.. Optimisation-topologique-par-la-méthode-d-'homogénéisation, 24 1.3.1 Position duprobì eme original, p.26

.. Applicationàapplication-`-applicationà-la-conception-d-'un-filtre-micro-ondes, 69 3.1.2 Position duprobì eme, p.73

.. De-bézier, Illustration du contrôle pseudo-local des courbes, p.44

.. Champ-de-vecteur-v-3, 88 3.17 Résultats -Champ de vecteur v 1, Résultats -Champ de vecteur v 3 . . . . . . . . . . . . . . . . . . . . . . . . 89

]. L. Afraites, M. Dambrine, K. Eppler, and D. Kateb, Déformations libres de contours pour l'optimisation de formes et application enélectromagnétisme enélectromagnétisme Detecting perfectly insulated obstacles by shape optimization techniques of order two, Discrete Contin. Dyn. Syst

G. Allaire, Shape Optimization by the Homogenization Method, Applied Mathematical Sciences
DOI : 10.1007/s002110050253

G. Allaire, C. Dapogny, and P. Frey, Shape optimization with a level set based mesh evolution method, Computer Methods in Applied Mechanics and Engineering, vol.282, pp.22-53, 2014.
DOI : 10.1016/j.cma.2014.08.028

URL : https://hal.archives-ouvertes.fr/hal-00933545

G. Allaire, F. De-gournay, F. Jouve, and A. Toader, Structural optimization using topological and shape sensitivity via a level set method, Control Cybernet, vol.34, issue.1, pp.59-80, 2005.

G. Allaire, F. Jouve, and A. Toader, Structural optimization using sensitivity analysis and a level-set method, Journal of Computational Physics, vol.194, issue.1, pp.363-393, 2004.
DOI : 10.1016/j.jcp.2003.09.032

G. Allaire, F. Jouve, and A. Toader, Structural optimization using sensitivity analysis and a level-set method, Journal of Computational Physics, vol.194, issue.1, pp.363-393, 2004.
DOI : 10.1016/j.jcp.2003.09.032

S. Amstutz, The topological asymptotic for the navier-stokes equations. ESAIM : Control, Optimisation and Calculus of Variations, pp.401-425

S. Amstutz, I. Horchani, and M. Masmoudi, Crack detection by the topological gradient method, Control and Cybernetics, vol.34, issue.1, pp.81-101, 2005.

S. Amstutz, T. Takahashi, and B. Vexler, Topological sensitivity analysis for timedependent problems. ESAIM : Control, Optimisation and Calculus of Variations, pp.427-455, 2007.
DOI : 10.1051/cocv:2007059

URL : https://hal.archives-ouvertes.fr/hal-00590615

M. Badra, F. Caubet, and M. Dambrine, DETECTING AN OBSTACLE IMMERSED IN A FLUID BY SHAPE OPTIMIZATION METHODS, Mathematical Models and Methods in Applied Sciences, vol.23, issue.10, pp.2069-2101, 2011.
DOI : 10.1007/BFb0004434

URL : https://hal.archives-ouvertes.fr/hal-00867183

M. Bauer, M. Bruveris, and P. W. Michor, Overview of the Geometries of Shape Spaces and Diffeomorphism Groups, Journal of Mathematical Imaging and Vision, vol.68, issue.3, pp.60-97, 2014.
DOI : 10.1137/060664707

C. Beltrán and L. M. Pardo, Fast Linear Homotopy to Find Approximate Zeros of??Polynomial Systems, Foundations of Computational Mathematics, vol.25, issue.2, pp.95-129, 2011.
DOI : 10.1145/317275.317286

L. Bourgeois and J. Dardé, A quasi-reversibility approach to solve the inverse obstacle problem, Inverse Problems and Imaging, vol.4, issue.3, pp.351-377, 2010.
DOI : 10.3934/ipi.2010.4.351

URL : https://hal.archives-ouvertes.fr/hal-00873059

M. Burger, B. Hackl, and W. Ring, Incorporating topological derivatives into level set methods, Journal of Computational Physics, vol.194, issue.1, pp.344-362, 2004.
DOI : 10.1016/j.jcp.2003.09.033

M. Burger, B. Hackl, and W. Ring, Incorporating topological derivatives into level set methods, Journal of Computational Physics, vol.194, issue.1, pp.344-362, 2004.
DOI : 10.1016/j.jcp.2003.09.033

M. Burger and S. J. Osher, A survey on level set methods for inverse problems and optimal design, European Journal of Applied Mathematics, vol.16, issue.2, pp.263-301, 2005.
DOI : 10.1017/S0956792505006182

F. Caubet, Instability of an Inverse Problem for the Stationary Navier--Stokes Equations, SIAM Journal on Control and Optimization, vol.51, issue.4, pp.2949-2975, 2013.
DOI : 10.1137/110836857

URL : https://hal.archives-ouvertes.fr/hal-00696174

F. Caubet, C. Conca, and M. Godoy, On the detection of several obstacles in 2D Stokes flow: Topological sensitivity and combination with shape derivatives, Inverse Problems and Imaging, vol.10, issue.2, pp.327-367, 2016.
DOI : 10.3934/ipi.2016003

URL : https://hal.archives-ouvertes.fr/hal-01191099

A. N. Christiansen, M. Nobel-jørgensen, N. Aage, O. Sigmund, and J. A. Baerentzen, Topology optimization using an explicit interface representation. Structural and Multidisciplinary Optimization, pp.387-399, 2014.
DOI : 10.1007/s00158-013-0983-9

M. T. Chu, A simple application of the homotopy method to symmetric eigenvalue problems, Linear Algebra and its Applications, vol.59, pp.85-90, 1984.
DOI : 10.1016/0024-3795(84)90160-5

D. Colton and R. Kress, Inverse acoustic and electromagnetic scattering theory, Applied Mathematical Sciences, vol.93, 1998.
DOI : 10.1007/978-3-662-03537-5

J. Dardé, Quasi-reversibility and level set methods applied to elliptic inverse problems. Theses, 2010.

M. J. De-ruiter and F. V. Keulen, Computational techniques for materials, composites and composite structures. chapter Topology of Optimization : Approaching the Material Distribution Problem Using a Topological Function Description, pp.111-119, 2000.

T. A. El-mihoub, A. A. Hopgood, L. Nolle, and A. Battersby, Hybrid genetic algorithms : A review

H. A. Eschenauer, V. V. Kobelev, and A. Schumacher, Bubble method for topology and shape optimization of structures. Structural optimization, pp.42-51, 1994.

G. Farin, Curves and Surfaces for CAGD : A Practical Guide, 2002.

L. Fogel, A. Owens, and M. Walsh, Artificial Intelligence through Simulated Evolution, 1966.
DOI : 10.1109/9780470544600.ch7

S. Garreau, P. Guillaume, and M. Masmoudi, The Topological Asymptotic for PDE Systems: The Elasticity Case, SIAM Journal on Control and Optimization, vol.39, issue.6, pp.1756-1778, 2001.
DOI : 10.1137/S0363012900369538

S. Garreau, P. Guillaume, and M. Masmoudi, The Topological Asymptotic for PDE Systems: The Elasticity Case, SIAM Journal on Control and Optimization, vol.39, issue.6, pp.1756-1778, 2001.
DOI : 10.1137/S0363012900369538

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, 1989.

P. Guillaume and K. S. Idris, The Topological Asymptotic Expansion for the Dirichlet Problem, SIAM Journal on Control and Optimization, vol.41, issue.4, pp.1042-1072, 2002.
DOI : 10.1137/S0363012901384193

K. Gupta, R. Garg, and R. Chadha, Computer-aided Design of Microwave Circuits, Artech, 1981.

S. Ha and S. Cho, Level set based topological shape optimization of geometrically nonlinear structures using unstructured mesh, Computers & Structures, vol.86, issue.13-14, pp.13-141447, 2008.
DOI : 10.1016/j.compstruc.2007.05.025

J. Hadamard, Mémoire sur leprobì eme d'analyse relatifàrelatifà l'´ equilibre des plaquesélastiques plaquesélastiques encastrées. Mémoires présentés par divers savantsàsavants`savantsà l'Académie des sciences de l, 1908.

F. Hecht, Finite Element Library Freefem++

J. H. Holland, Adaptation in Natural and Artificial Systems : An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence, 1992.

Y. Hsu, A review of structural shape optimization, Computers in Industry, vol.25, issue.1, pp.3-13, 1994.
DOI : 10.1016/0166-3615(94)90028-0

D. Hutton, Fundamentals of Finite Element Analysis. Engineering Series, 2003.

V. Isakov, Inverse problems for partial differential equations, 2006.

J. M. Johnson, Genetic algorithms in engineering electromagnetics, IEEE Antennas and Propagation Magazine, vol.39, issue.4, 1997.
DOI : 10.1109/74.632992

H. Khalil, Développement des techniques d'optimisation de forme pour la conception de composants hyperfréquences, Faculté des Sciences et Techniques de Limoges, 2009.

S. Larnier, J. Fehrenbach, and M. Masmoudi, The Topological Gradient Method: From Optimal Design to Image Processing, Milan Journal of Mathematics, vol.11, issue.2, pp.411-441, 2012.
DOI : 10.1007/978-3-7091-6586-7_13

URL : https://hal.archives-ouvertes.fr/hal-01333752

N. Mahdi, Développement d'une bibliothèque de techniques d'optimisation de formes pour la conception assistée par ordinateur de composants et de circuits hyperfréquences, Faculté des Sciences et Techniques de Limoges, 2012.

]. A. Marco and J. Martinez, A fast and accurate algorithm for solving Bernstein???Vandermonde linear systems, Linear Algebra and its Applications, vol.422, issue.2-3, pp.616-628, 2007.
DOI : 10.1016/j.laa.2006.11.020

M. Masmoudi, J. Pommier, and B. Samet, The topological asymptotic expansion for the Maxwell equations and some applications, Inverse Problems, vol.21, issue.2, 2005.
DOI : 10.1088/0266-5611/21/2/008

F. Murat and J. Simon, Quelques résultats sur le contrôle par un domaine géométrique. VI Laboratoire d'Analyse Numérique, 1974.

J. O. Rourke, Computational Geometry in C, 1998.

S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988.
DOI : 10.1016/0021-9991(88)90002-2

URL : http://www.ann.jussieu.fr/~frey/papers/levelsets/Osher S., Fronts propagating with curvature dependent speed.pdf

S. J. Osher and F. Santosa, Level Set Methods for Optimization Problems Involving Geometry and Constraints, Journal of Computational Physics, vol.171, issue.1, pp.272-288, 2001.
DOI : 10.1006/jcph.2001.6789

O. Pantz and K. Trabelsi, Simultaneous shape, topology, and homogenized properties optimization, Structural and Multidisciplinary Optimization, vol.37, issue.4, pp.361-365, 2007.
DOI : 10.1007/978-3-642-87722-3

P. Persson, Mesh Generation for Implicit Geometries, p.807802, 2005.

J. Pommier and B. Samet, The Topological Asymptotic for the Helmholtz Equation with Dirichlet Condition on the Boundary of an Arbitrarily Shaped Hole, SIAM Journal on Control and Optimization, vol.43, issue.3, pp.899-921, 2004.
DOI : 10.1137/S036301290241616X

]. I. Rechenberg, Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Problemata, 15. Frommann-Holzboog, 1973.

A. Schumacher, Topologieoptimierung von Bauteilstrukturen unter Verwendung von Lochpositionierungskriterien, 1995.

A. Schumacher, Topologieoptimisierung von Bauteilstrukturen unter Verwendung von Lopchpositionierungkrieterien, 1995.

H. Schwefel, Numerical Optimization of Computer Models, 1981.

J. Sethian, Level Set Methods and Fast Marching Methods : Evolving Interfaces in Computational Geometry, Fluid Mechanics

J. Sethian, Level set methods and fast marching methods Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, 1999.

J. Sethian and A. Wiegmann, Structural Boundary Design via Level Set and Immersed Interface Methods, Journal of Computational Physics, vol.163, issue.2, pp.489-528, 2000.
DOI : 10.1006/jcph.2000.6581

URL : http://www.math.berkeley.edu/~sethian/Publications/../Papers/sethian.optimal_design.ps.gz

M. Shub, Complexity of Bezout???s Theorem VI: Geodesics in the Condition (Number) Metric, Foundations of Computational Mathematics, vol.133, issue.2, pp.171-178, 2009.
DOI : 10.1137/0733008

J. Sokolowski and A. Zochowski, On the topological derivative in shape optimization

J. Soko-lowski and A. Zochowski, On the topological derivative in shape optimization

P. Wei, M. Y. Wang, and X. Xing, A study on X-FEM in continuum structural optimization using a level set model, Computer-Aided Design, vol.42, issue.8, pp.708-719, 2010.
DOI : 10.1016/j.cad.2009.12.001

L. Younes, Shapes and diffeomorphisms, 2010.
DOI : 10.1007/978-3-642-12055-8

URL : https://link.springer.com/content/pdf/bfm%3A978-3-642-12055-8%2F1.pdf