Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 2, p. 227-240

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.

DOI : https://doi.org/10.1051/m2an:2003024
Classification:  35J20,  35B27,  35R30
Keywords: conductivity inhomogeneities, volume estimates, low volume fraction
@article{M2AN_2003__37_2_227_0,
     author = {Capdeboscq, Yves and Vogelius, Michael S.},
     title = {Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {2},
     year = {2003},
     pages = {227-240},
     doi = {10.1051/m2an:2003024},
     zbl = {1137.35347},
     mrnumber = {1991198},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2003__37_2_227_0}
}
Capdeboscq, Yves; Vogelius, Michael S. Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 2, pp. 227-240. doi : 10.1051/m2an:2003024. http://www.numdam.org/item/M2AN_2003__37_2_227_0/

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