Reconstruction of the shape of the inclusion by boundary measurements

Ikehata, Masaru

doi:10.1080/03605309808821390

Cited by 112 publications

(120 citation statements)

References 8 publications

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“…When this point approaches the obstacle, these indicator functions blowup. The linear sampling method [7], the factorization method [16] and the singular sources method [21] construct the indicator functions from the far-field pattern directly, while the probe method [13,14] constructs the indicator in terms of the near field. The near field can be obtained from the far field by some regularization procedures [21].…”

Section: Introduction and Examplesmentioning

confidence: 99%

Reconstruction of the Shape and Surface Impedance from Acoustic Scattering Data for an Arbitrary Cylinder

Liu¹,

Nakamura²,

Sini³

2007

SIAM J. Appl. Math.

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Abstract. The inverse scattering for an obstacle D ⊂ R 2 with mixed boundary condition can be considered as a prototype for radar detection of complex obstacles with coated and non-coated parts of the boundary. We construct some indicator functions for this inverse problem using the far-field pattern directly, without the necessity to transform the far-field to the near field. Based on the careful singularity analysis, these indicator functions enable us to reconstruct the shape of the obstacle and distinguish the coated from the non-coated part of the boundary. Moreover, an explicit representation formula for the surface impedance in the coated part of the boundary is also given. Our reconstruction scheme reveals that the coated part of the obstacle is less visible than the non-coated one, which corresponds to the physical fact that the coated boundary absorbs some part of the scattered wave. Numerics are presented for the reconstruction formulas, which show that both the boundary shape and the surface impedance in the coated part of boundary can be reconstructed accurately. The theoretical reconstruction techniques proposed in this work can be applied in the practical 3-dimensional electromagnetic inverse scattering problems with hopeful numerical performances, which are of great importance in the design of non-detectable obstacles.

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Section: Introduction and Examplesmentioning

confidence: 99%

Reconstruction of the Shape and Surface Impedance from Acoustic Scattering Data for an Arbitrary Cylinder

Liu¹,

Nakamura²,

Sini³

2007

SIAM J. Appl. Math.

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“…The main motivation behind the adjoint state approach is to evaluate the shape sensitivity (24) in an indirect, and computationally faster, manner by circumventing the actual computation of field sensitivities • u. Interpreting the integral in (24) as a virtual work and treating the sensitivity • u therein as a test function leads to define the adjoint state (v,v) ∈ V(0) by the weak statement…”

Section: Adjoint Solutionmentioning

confidence: 99%

Elastic-wave identification of penetrable obstacles using shape-material sensitivity framework

Bonnet

Guzina

2009

Journal of Computational Physics

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This study deals with elastic-wave identification of discrete heterogeneities (inclusions) in an otherwise homogeneous "reference" solid from limited-aperture waveform measurements taken on its surface. On adopting the boundary integral equation (BIE) framework for elastodynamic scattering, the inverse query is cast as a minimization problem involving experimental observations and their simulations for a trial inclusion that is defined through its boundary, elastic moduli, and mass density. For an optimal performance of the gradient-based search methods suited to solve the problem, explicit expressions for the shape (i.e. boundary) and material sensitivities of the misfit functional are obtained via the adjoint field approach and direct differentiation of the governing BIEs. Making use of the message-passing interface, the proposed sensitivity formulas are implemented in a data-parallel code and integrated into a nonlinear optimization framework based on the direct BIE method and an augmented Lagrangian whose inequality constraints are employed to avoid solving forward scattering problems for physically inadmissible (or overly distorted) trial inclusion configurations. Numerical results for the reconstruction of an ellipsoidal defect in a semi-infinite solid show the effectiveness of the proposed shape-material sensitivity formulation, which constitutes an essential computational component of the defect identification algorithm.

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“…It is well known that Runge's approximation property is an easy consequence of the UCP. Here the reconstruction algorithms of determining the inclusion or cavity are based the probe method developed by Ikehata in [9] (see [10] and references therein for related results). It should be noted that Runge's approximation theorem for the anisotropic elasticity was proved in [11] and [12].…”

Section: Introductionmentioning

confidence: 99%

Unique continuation for the two-dimensional anisotropic elasticity system and its applications to inverse problems

Nakamura

Wang

2006

Trans. Amer. Math. Soc.

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Abstract. Under some generic assumptions we prove the unique continuation property for the two-dimensional inhomogeneous anisotropic elasticity system. Having established the unique continuation property, we then investigate the inverse problem of reconstructing the inclusion or cavity embedded in a plane elastic body with inhomogeneous anisotropic medium by infinitely many localized boundary measurements.

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Reconstruction of the shape of the inclusion by boundary measurements

Cited by 112 publications

References 8 publications

Reconstruction of the Shape and Surface Impedance from Acoustic Scattering Data for an Arbitrary Cylinder

Reconstruction of the Shape and Surface Impedance from Acoustic Scattering Data for an Arbitrary Cylinder

Elastic-wave identification of penetrable obstacles using shape-material sensitivity framework

Unique continuation for the two-dimensional anisotropic elasticity system and its applications to inverse problems

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