Boundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method

In this paper, we consider an inverse boundary value prob- lem for two-dimensional heat equation in an annular domain. This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat ux) on the exterior boundary curve. To this end, the boundary integral equation method is used. Since the resulting system of linear algebraic equations is ill-posed, the Tikhonov rst-order regularization procedure is employed to obtain a stable solution. Determination of regularization parameter is based on L-curve technique. Some numerical examples for the feasibility of the proposed method are presented.