Asymptotic Imaging of Perfectly Conducting Cracks

  title={Asymptotic Imaging of Perfectly Conducting Cracks},
  author={Habib M. Ammari and Hyeonbae Kang and Hyundae Lee and Won-Kwang Park},
  journal={SIAM J. Sci. Comput.},
In this paper, we consider cracks with Dirichlet boundary conditions. We first derive an asymptotic expansion of the boundary perturbations that are due to the presence of a small crack. Based on this formula, we design a noniterative approach for locating a collection of small cracks. In order to do so, we construct a response matrix from the boundary measurements. The location and the length of the crack are estimated, respectively, from the projection onto the noise space and the first… 
Boundary Perturbations Due to the Presence of Small Linear Cracks in an Elastic Body
In this paper, Neumann cracks in elastic bodies are considered. We establish a rigorous asymptotic expansion for the boundary perturbations of the displacement (and traction) vectors that are due to
Imaging Schemes for Perfectly Conducting Cracks
An analytic framework that uses asymptotic expansions which are uniform with respect to the wavelength-to-crack size ratio in combination with a hypothesis test based formulation to construct specific procedures for detection of perfectly conducting cracks is introduced.
Direct sampling method for retrieving small perfectly conducting cracks
  • W. Park
  • Mathematics
    J. Comput. Phys.
  • 2018
The wave scattering problem by a crack in R 2 with impedance type boundary is considered. This problem models the diffraction of waves by thin two-sided cylindrical screens. A numerical method for
Fast Imaging of Short Perfectly Conducting Cracks in Limited-Aperture Inverse Scattering Problem
In this paper, we consider the application and analysis of subspace migration technique for a fast imaging of a set of perfectly conducting cracks with small length in two-dimensional
Structure and properties of linear sampling method for perfectly conducting, arc-like cracks
We consider the imaging of arbitrary shaped, arc-like perfectly conducting cracks located in the two-dimensional homogeneous space via linear sampling method. Based on the structure of eigenvectors


A boundary integral equation method for an inverse problem related to crack detection
This paper discusses an application of a boundary integral equation method (BIEM) to an inverse problem of determining the shape and the location of cracks by boundary measurements. Suppose that a
On derivative of energy functional for elastic bodies with cracks and unilateral conditions
In this paper we consider elasticity equations in a domain having a cut (a crack) with unilateral boundary conditions considered at the crack faces. The boundary conditions provide a mutual
Regular Perturbation Methods for a Region with a Crack
The paper considers a model problem for Poisson's equation for a region containing a crack or a set of cracks under arbitrary linear perturbation. Variational formulation of the problem using smooth
Shape sensitivity of a plane crack front
The 3D‐elasticity model of a solid with a plane crack under the stress‐free boundary conditions at the crack is considered. We investigate variations of a solution and of energy functionals with
Identification of planar cracks by complete overdetermined data: inversion formulae
The problem of determining a crack by overspecified boundary data is considered. When complete data are available on the external boundary, a reciprocity gap concept is introduced. This concept
Stability and Uniqueness for the Crack Identification Problem
A new pointwise regularity concept at the boundary of an open set is introduced and analyzed which proves the unique identifiability for a large class of closed sets, including sets with an infinite number of connected components of positive capacity and totally disconnected sets.
Identifying Scattering Obstacles by the Construction of Nonscattering Waves
The view is that the connections between algorithms are more illuminating than their differences, particularly with regard to the linear sampling method, and it is shown that, for a scatterer with Dirichlet boundary conditions, there is a nontrivial incident field that does not generate a scattered field.
Determining a Surface Breaking Crack from Steady-State Electrical Boundary Measurements Reconstruction Method
We seek a non-destructive testing method to detect a radial surface breaking crack in a two-dimensional circular disk. The detection method utilizes steady-state electrical boundary measurements. A
On finding a surface crack from boundary measurements
We prove the uniqueness of the determination of a surface crack from one special boundary measurement of an electrical or elastic field. Then we suggest and test a numerical algorithm for