Shape Optimization by the Homogenization Method, vol.146, p.157, 2001. ,
Structural optimization using sensitivity analysis and a level-set method, Journal of computational physics, vol.194, p.48, 2004. ,
, Conception optimale de structures, vol.58, pp.31-34, 2007.
A linearized approach to worst-case design in parametric and geometric shape optimization, Mathematical Models and Methods in Applied Sciences, vol.24, issue.11, p.103, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00918896
Multi-phase structural optimization via a level set method, ESAIM: control, optimisation and calculus of variations, vol.20, pp.576-611, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00839464
A deterministic approximation method in shape optimization under random uncertainties, SMAI Journal of Computational Mathematics, vol.1, p.103, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01160256
Level set approach to mean curvature flow in arbitrary codimension, Journal of Differential Geometry, vol.43, p.135, 1994. ,
Aspects théoriques et numériques en optimisation de forme topologique, p.39, 2003. ,
A notion of compliance robustness in topology optimization, ESAIM: Control, Optimisation and Calculus of Variations, vol.22, p.103, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-00947108
Shape derivative of cost function for singular point: Evaluation by the generalized J integral, JSIAM Letters, vol.6, p.139, 2014. ,
The p-and hp versions of the finite element method, an overview, Computer Methods in Applied Mechanics and Engineering, vol.80, p.143, 1990. ,
Optimal arrangement of holes in a two-dimensional heat conductor by a special boundary integral method, International Journal for Numerical Methods in Engineering, vol.18, p.128, 1982. ,
Manufacturing processes-II, vol.2, p.154, 2004. ,
Topology optimization: theory, methods, and applications, p.157, 2013. ,
Functional analysis, Sobolev spaces and partial differential equations, 2010. ,
Inverse design of an ultra-compact broadband optical diode based on asymmetric spatial mode conversion, In: Scientific reports, vol.6, p.101, 2016. ,
The shape and topological optimizations connection, Computer methods in applied mechanics and engineering, vol.188, p.40, 2000. ,
Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût, ESAIM: Mathematical Modelling and Numerical Analysis, vol.20, p.41, 1986. ,
A new level-set based approach to shape and topology optimization under geometric uncertainty, Structural and Multidisciplinary Optimization, vol.44, p.114, 2011. ,
Boundary integral operators on Lipschitz domains: elementary results, SIAM Journal on Mathematical Analysis, vol.19, p.151, 1988. ,
A Singularly mixed boundary value problem, Communications in Partial Differential Equations 21, p.149, 1996. ,
Shape optimization, level set methods on unstructured meshes and mesh evolution, 2013. ,
URL : https://hal.archives-ouvertes.fr/tel-00916224
Optimization of the shape of regions supporting boundary conditions, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02064477
Elliptic boundary value problems on corner domains: smoothness and asymptotics of solutions, vol.1341, p.132, 2006. ,
Mathematical analysis and numerical methods for science and technology: volume 3 Spectral Theory and Applications, vol.75, p.66, 2012. ,
Shape optimization by the level-set method, vol.58, p.31, 2005. ,
URL : https://hal.archives-ouvertes.fr/tel-00446039
An optimization method for elastic shape matching, Comptes Rendus Mathématique, vol.354, p.112, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01280621
Shapes and geometries: metrics, analysis, differential calculus, and optimization, vol.22, p.43, 2011. ,
Multiple-gradient descent algorithm (MGDA) for multiobjective optimization, Comptes Rendus Mathematique, vol.350, p.97, 2012. ,
Topology optimization in acoustics and elasto-acoustics via a level-set method, Journal of Sound and Vibration, vol.420, pp.73-103, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01957243
Hitchhiker's guide to the fractional Sobolev spaces, Bulletin des Sciences Mathématiques, vol.136, p.133, 2012. ,
Level-set methods for structural topology optimization: a review, Structural and Multidisciplinary Optimization, vol.48, p.52, 2013. ,
Introducing the sequential linear programming levelset method for topology optimization, Structural and Multidisciplinary Optimization, vol.51, p.143, 2015. ,
Design of robust and efficient photonic switches using topology optimization, Photonics and nanostructures-Fundamentals and Applications, vol.10, p.103, 2012. ,
Solving Laplacian problems with boundary singularities: a comparison of a singular function boundary integral method with the p/hp version of the finite element method, Applied Mathematics and Computation, vol.169, p.143, 2005. ,
Shape optimization of a coupled thermal fluid-structure problem in a level set mesh evolution framework, SeMA Journal, p.47, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01686770
Shape sensitivity analysis of problems with singularities, Lecture notes in pure and applied mathematics, vol.139, p.129, 2001. ,
Mathematical problems in electron beam lithography, p.110, 1989. ,
Volumetric expressions of the shape gradient of the compliance in structural shape optimization, p.143, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01441943
Low modal volume dipole-like dielectric slab resonator, Optics express, vol.16, p.63, 2008. ,
Etude mathématique et numérique de guides d'ondes ouverts non uniformes, par approche modale, vol.8, 2010. ,
Elliptic problems in nonsmooth domains. SIAM, vol.136, pp.132-134, 2011. ,
Optical Waveguide Theory, 2017. ,
Adjoint sensitivity analysis for nanophotonic structures, p.76, 2014. ,
New development in FreeFem++, J. Numer. Math, vol.20, p.28, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-01476313
Variation et optimisation de formes: une analyse géométrique, vol.48, pp.34-36, 2006. ,
Comparison of approximate shape gradients, BIT Numerical Mathematics, vol.55, p.143, 2015. ,
Adjoint Method and Inverse Design for Nonlinear Nanophotonic Devices, ACS Photonics 5, vol.12, p.168, 2018. ,
On the similarities between micro/nano lithography and topology optimization projection methods, Structural and Multidisciplinary Optimization, vol.48, p.112, 2013. ,
A survey on the reactive ion etching of silicon in microtechnology, Journal of micromechanics and microengineering, vol.6, p.111, 1996. ,
Topology optimization for nano-photonics, In: Laser & Photonics Reviews, vol.5, p.64, 2011. ,
The finite element method in electromagnetics, vol.28, pp.14-17, 2014. ,
Perturbation theory for Maxwell's equations with shifting material boundaries, Physical review E, vol.65, p.66, 2002. ,
Maximizing band gaps in two-dimensional photonic crystals by using level set methods, Applied Physics B, vol.81, p.65, 2005. ,
Machining fixture locating and clamping position optimization using genetic algorithms, Computers in Industry, vol.57, issue.2, p.154, 2006. ,
Perturbation theory for anisotropic dielectric interfaces, and application to subpixel smoothing of discretized numerical methods, Physical Review E, vol.77, p.76, 2008. ,
Elliptic boundary value problems in domains with point singularities, vol.52, p.132, 1997. ,
Adjoint shape optimization applied to electromagnetic design". en, Optics Express, vol.21, p.65, 2013. ,
, Fundamentals of differential geometry, vol.191, p.46, 2012.
Topology optimization with geometric uncertainties by perturbation techniques, International Journal for Numerical Methods in Engineering, vol.90, p.103, 2012. ,
Robust shape and topology optimization of nanophotonic devices using the level set method, Journal of Computational Physics, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-01860882
High-efficiency and broadband photonic polarization rotator based on multilevel shape optimization, Optics Letters, vol.44, pp.1960-1963, 2019. ,
URL : https://hal.archives-ouvertes.fr/cea-02091228
Shape optimization for the design of passive mid-infrared photonic components, Optical and Quantum Electronics, vol.51, pp.166-179, 2019. ,
URL : https://hal.archives-ouvertes.fr/cea-02095365
Full-wave analysis of dielectric waveguides using tangential vector finite elements, IEEE Transactions on Microwave Theory and Techniques, vol.39, pp.1262-1271, 1991. ,
Singularities and treatments of elliptic boundary value problems, In: Mathematical and Computer Modelling, vol.31, p.143, 2000. ,
Problèmes aux limites non homogènes et applications. Volume I, p.151, 1968. ,
Very sharp adiabatic bends based on an inverse design, Optics letters, vol.43, p.64, 2018. ,
Nanophotonic Computational Design, p.64, 2013. ,
Compliant fixture layout design using topology optimization method, Robotics and Automation (ICRA), vol.154, p.128, 2011. ,
Level set equations on surfaces via the Closest Point Method, Journal of Scientific Computing, vol.35, issue.2-3, p.170, 2008. ,
Ultra-compact polarization rotation in integrated silicon photonics using digital metamaterials, Optics express, vol.25, p.64, 2017. ,
Binary particle swarm optimized 2× 2 power splitters in a standard foundry silicon photonic platform, Optics letters 41, vol.16, p.63, 2016. ,
Méthode des Éléments Finis: vulgarisation des aspects mathématiques et illustration de la méthode, vol.150, p.20, 2018. ,
Robust shape optimization of continuous structures via the level set method, Computer Methods in Applied Mechanics and Engineering, vol.305, p.103, 2016. ,
The topological asymptotic expansion for the Maxwell equations and some applications, Inverse Problems, vol.21, p.170, 2005. ,
Topology optimization under uncertainty, Topology optimization in structural and continuum mechanics, p.103, 2014. ,
Strongly elliptic systems and boundary integral equations. Cambridge university press, p.150, 2000. ,
Manufacturing constraints and multi-phase shape and topology optimization via a level-set method, vol.89, 2014. ,
URL : https://hal.archives-ouvertes.fr/pastel-00937306
Leveraging continuous material averaging for inverse electromagnetic design, Optics express 26, vol.24, p.76, 2018. ,
Photonic design: From fundamental solar cell physics to computational inverse design, p.66, 2013. ,
Inverse design in nanophotonics, Nature Photonics, vol.12, p.103, 2018. ,
Finite element methods for Maxwell's equations, 2003. ,
Etude de problèmes d'optimal design, p.32, 1975. ,
Acoustic and electromagnetic equations: integral representations for harmonic problems, p.4, 2001. ,
Electromagnetic waves and antennas, 2002. ,
Halfspace Matching: a Domain Decomposition Method for Scattering by 2D Open Waveguides, p.17 ,
Matrix optimization on universal unitary photonic devices, Physical Review Applied, vol.11, p.169, 2019. ,
Sensibilité de l'équation de la chaleur aux sauts de conductivité, Comptes Rendus Mathematique, vol.341, pp.333-337, 2005. ,
Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer, Nature Photonics, vol.9, p.64, 2015. ,
Fabrication-constrained nanophotonic inverse design, Scientific reports, vol.7, p.65, 2017. ,
Optimal shape design for elliptic systems, vol.36, 1982. ,
Understanding the finite-difference time-domain method, vol.29, p.28, 2010. ,
Design and optimization of machining fixture layout using ANN and DOE, The International Journal of Advanced Manufacturing Technology, vol.65, p.154, 2013. ,
Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, vol.3, pp.53-55, 1999. ,
An integrated-nanophotonics polarization beamsplitter with 2.4× 2.4 µm 2 footprint, Nature Photonics, vol.9, p.64, 2015. ,
Manufacturing tolerant topology optimization, Acta Mechanica Sinica, vol.25, p.111, 2009. ,
Optical waveguide theory, 1983. ,
Topological derivative in shape optimization, Encyclopedia of Optimization, vol.39, p.31, 2009. ,
URL : https://hal.archives-ouvertes.fr/inria-00073518
Deep Neural Network Inverse Design of Integrated Photonic Power Splitters, Scientific reports, vol.9, p.63, 2019. ,
Boundary condition for the efficient excitation and absorption of hybrid waveguide modes in finite element formulations, Microwave and Optical Technology Letters, vol.53, p.15, 2011. ,
Analytical level set fabrication constraints for inverse design, Scientific reports, vol.9, p.65, 2019. ,
Topological Optimization with Interfaces". In: Architectured Materials in Nature and Engineering, p.75, 2019. ,
Second-order derivatives for shape optimization with a level-set method, vol.56, p.31, 2016. ,
Robust topology optimization of photonic crystal waveguides with tailored dispersion properties, vol.111, p.103, 2011. ,
Silicon Photonics, pp.2053-2563, 2017. ,
A level set method for shape and topology optimization of both structure and support of continuum structures, Computer Methods in Applied Mechanics and Engineering, vol.272, p.128, 2014. ,
Topology optimization of compliant mechanism and its support through a level set method, Computer Methods in Applied Mechanics and Engineering, vol.305, p.128, 2016. ,
Integrated photonic power divider with arbitrary power ratios, Optics letters, vol.42, p.64, 2017. ,
Topology optimization for optical projection lithography with manufacturing uncertainties, Applied optics 53, vol.12, pp.2720-2729, 2014. ,
Minimum length scale in topology optimization by geometric constraints, Computer Methods in Applied Mechanics and Engineering, vol.293, p.88, 2015. ,
Multigrid finite element methods for electromagnetic field modeling, vol.28, p.24, 2006. ,
, Vient ensuite Charles Dapogny, que ce soit pour la modélisation mathématique et physique, les calculs numériques ou l'analyse des résultats, j'ai toujours pu compter sur toi et je t'en remercie chaleureusement. Merci aussi à mon directeur de thèse Édouard Oudet de m'avoir soutenu du début à la fin et ce toujours avec le sourire ! Et enfin merci à Karim Hassan d'avoir toujours su trouver des moments pour moi dans son emploi du temps pour toutes mes questions, Remerciements Je tiens à commencer mes remerciements en saluant individuellement chacun de mes quatre encadrants de thèse sans qui le contenu de ce manuscrit ne pourrait être aussi abouti aujourd'hui
, Concernant la réalisation des composants justement, je me dois de remercier l'ensemble des ingénieurs et techniciens du CEA avec qui nous avons collaboré et qui, pendant plusieurs années, ont dû subir les demandes farfelues d'un jeune mathématicien qui souhaitait fabriquer des composants aux formes quelque peu extravagantes !
, Merci aussi à François Jouve et Stéphane Lantéri d'avoir accepté de faire le déplacement jusqu'à Grenoble pour ma présentation et pour le temps consacré à la lecture de mon manuscrit
Joël (bon courage pour reprendre le flambeau du débogage de code !) et Jhouben (dans deux ans tu fais ta soutenance en français n'est-ce pas ?). Je remercie aussi tous les permanents et non-permanents du labo avec qui j'ai pris beaucoup de plaisir à discuter. Il m'est malheureusement impossible de citer tout le monde sans oublier de nom aussi j'espère que les oubliés me pardonneront, Arrivent à présent les remerciements de tous les membres du laboratoire des capteurs optiques du CEA avec qui j'ai passé trois années très enrichissantes, tant d'un point de vue humain que scientifique. Par ordre d'ancienneté pour les thésards ,
Une pensée particulière pour Lucie, Florian et Raphaël avec qui j'ai commencé ma thèse au même moment après notre école d'ingénieur et qui ont été de précieux soutiens pour moi, vol.179, p.182 ,
, Index Boundary conditions Absorbing Boundary Condition (ABC), vol.16, p.17
, Continuity relations, vol.4, p.22
, DtN), vol.16, p.70
, Perfect Electric Conductor (PEC), vol.5, p.25
, Perfect Magnetic Conductor (PMC), p.5
, Perfectly Matched Layer (PML), vol.12, p.16
, Scattering Boundary Conditions (SBC), p.14
, , vol.3
, , p.26
, Decibel (dB), 10 Devices Bend, xi, p.166
, , p.85
, Clamping locator system, p.154
, , vol.19, p.105
, , vol.19, p.101
, , vol.19, p.166
, , vol.19, p.119
, Mode converter, vol.19, p.89
, Power divider, vol.19, p.167