Corrosion detection in a 2D domain with a polygonal boundary.

We consider the problem of quantitative non-destructive evaluation of corrosion in a 2-D 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 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 Brackage semi-iterative scheme. Numerical results show the reliability of this approach in general situations, including nongraph corroded boundaries.