Approximate cloaking for the Helmholtz equation via transformation optics and consequences for perfect cloaking

2011/09/29 by Hoai-Minh Nguyen, Nguyen, Hoai-Minh
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1109.6583

To appear in Comm. Pure Appl. Math

arxiv created 2011/09/29 · arxiv updated 2011/09/30

Abstract

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 in \citeKohnShenVogeliusWeinstein. 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.

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