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arXiv · 1906.06221

On the numerical solution of a time-dependent shape optimization problem for the heat equation

Rahel Brügger·Helmut Harbrecht·Johannes Tausch
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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.

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Rahel Brügger, Helmut Harbrecht, Johannes Tausch. 2019-06-14. On the numerical solution of a time-dependent shape optimization problem for the heat equation. https://arxiv.org/abs/1906.06221

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