Enhanced Approximate Cloaking by SH and FSH Lining

TL;DR

This paper introduces enhanced approximate cloaking techniques using sound-hard and lossy layers, significantly improving cloaking performance in electromagnetic and acoustic applications through theoretical analysis and numerical validation.

Contribution

It demonstrates that employing sound-hard or lossy layers can optimally enhance approximate cloaking, achieving better regularization effects than previous methods.

Findings

Sound-hard layer achieves $ ho^N$ cloaking performance.

Lossy layer can replicate sound-hard layer performance.

Numerical experiments confirm the theoretical improvements.

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 $\mathbb{R}^N,\ N\geq 2$, 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.