2015/12/06 by Alessandro Alla, Alla, Alessandro, Carmen Graessle +3
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Nuclear reactor physics and engineering #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1512.01813
openalex publication_date 2015/12/06 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
In this paper we study the approximation of a distributed optimal control\nproblem for linear para -bolic PDEs with model order reduction based on Proper\nOrthogonal Decomposition (POD-MOR). POD-MOR is a Galerkin approach where the\nbasis functions are obtained upon information contained in time snapshots of\nthe parabolic PDE related to given input data. In the present work we show that\nfor POD-MOR in optimal control of parabolic equations it is important to have\nknowledge about the controlled system at the right time instances. For the\ndetermination of the time instances (snapshot locations) we propose an\na-posteriori error control concept which is based on a reformulation of the\noptimality system of the underlying optimal control problem as a second order\nin time and fourth order in space elliptic system which is approximated by a\nspace-time finite element method. Finally, we present numerical tests to\nillustrate our approach and to show the effectiveness of the method in\ncomparison to existing approaches.\n