Thin cylindrical conductivity inclusions in a three-dimensional domain: A polarization tensor and unique determination from boundary data

Elena Beretta, Yves Capdeboscq, Frédéric De Gournay, Elisa Francini

Research output: Contribution to journalArticle

Abstract

We consider a three-dimensional conductor containing an inclusion that can be represented as a cylinder with a fixed axis and a small basis. As the size of the basis of the cylinder approaches zero, the voltage perturbation can be described by means of a polarization tensor. We give an explicit characterization of the polarization tensor of cylindrical inclusions in terms of the polarization tensor of its base, and we use this result to show that the axis of the inclusion can be uniquely determined by boundary values of the voltage perturbation. We also present a reconstruction algorithm and some numerical simulations.

Original languageEnglish (US)
Article number065004
JournalInverse Problems
Volume25
Issue number6
DOIs
StatePublished - Oct 28 2009

Fingerprint

Conductivity
Tensors
Polarization
Tensor
Inclusion
Three-dimensional
Voltage
Perturbation
Electric potential
Reconstruction Algorithm
Conductor
Boundary Value
Numerical Simulation
Computer simulation
Zero

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

Cite this

Thin cylindrical conductivity inclusions in a three-dimensional domain : A polarization tensor and unique determination from boundary data. / Beretta, Elena; Capdeboscq, Yves; De Gournay, Frédéric; Francini, Elisa.

In: Inverse Problems, Vol. 25, No. 6, 065004, 28.10.2009.

Research output: Contribution to journalArticle

@article{033d47b5f4d1419fb583b61a8d541494,
title = "Thin cylindrical conductivity inclusions in a three-dimensional domain: A polarization tensor and unique determination from boundary data",
abstract = "We consider a three-dimensional conductor containing an inclusion that can be represented as a cylinder with a fixed axis and a small basis. As the size of the basis of the cylinder approaches zero, the voltage perturbation can be described by means of a polarization tensor. We give an explicit characterization of the polarization tensor of cylindrical inclusions in terms of the polarization tensor of its base, and we use this result to show that the axis of the inclusion can be uniquely determined by boundary values of the voltage perturbation. We also present a reconstruction algorithm and some numerical simulations.",
author = "Elena Beretta and Yves Capdeboscq and {De Gournay}, Fr{\'e}d{\'e}ric and Elisa Francini",
year = "2009",
month = "10",
day = "28",
doi = "10.1088/0266-5611/25/6/065004",
language = "English (US)",
volume = "25",
journal = "Inverse Problems",
issn = "0266-5611",
publisher = "IOP Publishing Ltd.",
number = "6",

}

TY - JOUR

T1 - Thin cylindrical conductivity inclusions in a three-dimensional domain

T2 - A polarization tensor and unique determination from boundary data

AU - Beretta, Elena

AU - Capdeboscq, Yves

AU - De Gournay, Frédéric

AU - Francini, Elisa

PY - 2009/10/28

Y1 - 2009/10/28

N2 - We consider a three-dimensional conductor containing an inclusion that can be represented as a cylinder with a fixed axis and a small basis. As the size of the basis of the cylinder approaches zero, the voltage perturbation can be described by means of a polarization tensor. We give an explicit characterization of the polarization tensor of cylindrical inclusions in terms of the polarization tensor of its base, and we use this result to show that the axis of the inclusion can be uniquely determined by boundary values of the voltage perturbation. We also present a reconstruction algorithm and some numerical simulations.

AB - We consider a three-dimensional conductor containing an inclusion that can be represented as a cylinder with a fixed axis and a small basis. As the size of the basis of the cylinder approaches zero, the voltage perturbation can be described by means of a polarization tensor. We give an explicit characterization of the polarization tensor of cylindrical inclusions in terms of the polarization tensor of its base, and we use this result to show that the axis of the inclusion can be uniquely determined by boundary values of the voltage perturbation. We also present a reconstruction algorithm and some numerical simulations.

UR - http://www.scopus.com/inward/record.url?scp=70350322119&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350322119&partnerID=8YFLogxK

U2 - 10.1088/0266-5611/25/6/065004

DO - 10.1088/0266-5611/25/6/065004

M3 - Article

AN - SCOPUS:70350322119

VL - 25

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 6

M1 - 065004

ER -