Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements
Yves Capdeboscq and Michael S. Vogelius
Department of Mathematics,
New Brunswick, NJ 08903, USA. firstname.lastname@example.org.
Revised: 6 November 2002
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.
Mathematics Subject Classification: 35J20 / 35B27 / 35R30
Key words: Conductivity inhomogeneities / volume estimates / low volume fraction.
© EDP Sciences, SMAI, 2003