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

Published online by Cambridge University Press:  15 November 2003

Yves Capdeboscq  and
Michael S. Vogelius
Yves Capdeboscq
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA. vogelius@hilbert.rutgers.edu.
Michael S. Vogelius
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA. vogelius@hilbert.rutgers.edu.
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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.

Keywords

Conductivity inhomogeneitiesvolume estimateslow volume fraction.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 2 , March 2003 , pp. 227 - 240
Copyright
© EDP Sciences, SMAI, 2003

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