Conjugate gradient method for the Robin inverse problem associated with the Laplace equation

Abstract

This paper studies a non-linear inverse problem associated with the Laplace equation of identifying the Robin coefficient from boundary measurements. A variational formulation of the problem is suggested, thereby transforming it into an optimization problem. Mathematical properties relevant to its numerical computation are established. The optimization problem is solved using the conjugate gradient method in conjunction with the discrepancy principle, and the algorithm is implemented using the boundary element method. Numerical results are presented for several benchmark problems with both exact and noisy data, and the convergence of the algorithm with respect to mesh refinement and decreasing the amount of noise in the data is investigated. Copyright © 2006 John Wiley & Sons, Ltd.