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BEM-Fading regularization algorithm for Cauchy problems in 2D anisotropic heat conduction

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Abstract

We investigate the numerical reconstruction of the missing thermal boundary data on a part of the boundary for the steady-state heat conduction equation in anisotropic solids from the knowledge of exact or noisy Cauchy data on the remaining and accessible boundary. This inverse boundary value problem is tackled by applying and adapting to the anisotropic case the algorithm based on the fading regularization method, originally proposed by Cimetière, Delvare, and Pons (Comptes Rendus de l’Académie des Sciences - Série IIb - Mécanique, 328 639–644 2000), and Cimetière, Delvare, et al. (Inverse Probl., 17 553–570 2001) for the isotropic heat conduction equation. The numerical implementation is realised for 2D homogeneous solids by using the boundary element method, whilst the numerical solution is stabilized/regularized by stopping the iterative process based on an L-curve type criterion (Hansen 1998).

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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

  4. Normandie University, F–14032, Caen, France

    Franck Delvare

  5. UNICAEN, LMNO, F–14032, Caen, France

    Franck Delvare

  6. CNRS, UMR 6139, F–14032, Caen, France

    Franck Delvare

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

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Voinea–Marinescu, A., Marin, L. & Delvare, F. BEM-Fading regularization algorithm for Cauchy problems in 2D anisotropic heat conduction. Numer Algor 88, 1667–1702 (2021). https://doi.org/10.1007/s11075-021-01090-0

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  • DOI: https://doi.org/10.1007/s11075-021-01090-0

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