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Fading regularization MFS algorithm for the Cauchy problem in anisotropic heat conduction. (English) Zbl 1478.80002

Summary: 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.

MSC:

80A23 Inverse problems in thermodynamics and heat transfer
80A19 Diffusive and convective heat and mass transfer, heat flow
35K05 Heat equation
35B65 Smoothness and regularity of solutions to PDEs
80M50 Optimization problems in thermodynamics and heat transfer
65K10 Numerical optimization and variational techniques
65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs
35R30 Inverse problems for PDEs
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