POD for optimal control of the Cahn-Hilliard system using spatially adapted snapshots
Optimization and Control
2018-03-08 v2
Abstract
The present work considers the optimal control of a convective Cahn-Hilliard system, where the control enters through the velocity in the transport term. We prove the existence of a solution to the considered optimal control problem. For an efficient numerical solution, the expensive high-dimensional PDE systems are replaced by reduced-order models utilizing proper orthogonal decomposition (POD-ROM). The POD modes are computed from snapshots which are solutions of the governing equations which are discretized utilizing adaptive finite elements. The numerical tests show that the use of POD-ROM combined with spatially adapted snapshots leads to large speedup factors compared with a high-fidelity finite element optimization.
Keywords
Cite
@article{arxiv.1712.06523,
title = {POD for optimal control of the Cahn-Hilliard system using spatially adapted snapshots},
author = {Carmen Gräßle and Michael Hinze and Nicolas Scharmacher},
journal= {arXiv preprint arXiv:1712.06523},
year = {2018}
}