127 4.3.3 Thickness reconstruction by minimizing a least square functional, p.128 ,
Handbook of mathematical functions with formulas , graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series. For sale by the Superintendent of Documents, U.S. Government Printing Oce, vol.55, 1964. ,
Conception optimale de structures, ) [Mathematics & Applications With the collaboration of Marc Schoenauer (INRIA) in the writing of Chapter, pp.49-54, 2007. ,
Weak and strong formulations for the time-harmonic eddy-current problem in general multi-connected domains, European Journal of Applied Mathematics, vol.14, issue.4, pp.387406-2003 ,
DOI : 10.1017/S0956792503005151
Eddy current approximation of Maxwell equations, volume 4 of MS&A. Modeling, Simulation and Applications Theory, algorithms and applications, pp.136-137, 2010. ,
An optimal design problem with perimeter penalization, Calculus of Variations and Partial Differential Equations, vol.39, issue.312, p.5569, 1993. ,
DOI : 10.1007/BF02163264
A justication of eddy currents model for the Maxwell equations, SIAM J. Appl. Math, vol.60, issue.5, p.18051823, 2000. ,
Theoretical tools to solve the axisymmetric Maxwell equations, Mathematical Methods in the Applied Sciences, vol.161, issue.1, p.4978, 2002. ,
DOI : 10.1002/mma.279
URL : https://hal.archives-ouvertes.fr/hal-00878222
Review of advances in quantitative eddy current nondestructive evaluation, Journal of Nondestructive Evaluation, vol.18, p.336, 1999. ,
Eddy-current signal analysis and inversion for semielliptical surface cracks, Journal of Nondestructive Evaluation, vol.7, issue.12, p.7994, 1988. ,
DOI : 10.1007/bf00565779
Bounds for Turánians of modied Bessel functions ,
Approximate model of eddy-current probe impedance for surface-breaking aws, Journal of Nondestructive Evaluation, vol.7, p.2534, 1988. ,
Topology Optimization: Theory, Methods and Applications. Engineering online library, 2003. ,
Numerical analysis of a nite-element method for the axisymmetric eddy current model of an induction furnace ,
Edge element formulations of eddy current problems, ):391405, 1999. ,
Electrical and Magnetic Methods of Non-Destructive Testing. Non-destructive evaluation series, 1997. ,
Sounding of nite solid bodies by way of topological derivative, Internat. J. Numer. Methods Engrg, vol.61, issue.13, p.23442373, 2004. ,
Analyse fonctionnelle Collection Mathématiques Appliquées pour la Maîtrise. [Collection of Applied Mathematics for the Master's Degree], Théorie et applications. [Theory and applications], pp.17-37, 1983. ,
Mixed and hybrid nite element methods, 1991. ,
Variational methods in shape optimization problems Progress in Nonlinear Dierential Equations and their Applications, 65, Birkhäuser Boston Inc, 2005. ,
N-Dimensional Shape Optimization under Capacitary Constraint, Journal of Differential Equations, vol.123, issue.2, p.504522, 1995. ,
DOI : 10.1006/jdeq.1995.1171
URL : http://doi.org/10.1006/jdeq.1995.1171
Shape optimization for Dirichlet problems: Relaxed formulation and optimality conditions, Applied Mathematics and Optimization, vol.40, issue.1, p.1749, 1991. ,
DOI : 10.1007/BF01442391
An existence result for a class of shape optimization problems, Archive for Rational Mechanics and Analysis, vol.3, issue.2, p.183195, 1993. ,
DOI : 10.1007/BF00378167
Numerical modeling in induction heating for axisymmetric geometries, IEEE Transactions on Magnetics, vol.33, pp.739-745, 1997. ,
Shape optimization for the Maxwell equations under weaker regularity of the data, Comptes Rendus Mathematique, vol.348, issue.21-22, 2010. ,
DOI : 10.1016/j.crma.2010.10.021
A Density Result in Two-Dimensional Linearized Elasticity, and Applications, Archive for Rational Mechanics and Analysis, vol.167, issue.3, p.211233, 2003. ,
DOI : 10.1007/s00205-002-0240-7
Characterization of small depth surface breaking defects with eddy current sensor measurements, Proc. ECNDT, 2006. ,
Modèles d'impédance généralisée en diraction inverse, École Polytechnique ,
On the existence of a solution in a domain identication problem, J. Math. Anal. Appl, vol.52, issue.2, p.189219, 1975. ,
Analyse asymptotique et numérique de la diraction d'ondes par des ls minces, 2008. ,
Inverse acoustic and electromagnetic scattering theory, Applied Mathematical Sciences, vol.93, 2013. ,
DOI : 10.1007/978-1-4614-4942-3
Singularities of electromagnetic elds in polyhedral domains, Arch. Ration. Mech. Anal, vol.151, issue.3, p.221276, 2000. ,
Singularities of eddy current problems, ESAIM: Mathematical Modelling and Numerical Analysis, vol.37, issue.5, p.807831, 2003. ,
DOI : 10.1051/m2an:2003056
Shape derivatives of boundary integral operators in electromagnetic scattering. Part I: Shape dierentiability of pseudo-homogeneous boundary integral operators. Integral Equations Operator Theory, pp.509535-2012 ,
URL : https://hal.archives-ouvertes.fr/hal-00453948
Mathematical analysis and numerical methods for science and technology Spectral theory and applications, With the collaboration of Michel Artola and Michel Cessenat, Translated from the French by, 1990. ,
Modèles et asymptotiques des interfaces nes et périodiques ,
Level set methods for inverse scattering???some recent developments, Inverse Problems, vol.25, issue.12, p.125001, 2009. ,
DOI : 10.1088/0266-5611/25/12/125001
URL : https://hal.archives-ouvertes.fr/hal-00440936
Applied Structural Mechanics: Fundamentals of Elasticity, Load-Bearing Structures, Structural Optimization : Including Exercises. U.S. Government Printing Oce, 1997. ,
DOI : 10.1007/978-3-642-59205-8
Introduction to partial dierential equations, 1995. ,
Topological derivative for the inverse scattering of elastic waves, The Quarterly Journal of Mechanics and Applied Mathematics, vol.57, issue.2, p.161179, 2004. ,
DOI : 10.1093/qjmam/57.2.161
URL : https://hal.archives-ouvertes.fr/hal-00092401
Small-inclusion asymptotic of mist functionals for inverse problems in acoustics, Inverse Problems, vol.22, issue.5, p.17611785, 2006. ,
Lectures on Cauchy's Problem in Linear Partial Dierential Equations, 1923. ,
Mémoire sur le problème d'analyse relatif à l'équilibre des plaques élastiques encastrées. Mémoires présentés par divers savants à l'Académie des sciences de l, 1908. ,
GENERALIZED IMPEDANCE BOUNDARY CONDITIONS FOR SCATTERING PROBLEMS FROM STRONGLY ABSORBING OBSTACLES: THE CASE OF MAXWELL'S EQUATIONS, Mathematical Models and Methods in Applied Sciences, vol.18, issue.10, p.17871827, 2008. ,
DOI : 10.1142/S0218202508003194
Variation et optimisation de formes, Mathématiques & Applications (Berlin) [Mathematics & Applications, vol.48, 2005. ,
DOI : 10.1007/3-540-37689-5
The domain derivative of time-harmonic electromagnetic waves at interfaces, Mathematical Methods in the Applied Sciences, vol.55, issue.14, pp.16811689-2012 ,
DOI : 10.1002/mma.2548
Inverse problem methodology and finite elements in the identification of cracks, sources, materials, and their geometry in inaccessible locations, IEEE Transactions on Magnetics, vol.27, issue.3, pp.3433-3443, 1991. ,
DOI : 10.1109/20.79086
Complete monotonicity of modied Bessel functions, Proc. Amer. Math. Soc, vol.108, issue.2, p.353361, 1990. ,
Perturbation theory for linear operators Classics in Mathematics, 1995. ,
An introduction to the mathematical theory of inverse problems, Applied Mathematical Sciences, vol.120, 2011. ,
On approximate boundary conditinos for electromagnetic elds on the surface of highly condcting bodies. Research in the propagation of radio waves, p.5 ,
Problèmes aux limites non homogènes et applications, Travaux et Recherches Mathématiques, p.20, 1968. ,
Quantitative Imaging of Corrosion in Plates by Eddy Current Methods, SIAM Journal on Applied Mathematics, vol.58, issue.5, p.15091531, 1998. ,
DOI : 10.1137/S0036139996313356
Application of the topological asymptotic expansion to inverse scattering problems, Numerical methods for scientic computing ,
The topological asymptotic expansion for the Maxwell equations and some applications, Inverse Problems, vol.21, issue.2, pp.547-564, 2005. ,
DOI : 10.1088/0266-5611/21/2/008
On Physical Lines of Force. 1861 ,
A Dynamical Theory of the Electromagnetic Field, 1865. ,
A Treatise on Electricity and Magnetism. 1873 ,
Nonlinear Diusion of Electromagnetic Fields: With Applications to Eddy Currents and Superconductivity. Electromagnetism Series, 1998. ,
Applied shape optimization for uids. Numerical Mathematics and Scientic Computation, 2001. ,
Finite element methods for Maxwell's equations. Numerical Mathematics and Scientic Computation, 2003. ,
Etude de problèmes d'optimal design Optimization Techniques Modeling and Optimization in the Service of Man Part 2, Lecture Notes in Computer Science, vol.41, p.5462, 1976. ,
Sur le contrôle par un domaine géométrique, 1976. ,
Couplage de méthodes d'échantillonnage et de méthodes d'optimisation de formes pour des problèmes de diraction inverse, École Polytechnique ,
Reconstruction of the electromagnetic eld in layered media using the concept of approximate transmission conditions. Antennas and Propagation, IEEE Transactions on, vol.59, issue.8, p.29642972, 2011. ,
Sensibilit?? de l'??quation de la chaleur aux sauts de conductivit??, Comptes Rendus Mathematique, vol.341, issue.5 ,
DOI : 10.1016/j.crma.2005.07.005
Sensitivity analysis based on analytic approach for shape optimization of electromagnetic devices: interface problem of iron and air. Magnetics, IEEE Transactions on, vol.27, issue.5, p.41424145, 1991. ,
Inverse Scattering from Two-Dimensional Thin Inclusions and Cracks, École Polytechnique ,
URL : https://hal.archives-ouvertes.fr/pastel-00004834
Development of a 3D Electromagnetic Model for Eddy Current Tubing Inspection: Application to Steam Generator Tubing, AIP Conference Proceedings, p.321328, 2003. ,
DOI : 10.1063/1.1711640
Approximate transmission conditions through a weakly oscillating thin layer, Mathematical Methods in the Applied Sciences, vol.67, issue.4, p.435453, 2009. ,
DOI : 10.1002/mma.1045
URL : https://hal.archives-ouvertes.fr/inria-00334772
Domain derivatives in electromagnetic scattering, Math. Methods Appl. Sci, vol.19, issue.15, p.11571175, 1996. ,
Introduction to structural optimization Course held at the Department of Mechanics of Solids, International Centre for Mechanical Sciences, International Centre for Mechanical Sciences, Courses and Lectures, issue.212, 1974. ,
Shape optimization of electromagnetic devices including eddy-currents. Magnetics, IEEE Transactions on, vol.31, issue.3, 1995. ,
A level-set approach for inverse problems involving obstacles, ESAIM Contrôle Optim. Calc. Var, vol.1, issue.96, p.1733, 1995. ,
High-order numerical modelling of highly conductive thin sheets, 2008. ,
Estimating the eddy-current modeling error. Magnetics, IEEE Transactions on, vol.44, issue.6, p.686689, 2008. ,
Approximate Boundary Conditions in Electromagnetics, IEE Publication Series. Institution of Electrical Engineers, 1995. ,
DOI : 10.1049/PBEW041E
On optimal shape design, J. Math. Pures Appl, vol.72, issue.96, p.537551, 1993. ,
Eddy currents in linear conducting media. Studies in electrical and electronic engineering, 1985. ,
On the solution of incorrectly put problems and the regularisation method, Outlines Joint Sympos. Partial Dierential Equations, p.261, 1963. ,
Méthodes Asymptotiques pour la Propagation des Ondes dans les Milieux comportant des Fentes, 2004. ,
Reconstruction de défauts à partir de données issues de capteurs à courants de Foucault avec modèle direct diérentiel, 2010. ,
Eddy current tomography based on a nite element forward model with additive regularization, AIP Conference Proceedings, p.782789, 2009. ,
Introduction to Shape Optimization Problems and Free Boundary Problems, Shape optimization and free boundaries, 1990. ,
DOI : 10.1007/978-94-011-2710-3_12
Eddy current testing of anomalies in conductive materials. i. qualitative imaging via diraction tomography techniques, Magnetics IEEE Transactions on, vol.27, issue.6, p.44164437, 1991. ,
URL : https://hal.archives-ouvertes.fr/hal-00643928
Eddy current testing of anomalies in conductive materials. II. Quantitative imaging via deterministic and stochastic inversion techniques, IEEE Transactions on Magnetics, vol.28, issue.3, p.18501862, 1992. ,
DOI : 10.1109/20.141295
URL : https://hal.archives-ouvertes.fr/hal-00643928