# 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

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topCapdeboscq, 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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- R.V. Kohn and G.W. Milton, On bounding the effective conductivity of anisotropic composites, in Homogenization and Effective Moduli of Materials and Media, J.L. Ericksen, D. Kinderlehrer, R. Kohn and J.-L. Lions Eds., Springer-Verlag, IMA Vol. Math. Appl.1 (1986) 97-125.
- O. Kwon, J.K. Seo and J.-R. Yoon, A real time algorithm for the location search of discontinuous conductivities with one measurement. Comm. Pure Appl. Math.55 (2002) 1-29. Zbl1032.78005
- R. Lipton, Inequalities for electric and elastic polarization tensors with applications to random composites. J. Mech. Phys. Solids41 (1993) 809-833. Zbl0797.73046

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