Snapshot location for POD in control of a linear heat equation |
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| Authors: | Alessandro Alla Carmen Gräßle Michael Hinze |
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| Institution: | 1. Florida State University, Department of Scientific Computing, 400 Dirac Science Library, Tallahassee, FL 32306, USA;2. Universität Hamburg, Department of Mathematics, Bundesstr. 55, 20146 Hamburg, Germany |
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| Abstract: | In the present work, we study the approximation of a distributed optimal control problem for a linear heat equation with model order reduction based on Proper Orthogonal Decomposition (POD-MOR). We show that snapshot location for control problems is crucial in model reduction. For the determination of the time instances (snapshot locations) we utilize an a-posteriori error control concept which 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. Finally, we present a numerical test to illustrate our approach. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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