The inverse scattering problem for a partially coated cavity with interior measurements

Yuqing Hu; Fioralba Cakoni; Jijun Liu

doi:10.1080/00036811.2013.801458

The inverse scattering problem for a partially coated cavity with interior measurements

Yuqing Hu, Fioralba Cakoni, Jijun Liu

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

We consider the interior inverse scattering problem of recovering the shape and the surface impedance of an impenetrable partially coated cavity from a knowledge of measured scatter waves due to point sources located on a closed curve inside the cavity. First, we prove uniqueness of the inverse problem, namely, we show that both the shape of the cavity and the impedance function on the coated part are uniquely determined from exact data. Then, based on the linear sampling method, we propose an inversion scheme for determining both the shape and the boundary impedance. Finally, we present some numerical examples showing the validity of our method.

Original language	English (US)
Pages (from-to)	936-956
Number of pages	21
Journal	Applicable Analysis
Volume	93
Issue number	5
DOIs	https://doi.org/10.1080/00036811.2013.801458
State	Published - May 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Keywords

boundary impedance
interior measurements
inverse scattering
linear sampling method
mixed boundary value problem

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10.1080/00036811.2013.801458

Cite this

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title = "The inverse scattering problem for a partially coated cavity with interior measurements",

abstract = "We consider the interior inverse scattering problem of recovering the shape and the surface impedance of an impenetrable partially coated cavity from a knowledge of measured scatter waves due to point sources located on a closed curve inside the cavity. First, we prove uniqueness of the inverse problem, namely, we show that both the shape of the cavity and the impedance function on the coated part are uniquely determined from exact data. Then, based on the linear sampling method, we propose an inversion scheme for determining both the shape and the boundary impedance. Finally, we present some numerical examples showing the validity of our method.",

keywords = "boundary impedance, interior measurements, inverse scattering, linear sampling method, mixed boundary value problem",

author = "Yuqing Hu and Fioralba Cakoni and Jijun Liu",

note = "Funding Information: The research of Y.Q.Hu and J.J.Liu are supported by NSFC No.11161130002, No.11071039 and the Fundamental Research Funds for the Central Universities No. 3207011102. The research of F. Cakoni is supported in part by the Air Force Office of Scientific Research Grant FA9550-11-1-0189 and NSF Grant DMS-1106972.",

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doi = "10.1080/00036811.2013.801458",

language = "English (US)",

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T1 - The inverse scattering problem for a partially coated cavity with interior measurements

AU - Hu, Yuqing

AU - Cakoni, Fioralba

AU - Liu, Jijun

N1 - Funding Information: The research of Y.Q.Hu and J.J.Liu are supported by NSFC No.11161130002, No.11071039 and the Fundamental Research Funds for the Central Universities No. 3207011102. The research of F. Cakoni is supported in part by the Air Force Office of Scientific Research Grant FA9550-11-1-0189 and NSF Grant DMS-1106972.

PY - 2014/5

Y1 - 2014/5

N2 - We consider the interior inverse scattering problem of recovering the shape and the surface impedance of an impenetrable partially coated cavity from a knowledge of measured scatter waves due to point sources located on a closed curve inside the cavity. First, we prove uniqueness of the inverse problem, namely, we show that both the shape of the cavity and the impedance function on the coated part are uniquely determined from exact data. Then, based on the linear sampling method, we propose an inversion scheme for determining both the shape and the boundary impedance. Finally, we present some numerical examples showing the validity of our method.

AB - We consider the interior inverse scattering problem of recovering the shape and the surface impedance of an impenetrable partially coated cavity from a knowledge of measured scatter waves due to point sources located on a closed curve inside the cavity. First, we prove uniqueness of the inverse problem, namely, we show that both the shape of the cavity and the impedance function on the coated part are uniquely determined from exact data. Then, based on the linear sampling method, we propose an inversion scheme for determining both the shape and the boundary impedance. Finally, we present some numerical examples showing the validity of our method.

KW - boundary impedance

KW - interior measurements

KW - inverse scattering

KW - linear sampling method

KW - mixed boundary value problem

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DO - 10.1080/00036811.2013.801458

M3 - Article

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VL - 93

SP - 936

EP - 956

JO - Applicable Analysis

JF - Applicable Analysis

IS - 5

ER -

The inverse scattering problem for a partially coated cavity with interior measurements

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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