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

Harbrecht, Helmut and Tausch, Johannes. (2013) On the numerical solution of a shape optimization problem for the heat equation. SIAM journal on scientific computing, Vol. 35, H. 1 , A104-A121.

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Official URL: http://edoc.unibas.ch/dok/A6070666

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Abstract

The present paper is concerned with the numerical solution of a shape identification problem for the heat equation. The goal is to determine of the shape of a void or inclusion of zero temperature from measurements of the temperature and the heat flux at the exterior boundary. This nonlinear and ill-posed shape identification problem is reformulated in terms of three different shape optimization problems: (a) minimization of a least-squares energy variational functional, (b) tracking of the Dirichlet data, and (c) tracking of the Neumann data. The states and their adjoint equations are expressed as parabolic boundary integral equations and solved using a Nyström discretization and a space-time fast multipole method for the rapid evaluation of thermal potentials. Special quadrature rules are derived to handle singularities of the kernel and the solution. Numerical experiments are carried out to demonstrate and compare the different formulations.
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:SIAM
ISSN:1064-8275
Note:Publication type according to Uni Basel Research Database: Journal article
Last Modified:13 Sep 2013 07:57
Deposited On:24 May 2013 08:58

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