Journal Article

FZJ-2025-03922

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Sampling methods for recovering buried corroded boundaries from partial electrostatic Cauchy data

Harris, I. (Corresponding author) ; Kleefeld, A.FZJ* ; Lee, H.

2025
Soc. Philadelphia, Pa.

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Please use a persistent id in citations: doi:10.1137/24M1694483

Abstract: 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.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs) and Research Groups (POF4-511) (POF4-511)

Appears in the scientific report 2025

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Database coverage:
; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; National-Konsortium ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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