Use of the boundary element method to determine the thermal conductivity tensor of an anisotropic medium

In this paper, we propose a numerical algorithm to simultaneously predict the unknown conductivity coefficients and the unknown boundary data for a steady-state heat conduction problem in an anisotropic medium. The algorithm is based on a classical boundary element method (BEM) which is combined with a least squares technique. The numerical convergence and stability of the method proposed is investigated with respect to increasing the number of additional measurements provided and decreasing the amount of noise added into the input data.