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An efficient numerical method for a shape-identification problem arising from the heat equation

Harbrecht, Helmut and Tausch, Johannes. (2011) An efficient numerical method for a shape-identification problem arising from the heat equation. Inverse problems, Vol. 27, H. 6 , 065013.

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Official URL: http://edoc.unibas.ch/dok/A6001463

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Abstract

This paper is dedicated to the determination of the shape of a compactly supported constant source in the heat equation from measurements of the heat flux through the boundary. This shape-identification problem is formulated as the minimization of a least-squares cost functional for the desired heat flux at the boundary. The shape gradient of the shape functional under consideration is computed by means of the adjoint method. A gradient-based nonlinear Ritz–Galerkin scheme is applied to discretize the shape optimization problem. The state equation and its adjoint are computed by a fast space-time multipole method for the heat equation. Numerical experiments are carried out to demonstrate the feasibility and scope of the present approach.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut
Item Type:Article, refereed
Article Subtype:Research Article
Bibsysno:Link to catalogue
Publisher:IOP Publ.
ISSN:0266-5611
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:08 Nov 2012 16:22
Deposited On:08 Nov 2012 16:11

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