| Issue |
ESAIM: M2AN
Volume 56, Number 1, January-February 2022
|
|
|---|---|---|
| Page(s) | 303 - 316 | |
| DOI | https://doi.org/10.1051/m2an/2022004 | |
| Published online | 10 February 2022 | |
On optimal cloaking-by-mapping transformations
1
Université de Paris, CNRS, Sorbonne Université, Laboratoire Jacques-Louis Lions (LJLL), F-75006 Paris, France
2
Department of Mathematics, Rutgers University, New Brunswick, NJ 08901, USA
* Corresponding author: yves.capdeboscq@u-paris.fr
Received:
6
September
2021
Accepted:
5
January
2022
A central ingredient of cloaking-by-mapping is the diffeomorphism which transforms an annulus with a small hole into an annulus with a finite size hole, while being the identity on the outer boundary of the annulus. The resulting meta-material is anisotropic, which makes it difficult to manufacture. The problem of minimizing anisotropy among radial transformations has been studied in Griesmaier and Vogelius [Inverse Prob. 30 (2014) 17]. In this work, as in Griesmaier and Vogelius [Inverse Prob. 30 (2014) 17], we formulate the problem of minimizing anisotropy as an energy minimization problem. Our main goal is to provide strong evidence for the conjecture that for cloaks with circular boundaries, non-radial transformations do not lead to lower degree of anisotropy. In the final section, we consider cloaks with non-circular boundaries and show that in this case, non-radial cloaks may be advantageous, when it comes to minimizing anisotropy.
Mathematics Subject Classification: 35R30 / 78A46
Key words: Cloak enhancement / pproximate cloaking / cloaking-by-mapping / optimal cloaking
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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