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On the reformulation of the classical Stefan problem as a shape optimization problem

Brügger, Rahel and Harbrecht, Helmut. (2021) On the reformulation of the classical Stefan problem as a shape optimization problem. Preprints Fachbereich Mathematik, 2021 (08).

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Abstract

This article is concerned with the multi-dimensional one-phase Stefan problem, which belongs to the class of moving boundary problems. We suggest to reformulate the classical Stefan problem as a shape optimization problem, consisting of an objective functional for the moving boundary and a partial differential equation corresponding to a heat type equation. Minimizing the objective functional subject to the differential equation under consideration is equivalent to solving the Stefan problem. In order to apply gradient-based optimization algorithms, we analytically compute the shape gradient of the objective functional. A numerical example justifies our approach.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Brügger, Rahel and Harbrecht, Helmut
Item Type:Preprint
Publisher:Universität Basel
Language:English
edoc DOI:
Last Modified:08 Apr 2021 17:03
Deposited On:08 Apr 2021 17:03

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