Inverse Heat Conduction Problem in Two-Dimensional Anisotropic Medium

Abstract

The study proposes a novel mesh-free scheme for a two-dimensional space and tests its efficiency for the inverse heat conduction problem in an anisotropic medium. It aims at determining unknown data at the inaccessible boundary with the help of an approximate solution constructed as a linear combination of fundamental solutions and heat polynomials. The advantage of using this combination lies in the fact that it yields ‘shape functions’ which are in turn solution of the considered equation. The crucial point to note here is that the proposed method yields highly accurate results and the number of collocation points required by the altered scheme are lesser than the standard method of fundamental solutions (MFS). As a direct consequence of the ill-posed problem, a highly ill-conditioned system is obtained, which is solved using regularization. Further, numerical results are provided for two-dimensional convex and non-convex domains to prove that the efficiency of the new scheme is slightly better than the traditional MFS, especially for noisy data.