Attainability by simply connected domains of optimal bounds for the polarization tensor

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The notion of polarization tensor is employed for the derivation of the leading-order boundary perturbations in the steady-state voltage potentials that are due to the presence of conductivity inclusions of small diameter. Recently, Capdeboscq and Vogelius obtained optimal bounds of Hashin-Shtrikman type for the trace of the polarization tensor, showing that every pair satisfying these optimal bounds arises as the eigenvalues of a polarization tensor associated with a coated ellipse. In this paper, we give numerical evidence of the fact that the set of possible polarization tensor eigenvalue pairs can also be obtained using simply connected domains. Our numerical computations are based on a boundary integral method.
Publisher
CAMBRIDGE UNIV PRESS
Issue Date
2006-04
Language
English
Article Type
Article
Keywords

STATE VOLTAGE POTENTIALS; CONDUCTIVITY INHOMOGENEITIES; COMPOSITE-MATERIALS; SMALL-DIAMETER; RECONSTRUCTION; VOLUME; TERMS

Citation

EUROPEAN JOURNAL OF APPLIED MATHEMATICS, v.17, pp.201 - 219

ISSN
0956-7925
DOI
10.1017/S0956792506006541
URI
http://hdl.handle.net/10203/90698
Appears in Collection
MA-Journal Papers(저널논문)
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