2016/08/30 by Alessandro Alla, Alla, Alessandro, Carmen Graessle +3
Decision Sciences · Engineering · 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
paper · pdf · doi:10.48550/arxiv.1608.08665
openalex publication_date 2016/08/30 · 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\nlinear para -bolic PDEs with model order reduction based on Proper Orthogonal\nDecomposition (POD-MOR). POD-MOR is a Galerkin approach where the basis\nfunctions are obtained upon information contained in time snapshots of the\nparabolic PDE related to given input data. In the present work we show that for\nPOD-MOR in optimal control of parabolic equations it is important to have\nknowledge about the controlled system at the right time instances. We propose\nto determine the time instances (snapshot locations) by an a-posteriori error\ncontrol concept. This method is based on a reformulation of the optimality\nsystem of the underlying optimal control problem as a second order in time and\nfourth order in space elliptic system which is approximated by a space-time\nfinite element method. Finally, we present numerical tests to illustrate our\napproach and to show the effectiveness of the method in comparison to existing\napproaches.\n