Enhanced approximate cloaking by SH and FSH lining

Li, Jingzhi1; Liu, Hongyu2; Sun, Hongpeng3

2012-07

10.1088/0266-5611/28/7/075011

INVERSE PROBLEMS   影响因子和分区

0266-5611

1361-6420

We consider approximate cloaking from a regularization viewpoint introduced in Kohn et al (2008 Inverse Problems 24 015016) for EIT and further investigated in Kohn et al (2010 Commun. Pure Appl. Math. 63 0973-1016) and Liu (2009 Inverse Problems 25 045006) for the Helmholtz equation. The cloaking schemes given by Kohn et al and Liu are shown to be (optimally) within vertical bar ln rho vertical bar(-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.

SCI ; EI

英语

第一 ; 通讯

Mathematics ; Physics

Mathematics, Applied ; Physics, Mathematical

WOS:000306085300011

IOP PUBLISHING LTD

20122915263755

Differential equations ; Numerical methods

Calculus:921.2 ; Numerical Methods:921.6

PHYSICS

Web of Science

1.S Univ Sci & Technol China, Shenzhen 518055, Peoples R China
2.Univ N Carolina, Dept Math & Stat, Charlotte, NC 28223 USA
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China

Li, Jingzhi,Liu, Hongyu,Sun, Hongpeng. Enhanced approximate cloaking by SH and FSH lining[J]. INVERSE PROBLEMS,2012,28(7).

Li, Jingzhi,Liu, Hongyu,&Sun, Hongpeng.(2012).Enhanced approximate cloaking by SH and FSH lining.INVERSE PROBLEMS,28(7).

Li, Jingzhi,et al."Enhanced approximate cloaking by SH and FSH lining".INVERSE PROBLEMS 28.7(2012).