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Approximate cloaking for the Helmholtz equation via transformation optics and consequences for perfect cloaking
Author(s) -
Nguyen HoaiMinh
Publication year - 2012
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20392
Subject(s) - cloaking , invisibility , helmholtz equation , mathematics , transformation optics , helmholtz free energy , limit (mathematics) , transformation (genetics) , dimension (graph theory) , space (punctuation) , field (mathematics) , mathematical analysis , scheme (mathematics) , metamaterial , pure mathematics , physics , computer science , quantum mechanics , optics , biochemistry , chemistry , gene , boundary value problem , operating system
In this paper, we study approximate cloaking of active devices for the Helmholtz equation in the whole space of dimension 2 or 3 using the scheme introduced by Kohn, Shen, Vogelius, and Weinstein. More precisely, we assess the degree of invisibility, determine the limit of the field inside the cloaked and cloaking regions, and show that the scheme is unstable with respect to the material parameters. As a consequence, we obtain some feasible properties of “perfect” cloaking. © 2011 Wiley Periodicals, Inc.