Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements

Yves Capdeboscq; Michael S. Vogelius

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 2, page 227-240
  • ISSN: 0764-583X

Abstract

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We recently derived a very general representation formula for the boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction ( cf. Capdeboscq and Vogelius (2003)). In this paper we show how this representation formula may be used to obtain very accurate estimates for the size of the inhomogeneities in terms of multiple boundary measurements. As demonstrated by our computational experiments, these estimates are significantly better than previously known (single measurement) estimates, even for moderate volume fractions.

How to cite

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Capdeboscq, Yves, and Vogelius, Michael S.. "Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements." ESAIM: Mathematical Modelling and Numerical Analysis 37.2 (2010): 227-240. <http://eudml.org/doc/194160>.

@article{Capdeboscq2010,
abstract = { We recently derived a very general representation formula for the boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction ( cf. Capdeboscq and Vogelius (2003)). In this paper we show how this representation formula may be used to obtain very accurate estimates for the size of the inhomogeneities in terms of multiple boundary measurements. As demonstrated by our computational experiments, these estimates are significantly better than previously known (single measurement) estimates, even for moderate volume fractions. },
author = {Capdeboscq, Yves, Vogelius, Michael S.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Conductivity inhomogeneities; volume estimates; low volume fraction.; conductivity inhomogeneities; low volume fraction},
language = {eng},
month = {3},
number = {2},
pages = {227-240},
publisher = {EDP Sciences},
title = {Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements},
url = {http://eudml.org/doc/194160},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Capdeboscq, Yves
AU - Vogelius, Michael S.
TI - Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 2
SP - 227
EP - 240
AB - We recently derived a very general representation formula for the boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction ( cf. Capdeboscq and Vogelius (2003)). In this paper we show how this representation formula may be used to obtain very accurate estimates for the size of the inhomogeneities in terms of multiple boundary measurements. As demonstrated by our computational experiments, these estimates are significantly better than previously known (single measurement) estimates, even for moderate volume fractions.
LA - eng
KW - Conductivity inhomogeneities; volume estimates; low volume fraction.; conductivity inhomogeneities; low volume fraction
UR - http://eudml.org/doc/194160
ER -

References

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Citations in EuDML Documents

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  1. Yves Capdeboscq, Michael S. Vogelius, A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction
  2. Yves Capdeboscq, Michael S. Vogelius, A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction
  3. Roland Griesmaier, A general perturbation formula for electromagnetic fields in presence of low volume scatterers
  4. Roland Griesmaier, A general perturbation formula for electromagnetic fields in presence of low volume scatterers
  5. Stanislas Larnier, Mohamed Masmoudi, The extended adjoint method
  6. Stanislas Larnier, Mohamed Masmoudi, The extended adjoint method

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