Thermal tomography with unknown boundary
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Authors
Date
2018-01-01
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Language
en
Pages
B662-B683
Series
SIAM Journal on Scientific Computing, Volume 40, issue 3
Abstract
Thermal tomography is an imaging technique for deducing information about the internal structure of a physical body from temperature measurements on its boundary. This work considers time-dependent thermal tomography modeled by a parabolic initial/boundary value problem without accurate information on the exterior shape of the examined object. The adaptive sparse pseudospectral approximation method is used to form a polynomial surrogate for the dependence of the temperature measurements on the thermal conductivity, the heat capacity, the boundary heat transfer coefficient, and the body shape. These quantities can then be efficiently reconstructed via nonlinear, regularized least squares minimization employing the surrogate and its derivatives. The functionality of the resulting reconstruction algorithm is demonstrated by numerical experiments based on simulated data in two spatial dimensions.Description
Keywords
Inaccurate measurement model, Inverse boundary value problems, Sparse pseudospectral approximation, Thermal tomography
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Citation
Hyvönen, N & Mustonen, L 2018, ' Thermal tomography with unknown boundary ', SIAM Journal on Scientific Computing, vol. 40, no. 3, pp. B662-B683 . https://doi.org/10.1137/16M1104573