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A projected iterative method based on integral equations for inverse heat conduction in domains with a cut
Ivan Franko National University of Lviv, Ukraine .
Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology. Östergötlands Läns Landsting, Heart and Medicine Center, Department of Nephrology.ORCID iD: 0000-0001-9066-7922
Ivan Franko National University of Lviv, Ukraine .
2013 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 29, no 6, 065003- p.Article in journal (Refereed) Published
Abstract [en]

The Cauchy problem for the parabolic heat equation, consisting of the reconstruction of the solution from knowledge of the temperature and heat flux on a part of the boundary of the solution domain, is investigated in a planar region containing a cut. This linear inverse ill-posed problem is numerically solved using an iterative regularization procedure, where at each iteration step mixed Dirichlet-Neumann problems for the parabolic heat equation are used. Using the method of Rothe these mixed problems are reduced to a sequence of boundary integral equations. The integral equations have a square root singularity in the densities and logarithmic and hypersingularities in the kernels. Moreover, the mixed parabolic problems have singularities near the endpoints of the cut. Special techniques are employed to handle each of these (four) types of singularities, and analysis is performed in weighted spaces of square integrable functions. Numerical examples are included showing that the proposed regularizing procedure gives stable and accurate approximations.

Place, publisher, year, edition, pages
Institute of Physics: Hybrid Open Access , 2013. Vol. 29, no 6, 065003- p.
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-96123DOI: 10.1088/0266-5611/29/6/065003ISI: 000320039200003OAI: oai:DiVA.org:liu-96123DiVA: diva2:640766
Available from: 2013-08-14 Created: 2013-08-14 Last updated: 2017-12-06

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