in this paper. Although the modeling problem has been solved to some extent, use of decomposition techniques still pose several difficulties. A prime one of this is the amount of data to be processed. Method of snapshots integrated with POD is a remedy. The second difficulty is the fact that the decomposition followed by a projection yields an autonomous set of finite dimensional ODEs that is not useful for developing a concise understanding of the input operator of the system. A numerical approach to handle this issue is presented in this paper. As the example, we study 2D heat flow problem. The results obtained confirm the theoretical claims of the paper and emphasize that the technique presented here is not only applicable to infinite dimensional linear systems but also to nonlinear ones.
Ordinary differential equations
Finite dimensional ordinary differential equations
Proper orthogonal decomposition
Reduced order modeling
Control system synthesis