Corrosion detection in conducting boundaries

Abstract

We consider a model for detecting corrosion on the (inaccessible) conducting top side of a metallic plate. We suppose that the effects of corrosion attack consist in material loss. The perturbation so induced in the geometry of the plate is described by a positive function θ . We prove that a suitable data set, collected on the bottom side of the plate, identifies θ uniquely.

Simultaneous numerical determination of a corroded boundary and its admittance

“…It is well-known that this inverse problem is nonlinear and ill-posed, as opposed to the direct problem which is linear and well-posed. We briefly note that the situation regarding the uniqueness/non-uniqueness of solution is much more settled in the case of the inverse shape boundary determination of Γ 2 when α is known, [6,7,9,17,18], or in the case of the inverse admittance determination of α when Γ 2 is known, [11,16]. We also mention that the case of the inverse determination of Γ 2 with α unknown but being either 0, i.e.…”

“…In (3.15), for the unknown part of the boundary Γ 2 , we use 17) while for the known part of the boundary Γ 1 , we simply calculate the derivative r ′ (ϑ) since we know the expansion of r(ϑ) there. (iv) The minimization of functional (3.12) is carried out using the MATLAB c ⃝ optimization toolbox routine lsqnonlin which solves nonlinear least squares problems.…”

The method of lines to reconstruct a moving boundary for a one-dimensional heat equation in a multilayer domain

“…Hence, a special regularization technique should be applied to stabilize the numerical computations [1,, [2,. Reconstruction of a corroded boundary from the Laplace equation has been investigated in [3][4][5][6][7][8][9][10]. However, for estimating a time-varying boundary of the heat-conduction problem, little information is available.…”

Numerical recovery of Robin boundary from boundary measurements for the Laplace equation

“…The support of the input g is usually taken to be Γ 0 in this model. See [7,6] and references therein for more discussions on the model. Similar problems arise from other non-destructive evaluation techniques in other applications, such as evaluation of metal-to-silicon contact quality in semiconductor devices (e.g.…”

“…[2,3,9,4] and reference therein). As for the inverse problem of recovering the unknown part Γ 1 from boundary measurements, there have been some theoretical and numerical studies; in particular, the authors in the series of papers [6,5] investigated this problem in the PDE setting (1.1) for the case of thin rectangular domains, while the authors in [1] studied a similar problem but in a boundary integral equation setting. In this paper, we present numerical methods of recovering the unknown boundary portion Γ 1 in an integral equation formulation.…”