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A posteriori snapshot location for POD in optimal control of linear parabolic equations

Journal Article · · Mathematical Modelling and Numerical Analysis
DOI:https://doi.org/10.1051/m2an/2018009· OSTI ID:1611199
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In this paper we study the approximation of an optimal control problem for linear parabolic PDEs with model order reduction based on Proper Orthogonal Decomposition (POD-MOR). POD-MOR is a Galerkin approach where the basis functions are obtained upon information contained in time snapshots of the parabolic PDE related to given input data. In the present work we show that for POD-MOR in optimal control of parabolic equations it is important to have knowledge about the controlled system at the right time instances. We propose to determine the time instances (snapshot locations) by ana posteriorierror control concept. The proposed method is based on a reformulation of the optimality system of the underlying optimal control problem as a second order in time and fourth order in space elliptic system which is approximated by a space-time finite element method. Finally, we present numerical tests to illustrate our approach and show the effectiveness of the method in comparison to existing approaches.

Research Organization:
Florida State Univ., Tallahassee, FL (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
SC0009324
OSTI ID:
1611199
Journal Information:
Mathematical Modelling and Numerical Analysis, Vol. 52, Issue 5; ISSN 0764-583X
Publisher:
EDP Sciences
Country of Publication:
United States
Language:
English

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