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Fading regularization MFS algorithm for the Cauchy problem in anisotropic heat conduction
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DOI：10.1007/s00466-021-02052-y.png)
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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 Cimetiere 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.
Keyword:
Inverse problem
Cauchy problem
Anisotropic heat conduction
Fading regularization method
Method of fundamental solutions
Meshless method
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