An inverse geometry problem for a one-dimensional heat equation: advances with complex temperatures

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TitreAn inverse geometry problem for a one-dimensional heat equation: advances with complex temperatures
Type de publicationArticle de revue
AuteurJolly, Jean-Claude , Perez, Laetitia , Autrique, Laurent
EditeurTaylor & Francis
TypeArticle scientifique dans une revue à comité de lecture
Année2014
LangueAnglais
Numéro1
Pagination63-83
Volume22
Titre de la revueInverse Problems in Science and Engineering
ISSN1741-5977
Résumé en anglais

This paper presents an inverse problem in heat conduction, namely the determination of thicknesses of three materials of known heat capacities and thermal conductivities inside a rod of given length subjected to periodic heat flows from measurements of temperatures at both ends. The unknowns are, therefore, the positions of the two interior frontiers between the three materials. Classically, they can be obtained by minimizing the least-squares, non-linear criterion, between the measured and calculated temperatures. Nevertheless, we show that the global minimum providing the solution is close to three local minima that act as traps for a descent algorithm. After providing theoretical justification of the complex temperature method, a method based in this case on the periodicity of boundary fluxes, we suggest a new criterion allowing the global characterization or not of an a priori local minimizer to be tested. It is a criterion of topological nature based on the identification of a singularity.

URL de la noticehttp://okina.univ-angers.fr/publications/ua5800
DOI10.1080/17415977.2013.827186
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http://dx.doi.org/10.1080/17415977.2013.827186