Comparative analysis of inverse coefficient problems for parabolic equations. Part II: Coarse-fine grid algorithm

This article presents a computational analysis of the adjoint problem approach for parabolic inverse coefficient problems based on boundary measured data. The proposed coarse-fine grid algorithm constructed on the basis of this approach is an effective computational tool for the numerical solution of inverse coefficient problems with various Neumann or/and Dirichlet type measured output data. In the previous Part I paper it was shown that the ill-posedness also depends on where Neumann and Dirichlet conditions are given: in the direct problem or as an output data. Based on integral identities relating solutions of direct problems to appropriate adjoint problems solutions, a coarse-fine grid algorithm for parabolic coefficient identification problems is constructed. It is shown that use of a coarse grid for the interpolation of the unknown coefficient and a fine grid for the numerical solution of the well-posed forward and backward parabolic problems guarantees an optimal compromise between the accuracy an...