On the numerical solution of a time-dependent shape optimization problem for the heat equation
Optimization and Control
2019-06-17 v1
Abstract
This article is concerned with the solution of a time-dependent shape identification problem. Specifically we consider the heat equation in a domain, which contains a time-dependent inclusion of zero temperature. The objective is to detect this inclusion from the given temperature and heat flux at the exterior boundary of the domain. To this end, for a given temperature at the exterior boundary, the mismatch of the Neumann data is minimized. This time-dependent shape optimization problem is then solved by a gradient-based optimization method. Numerical results are presented which validate the present approach.
Keywords
Cite
@article{arxiv.1906.06221,
title = {On the numerical solution of a time-dependent shape optimization problem for the heat equation},
author = {Rahel Brügger and Helmut Harbrecht and Johannes Tausch},
journal= {arXiv preprint arXiv:1906.06221},
year = {2019}
}