A combination of shape and conductivity function reconstruction methods for an inverse boundary value problem

Yaman, Fatih

doi:10.1016/j.wavemoti.2009.10.004

Cited by 3 publications

(4 citation statements)

References 14 publications

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“…In the current study, we show results of numerical experiments for new problem geometries such that the reconstructions which were presented in [2,27,28] support the verification of the proposed algorithms. It is observed that the localization of the unknown buried objects are succeeded with an acceptable accuracy for different types of objects and conductivity functions.…”

Section: Resultssupporting

confidence: 57%

“…We note that regularization parameters α in (3.7), β for the equation system (3.14)-(3.17), γ for Eq. (3.15) and m in (4.2) are chosen by trial and error as a typical procedure which is applied in [23][24][25][26][27][28]. However, it is important to emphasize that the selection of the mentioned parameters do not affect the quality of the reconstructions if Table 1.…”

Section: Applications and Resultsmentioning

confidence: 99%

“…Density functions and related integral representations allow us to calculate the scattered and the total fields in each region. Then we employ iterative reconstruction algorithms introduced in [24,23] which were tested for shape reconstructions of objects in free-space [24][25][26] and for the ones buried in bounded domains [27,28].…”

Section: Introductionmentioning

confidence: 99%

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Inhomogeneity reconstructions in tendon ducts via boundary integral equations

Yaman¹,

Weiland²

2014

NDT & E International

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a b s t r a c tIn this study, as an alternative to the formerly presented investigations, Newton-type numerical algorithms are proposed to find location and shape of an air void inside of a tendon duct and to identify gathered metallic bars in a concrete column. The simulated structures are illuminated by four acoustic sources at a fixed frequency such that the scattered field is measured in a near-field region at 128 points. According to the nature of physical problems, the Dirichlet boundary condition is employed to model air-filled cavities and transmission conditions are assumed for metallic objects. Additionally, conductive boundary conditions are suggested for a more realistic representation of the inhomogeneities for the rusty metallic skin of the duct. Potential approaches are used to derive boundary integral equations. The proper treatment of the ill-conditioned equations is established via Tikhonov regularization. Applicability of the proposed inversion algorithms is tested with realistic parameters for different scenarios using noisy scattered field data and accurate numerical results are presented at 10 kHz for the unknown physical properties of the duct's skin.

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Section: Resultssupporting

confidence: 57%

Section: Applications and Resultsmentioning

confidence: 99%

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Inhomogeneity reconstructions in tendon ducts via boundary integral equations

Yaman¹,

Weiland²

2014

NDT & E International

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“…Finally, is obtained from (6) in the least squares sense. This method is also extended for the reconstructions of the conductivity functions of the obstacles in free space [99], for the obstacles buried in penetrable cylinders [100] and for a combination of a shape and conductivity function reconstruction problem [101], firstly by Yaman [6]. Moreover, [64,95,96] are devoted for the shape and impedance reconstructions of 2D obstacles in acoustics.…”

Section: Parameter On the Boundary Reconstruction Problems Of Acoustic Wavesmentioning

confidence: 99%

A Survey on Inverse Problems for Applied Sciences

Yaman

Yakhno²,

Potthast³

2013

Mathematical Problems in Engineering

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The aim of this paper is to introduce inversion-based engineering applications and to investigate some of the important ones from mathematical point of view. To do this we employ acoustic, electromagnetic, and elastic waves for presenting different types of inverse problems. More specifically, we first study location, shape, and boundary parameter reconstruction algorithms for the inaccessible targets in acoustics. The inverse problems for the time-dependent differential equations of isotropic and anisotropic elasticity are reviewed in the following section of the paper. These problems were the objects of the study by many authors in the last several decades. The physical interpretations for almost all of these problems are given, and the geophysical applications for some of them are described. In our last section, an introduction with many links into the literature is given for modern algorithms which combine techniques from classical inverse problems with stochastic tools into ensemble methods both for data assimilation as well as for forecasting.

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