Electromagnetic inverse shape problem for coated obstacles

Chaulet, Nicolas; Haddar, Houssem

doi:10.1007/s10444-015-9406-3

Cited by 2 publications

(3 citation statements)

References 28 publications

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“…We extend the Lagrangian approach to derive the shape gradient on the basis of complex‐valued solutions of adjoint P and state E boundary value problems. The shape sensitivity analysis for Maxwell's equations gets more complicated because of the regularity preservation . In Section 2, it is discussed that we need to use the covariant transformation to guarantee that solutions of adjoint and state problems in the mapped domain are still H (curl; Ω) functions.…”

Section: Introductionmentioning

confidence: 99%

“…The shape sensitivity analysis for Maxwell's equations gets more complicated because of the regularity preservation. 14,15 In Section 2, it is discussed that we need to use the covariant transformation to guarantee that solutions of adjoint and state problems in the mapped domain are still H(curl; Ω) functions. The final formula is of a volume integral, which is continuous in the energy norm and well defined on the natural variational space.…”

Section: Introductionmentioning

confidence: 99%

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Shape sensitivity analysis of metallic nano particles

Sargheini

Paganini

Hiptmair

et al. 2016

Int J Numerical Modelling

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Shape sensitivity measures the impact of small perturbations of geometric features of a problem on certain quantities of interest. The shape sensitivity of PDE (partial differential equation) constrained output functionals is derived with the help of shape gradients. In electromagnetic scattering problems, the standard procedure of the Lagrangian approach cannot be applied because of solution of the state problem is complex valued. We derive a closed‐form formula of the shape gradient of a generic output functional constrained by Maxwell's equations. We employ cubic B‐splines to model local deformations of the geometry and derive sensitivity probings over the surface of the scatterer. We also define a sensitivity representative function over the surface of the scatterer on the basis of local sensitivity measurements. Several numerical experiments are conducted to investigate the shape sensitivity of different output functionals for different geometric settings.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Shape sensitivity analysis of metallic nano particles

Sargheini

Paganini

Hiptmair

et al. 2016

Int J Numerical Modelling

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“…For example, we can mention the works of Cakoni et al [15,14] and Caubet et al [17] for the Laplace's equation, of Bourgeois et al [12] and Kateb et al [37] for the Helmholtz equation and of Chaulet et al [19] for the Maxwell's equations.…”

Section: Introduction and General Notationsmentioning

confidence: 99%

Shape Sensitivity Analysis for Elastic Structures with Generalized Impedance Boundary Conditions of the Wentzell Type—Application to Compliance Minimization

Caubet

Kateb

Louër

2018

J Elast

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To cite this version:Fabien Caubet, Djalil Kateb, Frédérique Le Louër. Shape sensitivity analysis for elastic structures with generalized impedance boundary conditions of the Wentzell type -Application to compliance minimization. Journal of Elasticity, Springer Verlag, In press, Journal of Elasticity. Abstract This paper focuses on Generalized Impedance Boundary Conditions (GIBC) with second order derivatives in the context of linear elasticity and general curved interfaces. A condition of the Wentzell type modeling thin layer coatings on some elastic structure is obtained through an asymptotic analysis of order one of the transmission problem at the thin layer interfaces with respect to the thickness parameter. We prove the well-posedness of the approximate problem and the theoretical quadratic accuracy of the boundary conditions. Then we perform a shape sensitivity analysis of the GIBC model in order to study a shape optimization/optimal design problem. We prove the existence and characterize the first shape derivative of this model. A comparison with the asymptotic expansion of the first shape derivative associated to the original thin layer transmission problem shows that we can interchange the asymptotic and shape derivative analysis. Finally we apply these results to the compliance minimization problem. We compute the shape derivative of the compliance in this context and present some numerical simulations.

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Electromagnetic inverse shape problem for coated obstacles

Cited by 2 publications

References 28 publications

Shape sensitivity analysis of metallic nano particles

Shape sensitivity analysis of metallic nano particles

Shape Sensitivity Analysis for Elastic Structures with Generalized Impedance Boundary Conditions of the Wentzell Type—Application to Compliance Minimization

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