Reconstruction of cracks in Calderón's inverse conductivity problem using energy comparisons

Henrik Garde*, Michael Vogelius

*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

Abstract

We derive exact reconstruction methods for cracks consisting of unions of Lipschitz hypersurfaces in the context of Calderón's inverse conductivity problem. Our first method obtains upper bounds for the unknown cracks, bounds that can be shrunk to obtain the exact crack locations upon verifying certain operator inequalities for differences of the local Neumann-to-Dirichlet maps. This method can simultaneously handle perfectly insulating and perfectly conducting cracks, and it appears to be the first rigorous reconstruction method capable of this. Our second method assumes that only perfectly insulating cracks or only perfectly conducting cracks are present. Once more using operator inequalities, this method generates approximate cracks that are guaranteed to be subsets of the unknown cracks that are being reconstructed.
OriginalsprogEngelsk
TidsskriftSIAM Journal on Mathematical Analysis
Vol/bind56
Nummer1
Sider (fra-til)727-745
Antal sider19
ISSN0036-1410
DOI
StatusUdgivet - 2024

Fingeraftryk

Dyk ned i forskningsemnerne om 'Reconstruction of cracks in Calderón's inverse conductivity problem using energy comparisons'. Sammen danner de et unikt fingeraftryk.

Citationsformater