TY  - JOUR
AU  - Harris, Isaac
AU  - Kleefeld, Andreas
AU  - Lee, Heejin
TI  - Sampling methods for recovering buried corroded boundaries from partial electrostatic Cauchy data
JO  - SIAM journal on applied mathematics
VL  - 85
IS  - 5
SN  - 0036-1399
CY  - Philadelphia, Pa.
PB  - Soc.
M1  - FZJ-2025-03922
SP  - 2215 - 2241
PY  - 2025
AB  - We consider the inverse shape and parameter problem for detecting corrosion from partial boundary measurements. This problem models the nondestructive 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 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:001607381900013
DO  - DOI:10.1137/24M1694483
UR  - https://juser.fz-juelich.de/record/1046703
ER  -