Applications of Mathematics, Vol. 63, No. 6, pp. 687-712, 2018


Application of Calderón's inverse problem in civil engineering

Jan Havelka, Jan Sýkora

Received November 20, 2017.   Published online December 3, 2018.

Abstract:  In specific fields of research such as preservation of historical buildings, medical imaging, geophysics and others, it is of particular interest to perform only a non-intrusive boundary measurements. The idea is to obtain comprehensive information about the material properties inside the considered domain while keeping the test sample intact. This paper is focused on such problems, i.e. synthesizing a physical model of interest with a boundary inverse value technique. The forward model is represented here by time dependent heat equation with transport parameters that are subsequently identified using a modified Calderón problem which is numerically solved by a regularized Gauss-Newton method. The proposed model setup is computationally verified for various domains, loading conditions and material distributions.
Keywords:  Calderón problem; finite element method; diffusion equation; boundary inverse value method; Neumann-to-Dirichlet map
Classification MSC:  65M32, 35K05
DOI:  10.21136/AM.2018.0323-17

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Affiliations:   Jan Havelka, Jan Sýkora, Czech Technical University in Prague, Faculty of Civil Engineering, Deparment of Mechanics, Thákurova 7, 166 29 Praha 6, Czech Republic, e-mail: jan.havelka.1@fsv.cvut.cz, jan.sykora.1@fsv.cvut.cz


 
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