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Enhanced approximate cloaking by SH and FSH lining

by J. Li and H. Liu and H. Sun

(Report number 2011-65)

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 $|ln \rho|^{-1}$ in 2D and \rho in 3D of perfect cloaking, where $\rho$ 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 $/rho^N$ in $R^N$;$N>2$, 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.

Keywords:

@Techreport{LLS11_125,
  author = {J. Li and H. Liu and H. Sun},
  title = {Enhanced approximate cloaking by SH and FSH lining},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-65},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-65.pdf },
  year = {2011}
}

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