Analysis of an enhanced approximate cloaking scheme for the conductivity problem

Article type: Research Article

Authors: Heumann, Holger | Vogelius, Michael S.^;

Affiliations: Fakultät für Mathematik, Technische Universität München, Boltzmannstr. 3, 85747 Garching bei München, Germany | Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA

Note: [] Corresponding author. E-mail: vogelius@math.rutgers.edu

Abstract: 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.

Keywords: enhanced cloaking, transmission setting, conductivity problem

DOI: 10.3233/ASY-131209

Journal: Asymptotic Analysis, vol. 87, no. 3-4, pp. 223-246, 2014