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Computational Mechanics
Published in: Computational Mechanics 4/2021

09-07-2021 | Original Paper

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

Authors: Andreea–Paula Voinea–Marinescu, Liviu Marin

Published in: Computational Mechanics | Issue 4/2021

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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.
previous article Hierarchical modeling of length-dependent force generation in cardiac muscles and associated thermodynamically-consistent numerical schemes
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Metadata
Title
Fading regularization MFS algorithm for the Cauchy problem in anisotropic heat conduction
Authors
Andreea–Paula Voinea–Marinescu
Liviu Marin
Publication date
09-07-2021
Publisher
Springer Berlin Heidelberg
Published in
Computational Mechanics / Issue 4/2021
Print ISSN: 0178-7675
Electronic ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-021-02052-y

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