The inverse conductivity problem via the calculus of functions of bounded variation

The inverse conductivity problem via the calculus of functions of bounded variation

In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV - functions. The space of the functions of bounded variation is here recommended as the most appro...

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Veröffentlicht in:arXiv.org 2019-05
Hauptverfasser: Charalambopoulos, Antonios, Markaki, Vanessa, Drosos Kourounis
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Calculus of variations
Conductivity
Functionals
Mathematical analysis
Mathematics - Analysis of PDEs
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Drosos Kourounis
description In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of BV - functions. The space of the functions of bounded variation is here recommended as the most appropriate functional space hosting the conductivity profile under reconstruction. For the numerical solution, we propose and implement a suitable minimization scheme of an enriched - constructed herein - functional, by exploiting the inner structure of BV - space. Finally, we validate and illustrate our theoretical results with numerical experiments.
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subjects Calculus of variations
Conductivity
Functionals
Mathematical analysis
Mathematics - Analysis of PDEs
title The inverse conductivity problem via the calculus of functions of bounded variation
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