Identification of the heterogeneous conductivity in an inverse heat conduction problem
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Publication:6129544
DOI10.1002/NME.7156arXiv2208.11165OpenAlexW4307987392MaRDI QIDQ6129544
Author name not available (Why is that?)
Publication date: 17 April 2024
Published in: (Search for Journal in Brave)
Abstract: This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in , from the knowledge of the state over the whole domain. We develop a method based on a variational approach leading to an optimality equation which is then projected into a finite dimensional space. Discretization yields a linear although severely ill-posed equation which is then regularized via appropriate ad-hoc penalizers resulting a in a generalized Tikhonov-Phillips functional. No smoothness assumptions are imposed on the conductivity. Numerical examples for the case in which the conductivity can take only two prescribed values (a two-materials case) show that the approach is able to produce very good reconstructions of the exact solution.
Full work available at URL: https://arxiv.org/abs/2208.11165
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