Corrosion detection in a 2D domain with a polygonal boundary

We consider the problem of quantitative non-destructive evaluation of corrosion in a 2D domain representing a thin metallic plate. Corrosion damage is assumed to occur in an inaccessible part of the domain. Reconstruction of the damaged profile is possible by measuring an electrostatic current properly induced by a potential in an accessible part of the boundary (electrical impedance tomography). We present here numerical methods and results based on a formulation of the problem introduced and analyzed in Bacchelli–Vessella, Inverse Problems 22 (2006), where the corroded profile is represented by a polygonal boundary. We resort in particular to the Landweber method and the Brakhage semi-iterative scheme. Numerical results show the reliability of this approach in general situations, including nongraph corroded boundaries.