On reconstruction of an unknown polygonal cavity in a linearized elasticity with one measurement

Ikehata, Masaru; Itou, Hiromichi

doi:10.1088/1742-6596/290/1/012005

Cited by 6 publications

(6 citation statements)

References 20 publications

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“…The procedure used to prove our central results is different from the ones used in [1,8,12,14,[16][17][18][21][22][23][24]. By means of specific test functions our first result can be read as an approximation to the Fourier transformation of the delta distributions at the centers of the inhomogeneities D j and this was suggested as an idea for a numerical reconstruction algorithm.…”

Section: Inverse Problem Reconstruct Unknown Polygonal Inclusionmentioning

confidence: 98%

Reconstruction of polygonal inclusions in a heat conductive body from dynamical boundary data

2017

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In this paper, we consider a reconstruction problem of small and polygonal heat-conducting inhomogeneities from dynamic boundary measurements on part of the boundary and for finite interval in time. Our identification procedure is based on asymptotic method combined with appropriate averaging of the partial dynamic boundary measurements. Our approach is expected to lead to an effective computational identification algorithms.

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Section: Inverse Problem Reconstruct Unknown Polygonal Inclusionmentioning

confidence: 98%

Reconstruction of polygonal inclusions in a heat conductive body from dynamical boundary data

2017

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“…A topological gradient method has been applied in [24], for the detection of an elastic scatterer, and in [50], for identification of a cavity in time-harmonic wave elastic systems. Ikehata and Itou use the so-called enclosure method for the reconstruction of polygonal cavities in an elastostatic setting [42] and of a general cavity in a homogeneous isotropic viscoelastic body [43]. More recently, Doubova and Fernández-Cara proposed an augmented Lagrangian method to identify rigid inclusions in a elastic waves system [31].…”

Section: Introductionmentioning

confidence: 99%

Identification of Cavities and Inclusions in Linear Elasticity with a Phase-Field Approach

et al. 2022

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In this paper we deal with the inverse problem of determining cavities and inclusions embedded in a linear elastic isotropic medium from boundary displacement’s measurements. For, we consider a constrained minimization problem involving a boundary quadratic misfit functional with a regularization term that penalizes the perimeter of the cavity or inclusion to be identified. Then using a phase field approach we derive a robust algorithm for the reconstruction of elastic inclusions and of cavities modelled as inclusions with a very small elasticity tensor.

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“…We finally mention that the mathematical literature on reconstruction methods for elastic inclusions and cavities is always of remarkable interest thanks to the intimate connection with the industrial applications. Among the vast literature on the subject, we refer the reader to [5,6,7,19,10,26,36,37,51,52,55,56,61] to have an idea of the reconstruction techniques applied in this context.…”

Section: Introductionmentioning

confidence: 99%

A phase-field approach for detecting cavities via a Kohn-Vogelius type functional

Aspri

2022

Preprint

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We deal with the geometrical inverse problem of the shape reconstruction of cavities in a bounded linear isotropic medium by means of boundary data. The problem is addressed from the point of view of optimal control: the goal is to minimize in the class of Lipschitz domains a Kohn-Vogelius type functional with a perimeter regularization term which penalizes the perimeter of the cavity to be reconstructed. To solve numerically the optimization problem, we use a phase-field approach, approximating the perimeter functional with a Modica-Mortola relaxation and modeling the cavity as an inclusion with a very small elastic tensor. We provide a detailed analysis showing the robustness of the algorithm through some numerical experiments.

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On reconstruction of an unknown polygonal cavity in a linearized elasticity with one measurement

Cited by 6 publications

References 20 publications

Reconstruction of polygonal inclusions in a heat conductive body from dynamical boundary data

Reconstruction of polygonal inclusions in a heat conductive body from dynamical boundary data

Identification of Cavities and Inclusions in Linear Elasticity with a Phase-Field Approach

A phase-field approach for detecting cavities via a Kohn-Vogelius type functional

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