On regularized full- and partial-cloaks in acoustic scattering

Abstract

ABSTRACTThe aim of this work is to derive sharp quantitative estimates of the qualitative convergence results developed by Li et al. (2015) for regularized full- and partial-cloaks through transformation optics approach. Let Γ0 be a compact set in ℝ3 and Γδ be a δ-neighborhood of Γ0 for δ∈ℝ+. Γδ represents the virtual domain used for the blow-up construction. By incorporating suitably designed lossy layers, it is shown that if the generating set Γ0 is a generic curve, then one would have an approximate full-cloak within δ2 to the perfect full-cloak, whereas if Γ0 is the closure of an open subset on a flat surface, then one would have an approximate partial-cloak within δ to its perfect counterpart. The estimates derived are independent of the contents being cloaked; that is, the cloaking devices are capable of nearly cloaking an arbitrary content. Furthermore, as a significant by-product, our argument allows the relaxation of the convexity requirement on Γ0 by Li et al. (2015), which is critical for the Mosco convergence argument therein.