Enhanced approximate cloaking by SH and FSH lining

Abstract

We consider approximate cloaking from a regularization viewpoint introduced in [13] for EIT and further investigated in [12, 17] for the Helmholtz equation. The cloaking schemes in [12] and [17] are shown to be (optimally) within | ln !|−1 in 2D and ! in 3D of perfect cloaking, where ! denotes the regularization parameter. In this paper, we show that by employing a sound-hard layer right outside the cloaked region, one could (optimally) achieve !N in RN, N ! 2, which significantly enhances the near-cloak. We then develop a cloaking scheme by making use of a lossy layer with well-chosen parameters. The lossy-layer cloaking scheme is shown to possess the same cloaking performance as the one with a sound-hard layer. Moreover, it is shown that the lossy layer could be taken as a finite realization of the sound-hard layer. Numerical experiments are also presented to assess the cloaking performances of all the cloaking schemes for comparisons.