A Linear Integral Equation Approach to the Robin Inverse Problem
We consider the numerical solution of an inverse problem for the Laplace equation where the Robin coefficient is to be recovered from a partial boundary measurement. We first formulate the problem by integral equations on the boundary. By introducing a new variable, the key integral equation involved becomes linear, and the ill-posedness of the inverse problem is clearly revealed. On the basis of this linearity, we then design linear least-squares-based methods for reconstruction of the Robin coefficient. A proper form of regularization is chosen, and both direct (non-iterative) and iterative methods are investigated. Numerical examples are presented to show the effectiveness of these methods in providing excellent estimates for the Robin coefficient from data with and without noise.
& Lin, F.
(2005). A Linear Integral Equation Approach to the Robin Inverse Problem. Inverse Problems, 21 (5), 1757-1772.