Adjoint-Based Optimal Control of Time-Dependent Free Boundary Problems
Abstract
In this paper we show a simplified optimisation approach for free boundary problems in arbitrary space dimensions. This approach is mainly based on an extended operator splitting which allows a decoupling of the domain deformation and solving the remaining partial differential equation. First we give a short introduction to free boundary problems and the problems occurring in optimisation. Then we introduce the extended operator splitting and apply it to a general minimisation subject to a time-dependent scalar-valued partial differential equation. This yields a time-discretised optimisation problem which allows us a quite simple application of adjoint-based optimisation methods. Finally, we verify this approach numerically by the optimisation of a flow problem (Navier-Stokes equation) and the final shape of a Stefan-type problem.
Cite
@article{arxiv.1212.3789,
title = {Adjoint-Based Optimal Control of Time-Dependent Free Boundary Problems},
author = {Jan Marburger},
journal= {arXiv preprint arXiv:1212.3789},
year = {2013}
}