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

Brügger, Rahel and Harbrecht, Helmut. (2022) On the reformulation of the Classical Stefan problem as a shape optimization problem. SIAM Journal on Control and Optimization (SICON), 60 (1). pp. 310-329.

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Official URL: https://edoc.unibas.ch/87474/

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This article is concerned with the multidimensional 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)
UniBasel Contributors:Harbrecht, Helmut and Brügger, Rahel Christina
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Society for Industrial and Applied Mathematics
Note:Publication type according to Uni Basel Research Database: Journal article
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edoc DOI:
Last Modified:04 Jul 2022 07:10
Deposited On:04 Jul 2022 07:10

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