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

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 ).