We consider a Robin inverse problem associated with the Laplace equation,
which is a severely ill-posed and nonlinear. We formulate the problem as a boundary
integral equation, and introduce a functional of the Robin coefficient as a regularisation
term. A conjugate gradient method is proposed for solving the consequent regularised
nonlinear least squares problem. Numerical examples are presented to illustrate the
effectiveness of the proposed method.
Robin inverse problem ill-posedness boundary integral equation regularisation conjugate gradient method