Performance analysis of multi-frequency topological derivative for reconstructing perfectly conducting cracks

Park, Won-Kwang

doi:10.1016/j.jcp.2017.02.007

Cited by 29 publications

(19 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, we consider multi-frequency approach as proposed in the papers by Park (2013) and Park (2017). More precisely, we follow the ideas introduced in the works by Louër and Rapún (2019) and Pena and Rapún (2020), which consist in defining a weighted topological derivative in the form (3.5)…”

Section: Numerical Resultsmentioning

confidence: 99%

Damage identification in plate structures based on the topological derivative method

Silva

Novotny

2021

Struct Multidisc Optim

View full text Add to dashboard Cite

In this work, a novel approach for solving a damage identification problem in plate structures based on the topological derivative method is proposed. The forward problems are governed by the elastodynamic Kirchhoff and Reissner-Mindlin plate bending models in the frequency domain. The inverse problem consists in finding a set of damages from pointwise domain measurements of the plate displacement field. The damage is represented by a variation in the plate thickness, which is assumed to be given by a piecewise constant function. A shape functional measuring the misfit between the available data (measurements) and the displacements computed from the model is minimized with respect to the geometrical support of the unknown damage distribution, by using the topological derivative method. Finally, some numerical experiments are presented, showing different features of the proposed approach in detecting and locating damages of varying sizes and shapes by taking into account noisy data.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

Damage identification in plate structures based on the topological derivative method

Silva

Novotny

2021

Struct Multidisc Optim

View full text Add to dashboard Cite

show abstract

“…Numerical examples for the 2D transmission case can be found in Carpio and Rapún (2008a, b) and Park (2012), while the 3D case is illustrated in Carpio and Rapún (2008b) and Guzina and Bonnet (2006). Multifrequency data experiments are shown in Masmoudi et al (2005), Pommier and Samet (2004) and Park (2017) for the 2D Dirichlet case; in Funes et al (2016) for the 2D Neumann problem and in Park (2013) for crack-like penetrable 2D objects. The reader might also find interesting the numerical experiments presented in Le Louër and Rapún (2019) for the 2D and 3D impedance case (not considered in the present paper), or in Rapún (2020), where scatterers of different nature simultaneously immersed in double-struckR2 are found without knowing their nature by topological energy methods.…”

Section: Numerical Examplesmentioning

confidence: 99%

Topological sensitivity analysis revisited for time-harmonic wave scattering problems. Part I: the free space case

Louër

Rapún

2021

View full text Add to dashboard Cite

PurposeIn this paper, the authors revisit the computation of closed-form expressions of the topological indicator function for a one step imaging algorithm of two- and three-dimensional sound-soft (Dirichlet condition), sound-hard (Neumann condition) and isotropic inclusions (transmission conditions) in the free space.Design/methodology/approachFrom the addition theorem for translated harmonics, explicit expressions of the scattered waves by infinitesimal circular (and spherical) holes subject to an incident plane wave or a compactly supported distribution of point sources are available. Then the authors derive the first-order term in the asymptotic expansion of the Dirichlet and Neumann traces and their surface derivatives on the boundary of the singular medium perturbation.FindingsAs the shape gradient of shape functionals are expressed in terms of boundary integrals involving the boundary traces of the state and the associated adjoint field, then the topological gradient formulae follow readily.Originality/valueThe authors exhibit singular perturbation asymptotics that can be reused in the derivation of the topological gradient function that generates initial guesses in the iterated numerical solution of any shape optimization problem or imaging problems relying on time-harmonic acoustic wave propagation.

show abstract

“…Two-dimensional plot for (19) is shown in Figure 5. By considering the oscillation pattern, we can easily observe that I AIF (x, L) yields better images owing to less oscillation than I IF (x) does.…”

Section: Improvement Of Indicator Function: Multiple Directions Of Inmentioning

confidence: 99%

Direct sampling method for retrieving small perfectly conducting cracks

Park

2018

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

We consider direct sampling method for finding location of a set of linear perfectly conducting cracks with small length from collected far-field data corresponding to the single incident field. To show the feasibility of direct sampling method, we first prove that the indicator function of direct sampling method can be represented by the Bessel function of order zero and the length of cracks. Results of numerical simulations are shown to support the fact that the imaging performance is highly depending on the length of cracks. To explain the fact that imaging performance is highly depending on the rotation of crack, we perform further analysis of direct sampling method by establishing a representation by the Bessel functions of order zero and one.

show abstract

Performance analysis of multi-frequency topological derivative for reconstructing perfectly conducting cracks

Cited by 29 publications

References 57 publications

Damage identification in plate structures based on the topological derivative method

Damage identification in plate structures based on the topological derivative method

Topological sensitivity analysis revisited for time-harmonic wave scattering problems. Part I: the free space case

Direct sampling method for retrieving small perfectly conducting cracks

Contact Info

Product

Resources

About