Bounds on the Volume Fractions of Two Materials in a Three-Dimensional Body from Boundary Measurements by the Translation Method

• Autores: Hyeonbae Kang, Graeme W. Milton
• Localización: Siam journal on applied mathematics, ISSN 0036-1399, Vol. 73, Nº 1, 2013, págs. 475-492
• Idioma: inglés
• DOI: 10.1137/120879713
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• Resumen

  • Using the translation method of Tartar, Murat, Lurie, and Cherkaev, bounds are derived on the volume occupied by an inclusion in a three-dimensional conducting body. The bounds assume that electrical impedance tomography measurements have been made for three sets of pairs of current flux and voltage measurements around the boundary. Additionally, the conductivity of the inclusion and the conductivity of the surrounding medium are assumed to be known. If the boundary data (Dirichlet or Neumann) is special, i.e., such that the fields inside the body would be uniform were the body homogeneous, then the bounds reduce to those of Milton and thus, when the volume fraction is small, to those of Capdeboscq and Vogelius