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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2022

On optimal cloaking-by-mapping transformations

Abstract

A central ingredient of cloaking-by-mapping is the diffeomorphisn 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 [4]. In this work, as in [4], 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.
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hal-03335152 , version 1 (06-09-2021)
hal-03335152 , version 2 (10-02-2022)

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Yves Capdeboscq, Michael S Vogelius. On optimal cloaking-by-mapping transformations. ESAIM: Mathematical Modelling and Numerical Analysis, 2022, 56 (1), pp.303 - 316. ⟨10.1051/m2an/2022004⟩. ⟨hal-03335152v2⟩
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