A second order Newton method for sound soft inverse obstacle scattering

Kreß, Rainer; Tezel, Necmi Serkan; Yaman, Fatih

doi:10.1515/jiip.2009.015

Cited by 7 publications

(13 citation statements)

References 14 publications

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“…The problem has been widely addressed in the literature; see, for example, . The formulation proposed here is similar in essence, but uses the single‐layer approach of .…”

Section: Analysis Of Shielding Effectiveness Of Bermmentioning

confidence: 99%

“…Because the field inside the berm

u_{1}

satisfies the wave equation in (1), it can be expressed in a single layer potential integral representation as

u_{1} (|, \vec{r}) = \int_{B}^{} ψ true({\overset{r}{true}}^{'} true) G_{1} true(\vec{r}, {\overset{r}{true}}^{'} true) d s true({\overset{r}{true}}^{'} true)

…”

Section: Respectively and The Boundary Conditionsmentioning

confidence: 99%

“…On the other hand, since the scattered field

u_{s}

also satisfies the wave equation in (1) and the radiation condition in (7), it too can be expressed as a single layer potential integral representation

u_{s} (|, \vec{r}) = \int_{normalB}^{} φ true({\overset{r}{true}}^{'} true) G_{0} true(\vec{r}, {\overset{r}{true}}^{'} true) d s true({\overset{r}{true}}^{'} true)

where

φ

is the single layer potential to be determined and

G_{0} true(\vec{r}, {\overset{r}{true}}^{'} true)

is the two‐dimensional Green's function of free space that contains the infinite PEC plane and is given by

G_{0} (|, \vec{r}, {\overset{r}{true}}^{'}) = \frac{- j}{4} (|, H_{0}^{(2)} (|, k_{0} (|||, \vec{r} - {\overset{r}{true}}^{'})) + H_{0}^{(2)} (|, k_{0} (|||, \vec{r} - (|, \hat{x} \hat{x} - \hat{y} \hat{y}) .)))

…”

Section: Respectively and The Boundary Conditionsmentioning

confidence: 99%

“…These integral equations can be approximated by a matrix equation through discretization using the point‐matching MoM technique . If the boundary of the berm is meshed into a total of N elements, we can approximate the integral equation by the matrix equation given in a compact form as

([]|, \begin{matrix} C & D \\ E & F \end{matrix}) ([]|, \begin{matrix} ψ \\ φ \end{matrix}) = ([]|, \begin{matrix} G \\ H \end{matrix})

where C, D, E, and F are N by N matrixes and G and H are N‐dimensional column vectors.…”

Section: Respectively and The Boundary Conditionsmentioning

confidence: 99%

“…It will be shown that the berm is sufficiently long for the 2D approximation to give useful engineering results. The scattering problem is then formulated as a computationally‐efficient single layer boundary integral equation and solved using the Method‐of‐Moments (MoM) .…”

Section: Introductionmentioning

confidence: 99%

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RFI shielding effectiveness of a soil berm

Tezel

Reader

Davidson

2016

Micro & Optical Tech Letters

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We investigate the electromagnetic (EM) shielding effectiveness (SE) properties of a berm which was created from soil due to construction works near a sensitive radio astronomy site. For the analysis, the berm is approximated as being located above an infinite perfectly electric conducting (PEC) plane. A two‐dimensional cross‐sectional analysis is shown to be sufficient to investigate the SE, which we compute using a computationally efficient single‐layer boundary integral equation method. To verify the method, we compare our results against those obtained by the commercially available Method of Moments (MoM) code, FEKO. Good agreement is demonstrated. It is observed that the berm provides about 25–30 dB SE at heights lower than 5 m and at distances of up to 50 m from the berm. © 2016 Wiley Periodicals, Inc. Microwave Opt Technol Lett 59:17–21, 2017

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“…The problem has been widely addressed in the literature; see, for example, . The formulation proposed here is similar in essence, but uses the single‐layer approach of .…”

Section: Analysis Of Shielding Effectiveness Of Bermmentioning

confidence: 99%

“…Because the field inside the berm

u_{1}

satisfies the wave equation in (1), it can be expressed in a single layer potential integral representation as

u_{1} (|, \vec{r}) = \int_{B}^{} ψ true({\overset{r}{true}}^{'} true) G_{1} true(\vec{r}, {\overset{r}{true}}^{'} true) d s true({\overset{r}{true}}^{'} true)

…”

Section: Respectively and The Boundary Conditionsmentioning

confidence: 99%

“…On the other hand, since the scattered field

u_{s}

also satisfies the wave equation in (1) and the radiation condition in (7), it too can be expressed as a single layer potential integral representation

u_{s} (|, \vec{r}) = \int_{normalB}^{} φ true({\overset{r}{true}}^{'} true) G_{0} true(\vec{r}, {\overset{r}{true}}^{'} true) d s true({\overset{r}{true}}^{'} true)

where

φ

is the single layer potential to be determined and

G_{0} true(\vec{r}, {\overset{r}{true}}^{'} true)

is the two‐dimensional Green's function of free space that contains the infinite PEC plane and is given by

G_{0} (|, \vec{r}, {\overset{r}{true}}^{'}) = \frac{- j}{4} (|, H_{0}^{(2)} (|, k_{0} (|||, \vec{r} - {\overset{r}{true}}^{'})) + H_{0}^{(2)} (|, k_{0} (|||, \vec{r} - (|, \hat{x} \hat{x} - \hat{y} \hat{y}) .)))

…”

Section: Respectively and The Boundary Conditionsmentioning

confidence: 99%

([]|, \begin{matrix} C & D \\ E & F \end{matrix}) ([]|, \begin{matrix} ψ \\ φ \end{matrix}) = ([]|, \begin{matrix} G \\ H \end{matrix})

where C, D, E, and F are N by N matrixes and G and H are N‐dimensional column vectors.…”

Section: Respectively and The Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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RFI shielding effectiveness of a soil berm

Tezel

Reader

Davidson

2016

Micro & Optical Tech Letters

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A second degree Newton method for an inverse obstacle scattering problem

Kreß

Lee

2011

Journal of Computational Physics

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A second degree Newton method in inverse scattering problem for a crack

Lee

2012

Journal of Mathematical Physics

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Inverse scattering pre-stack depth imaging and it's comparison to some depth migration methods for imaging rich fault complex structure AIP Conf.For the inverse scattering problem from a sound-soft crack a second degree Newton method is proposed in this paper. Based on integral equations method, our scheme splits the inverse problem into a well-posed problem and a nonlinear ill-posed problem which will be linearized using a second degree method. Some reconstructions will be given to demonstrate the feasibility of the proposed method. C 2012 American Institute of Physics. [http://dx.

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A second order Newton method for sound soft inverse obstacle scattering

Cited by 7 publications

References 14 publications

RFI shielding effectiveness of a soil berm

RFI shielding effectiveness of a soil berm

A second degree Newton method for an inverse obstacle scattering problem

A second degree Newton method in inverse scattering problem for a crack

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