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| - On optimal cloaking-by-mapping transformations
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| - 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.
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| - © The authors. Published by EDP Sciences, SMAI 2022
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| - The authors. Published by EDP Sciences, SMAI 2022
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