The method of fundamental solutions for inverse boundary value problems associated with the steady-state heat conduction in anisotropic media

In this paper, the method of fundamental solutions is applied to solve some inverse boundary value problems associated with the steady-state heat conduction in an anisotropic medium. Since the resulting matrix equation is severely ill-conditioned, a regularized solution is obtained by employing the truncated singular value decomposition, while the optimal regularization parameter is chosen according to the L-curve criterion. Numerical results are presented for both two- and three-dimensional problems, as well as exact and noisy data. The convergence and stability of the proposed numerical scheme with respect to increasing the number of source points and the distance between the fictitious and physical boundaries, and decreasing the amount of noise added into the input data, respectively, are analysed. A sensitivity analysis with respect to the measure of the accessible part of the boundary and the distance between the internal measurement points and the boundary is also performed. The numerical results obtained show that the proposed numerical method is accurate, convergent, stable and computationally efficient, and hence it could be considered as a competitive alternative to existing methods for solving inverse problems in anisotropic steady-state heat conduction