Analysis of an enhanced approximate cloaking scheme for the conductivity problem

We extend and analyse an enhanced approximate cloaking scheme, which was recently introduced by Ammari, Kang, Lee and Lim [Comm. Math. Phys. 317(1) (2013), 253–266] to cloak a domain with a fixed, homogeneous Neumann boundary condition. Subject to the solvability of a finite set of algebraic equatio...

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Published inAsymptotic analysis Vol. 87; no. 3-4; pp. 223 - 246
Main Authors Heumann, Holger, Vogelius, Michael S.
Format Journal Article
LanguageEnglish
Published London, England SAGE Publications 01.01.2014
IOS Press
Subjects
Algebra
Approximation
Asymptotic properties
Boundary conditions
Estimates
Inverse problems
Mathematical analysis
Mathematics
Visibility
transmission setting
enhanced cloaking
conductivity problem
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Summary:We extend and analyse an enhanced approximate cloaking scheme, which was recently introduced by Ammari, Kang, Lee and Lim [Comm. Math. Phys. 317(1) (2013), 253–266] to cloak a domain with a fixed, homogeneous Neumann boundary condition. Subject to the solvability of a finite set of algebraic equations we construct an approximate cloak for the two dimensional transmission case, which achieves invisibility of the order ρ2N+2 while maintaining the same level of local anisotropy as earlier schemes of order ρ2 [Inverse Problems 24(1) (2008), 015016]. The approximate cloak and the invisibility estimate is independent of the objects being cloaked. Finally, we present analytical as well as numerical evidence for the solvability of the required algebraic equations.
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ISSN:0921-7134
1875-8576
DOI:10.3233/ASY-131209