An adaptive POD approximation method for the control of advection-diffusion equations
Optimization and Control
2016-02-22 v1
Abstract
We present an algorithm for the approximation of a finite horizon optimal control problem for advection-diffusion equations. The method is based on the coupling between an adaptive POD representation of the solution and a Dynamic Programming approximation scheme for the corresponding evolutive Hamilton-Jacobi equation. We discuss several features regarding the adaptivity of the method, the role of error estimate indicators to choose a time subdivision of the problem and the computation of the basis functions. Some test problems are presented to illustrate the method.
Cite
@article{arxiv.1302.4072,
title = {An adaptive POD approximation method for the control of advection-diffusion equations},
author = {Alessandro Alla and Maurizio Falcone},
journal= {arXiv preprint arXiv:1302.4072},
year = {2016}
}
Comments
17 pages, 18 figures