2024/09/04 by Isaac Harris, Andreas Kleefeld, Harris, Isaac +3
Earth and Planetary Sciences · Engineering · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geophysical Methods and Applications #Geophysical and Geoelectrical Methods #Non-Destructive Testing Techniques
paper · pdf · doi:10.48550/arxiv.2409.02761
openalex publication_date 2024/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the inverse shape and parameter problem for detecting corrosion from partial boundary measurements. This problem models the non-destructive testing for a partially buried object from electrostatic measurements on the accessible part of the boundary. The main novelty is the extension of the linear sampling and factorization methods to an electrostatic problem with partial measurements. These methods so far have only mainly applied to recovering interior defects which is a simpler problem. Another important aspect of this paper is in our numerics, where we derive a system of boundary integral equations to recover the mixed Green's function which is needed for our inversion. With this, we are able to analytically and numerically solve the inverse shape problem. For the inverse parameter problem, we prove uniqueness and Lipschitz-stability (in a finite dimensional function space) assuming that one has the associated Neumann-to-Dirichlet operator on the accessible part of the boundary.