An iterative BEM for the Cauchy steady state heat conduction problem in ananisotropic medium with unknown thermal conductivity tensor

In this paper we propose an alternating iterative boundary element method ( BEM) to simultaneously predict the unknown conductivity coefficients and th e unknown boundary data for a Cauchy steady state heat conduction problem i n an anisotropic medium. This complex ill-posed problem is obtained by comb ining a Cauchy inverse thermal problem with a parameter estimation problem. The numerical algorithm is based on an iterative (BEM) combined with a lea st squares technique. The numerical results obtained confirm that provided that an appropriate stopping regularization criterion is imposed, the itera tive BEM produces a convergent and stable numerical solution with respect t o increasing the number of boundary elements and decreasing the amount of n oise added into the input data. An efficient stopping regularization criter ion to cease the iterative process is proposed and a variable relaxation fa ctor is used to increase the rate of convergence of the algorithm.