2016/08/30 by Alessandro Alla, Alla, Alessandro, Carmen Graessle +3
Decision Sciences · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Hydraulic Fracturing and Reservoir Analysis #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #math.OC
paper · pdf · doi:10.48550/arxiv.1608.08665
23 pages. arXiv admin note: text overlap with arXiv:1512.01813
arxiv created 2016/08/30 · openalex publication_date 2016/08/30 · arxiv updated 2016/09/01 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
In this paper we study the approximation of an optimal control problem for linear para\-bolic 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 an a-posteriori error control concept. This 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 to show the effectiveness of the method in comparison to existing approaches.