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Fading regularization MFS algorithm for the Cauchy problem in anisotropic heat conduction

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Abstract

The Cauchy problem in 2D and 3D steady-state anisotropic heat conduction is investigated for both exact and perturbed data, i.e. the numerical reconstruction of the missing temperature and normal heat flux on a part of the boundary from the knowledge of exact or noisy Cauchy data on the remaining and accessible boundary. This inverse Cauchy problem is solved by applying and adapting the fading regularization method, proposed by Cimetière et al.  [7, 8] for the steady-state isotropic heat conduction, to the anisotropic case. An appropriate stabilizing/regularizing stopping criterion for the resulting iterative algorithm is provided for each type of Cauchy data considered. The numerical implementation is realized for 2D and 3D homogeneous solids by using the meshless method of fundamental solutions.

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Funding

This work was supported by a grant of Ministry of Research and Innovation, CNCS–UEFISCDI, Project Number PN–III–P4–ID–PCE–2016–0083, within PNCDI III.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics and Computer Science, University of Bucharest, 14 Academiei, 010014, Bucharest, Romania

    Andreea–Paula Voinea–Marinescu & Liviu Marin

  2. Research Institute of the University of Bucharest (ICUB), University of Bucharest, 90–92 Şos. Panduri, 050663, Bucharest, Romania

    Andreea–Paula Voinea–Marinescu & Liviu Marin

  3. Gheorghe Mihoc – Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 13 Calea 13 Septembrie, 050711, Bucharest, Romania

    Liviu Marin

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  1. Andreea–Paula Voinea–Marinescu
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  2. Liviu Marin
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Correspondence to Liviu Marin.

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Voinea–Marinescu, A., Marin, L. Fading regularization MFS algorithm for the Cauchy problem in anisotropic heat conduction. Comput Mech 68, 921–941 (2021). https://doi.org/10.1007/s00466-021-02052-y

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