Edit Profile (opens in new tab) Allaire, Grégoire Compute Distance To: Compute Author ID: allaire.gregoire Published as: Allaire, Grégoire; Allaire, G.; Allaire, Gregoire; Allaire, Grégire more...less External Links: MGP · Wikidata · IdRef · theses.fr Documents Indexed: 156 Publications since 1989, including 6 Books Co-Authors: 96 Co-Authors with 128 Joint Publications 1,387 Co-Co-Authors all top 5 Co-Authors 26 single-authored 20 Jouve, François 15 Dapogny, Charles 14 Piatnitski, Andrey L. 9 Conca, Carlos 7 Kokh, Samuel 7 Mikelić, Andro 6 Capdeboscq, Yves 6 Rauch, Jeffrey B. 6 Vanninathan, Muthusamy 5 Feppon, Florian 5 Palombaro, Mariapia 4 Brizzi, Robert 4 Dufrêche, Jean-François 4 Faccanoni, Gloria 4 Kohn, Robert Vita 4 Michailidis, Georgios E. 4 Pantz, Olivier 4 Toader, Anca-Maria 3 Bal, Guillaume 3 Briane, Marc 3 Faure, Alexis 3 Francfort, Gilles A. 3 Hutridurga, Harsha 2 Aubry, Sylvie 2 Bogoşel, Beniamin 2 Bonnetier, Eric 2 Bordeu, Felipe 2 Clerc, Sébastien 2 de Gournay, Frédéric 2 Delgado, Gabriel 2 Desai, Jeet 2 Estevez, Rafael 2 Frey, Pascal Jean 2 Friz, Luis 2 Geoffroy-Donders, Perle 2 Habibi, Zakaria 2 Henrot, Antoine 2 Jolivet, Pierre 2 Maillot, Hervé 2 Maury, Aymeric 2 Orive Illera, Rafael 2 Pankratova, Iryna L. 2 Periago, Francisco 2 Siess, Vincent 2 Van Goethem, Nicolas 1 Abballe, Thomas 1 Amar, Micol 1 Barré, Sébastien 1 Belhachmi, Zakaria 1 Bendsøe, Martin Philip 1 Bernard, Olivier 1 Betbeder-Lauque, Xavier 1 Bihr, Martin 1 Bissuel, Aloïs 1 Blanc, Xavier 1 Cavallina, Lorenzo 1 Cortial, Julien 1 Couvelas, Agnes 1 Daumas, Laurent 1 Després, Bruno 1 Desroziers, Sylvain 1 Dombre, Emmanuel 1 El Ganaoui, Karima 1 Enchéry, Guillaume 1 Feng, Qingqing 1 Ferriero, Alessandro 1 Ghosh, Tuhin 1 Godoy, Matías 1 Golse, François 1 Gutiérrez, Sergio 1 Jakabčin, Lukáš 1 Kaber, Sidimahmoud 1 Kelly, Alex 1 Lamacz-Keymling, Agnes 1 Laucoin, Éli 1 Lods, Véronique 1 Malige, François 1 Martínez-Frutos, Jesús 1 Miyake, Nobuhito 1 Montarnal, Philippe 1 Münch, Arnaud 1 Murat, François 1 Oka, Tomoyuki 1 Omnes, Pascal 1 Ortega, Jaime H. 1 Orval, Patrick 1 Ouaki, Franck 1 Planchard, Jacques 1 Puel, Marjolaine 1 Querois, Julie 1 Rakotondrainibe, Lalaina 1 Raphael, Anne-Lise 1 Rey, Floriane 1 Schmitt, Damien 1 Yachimura, Toshiaki 1 Zelmanse, Alain all top 5 Serials 8 Computer Methods in Applied Mechanics and Engineering 7 Journal of Computational Physics 6 Archive for Rational Mechanics and Analysis 6 Comptes Rendus de l’Académie des Sciences. Série I 6 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 6 Discrete and Continuous Dynamical Systems. Series B 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 SIAM Journal on Mathematical Analysis 4 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 4 S\(\vec{\text{e}}\)MA Journal 3 Numerische Mathematik 3 Quarterly of Applied Mathematics 3 Asymptotic Analysis 3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 3 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 3 Multiscale Modeling & Simulation 3 Structural and Multidisciplinary Optimization 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Applicable Analysis 2 Journal of Mathematical Physics 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Control and Cybernetics 2 SIAM Journal on Control and Optimization 2 Revue Européenne des Éléments Finis 2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 Portugaliae Mathematica. Nova Série 2 Networks and Heterogeneous Media 2 Matapli 2 SMAI Journal of Computational Mathematics 1 Computers and Fluids 1 Computers & Mathematics with Applications 1 Communications in Mathematical Physics 1 Communications on Pure and Applied Mathematics 1 IMA Journal of Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Journal of the Mechanics and Physics of Solids 1 Nonlinearity 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Indiana University Mathematics Journal 1 International Journal for Numerical Methods in Engineering 1 Journal of Functional Analysis 1 Journal of Optimization Theory and Applications 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Physica D 1 Revista Matemática Iberoamericana 1 Computational Mechanics 1 European Journal of Mechanics. A. Solids 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Séminaire Équations aux Dérivées Partielles 1 Computational and Applied Mathematics 1 Engineering Analysis with Boundary Elements 1 European Journal of Mechanics. A. Solids 1 Interdisciplinary Information Sciences (IIS) 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Computational Geosciences 1 Communications in Contemporary Mathematics 1 Comptes Rendus de l’Académie des Sciences. Série IIb. Mécanique 1 Applied Mathematical Sciences 1 Mathématiques & Applications (Berlin) 1 Texts in Applied Mathematics 1 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 1 Numerical Mathematics and Scientific Computation all top 5 Fields 83 Partial differential equations (35-XX) 72 Mechanics of deformable solids (74-XX) 43 Calculus of variations and optimal control; optimization (49-XX) 36 Fluid mechanics (76-XX) 32 Numerical analysis (65-XX) 12 Statistical mechanics, structure of matter (82-XX) 8 Operations research, mathematical programming (90-XX) 5 Optics, electromagnetic theory (78-XX) 5 Classical thermodynamics, heat transfer (80-XX) 2 Operator theory (47-XX) 2 Quantum theory (81-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 139 Publications have been cited 4,056 times in 2,560 Documents Cited by ▼ Year ▼ Homogenization and two-scale convergence. Zbl 0770.35005Allaire, Grégoire 790 1992 Structural optimization using sensitivity analysis and a level-set method. Zbl 1136.74368Allaire, Grégoire; Jouve, François; Toader, Anca-Maria 475 2004 Shape optimization by the homogenization method. Zbl 0990.35001Allaire, Grégoire 327 2002 A five-equation model for the simulation of interfaces between compressible fluids. Zbl 1169.76407Allaire, Grégoire; Clerc, Sébastien; Kokh, Samuel 146 2002 Structural optimization using topological and shape sensitivity via a level set method. Zbl 1167.49324Allaire, Grégoire; de Gournay, Frédéric; Jouve, François; Toader, Anca-Maria 110 2005 Multiscale convergence and reiterated homogenisation. Zbl 0866.35017Allaire, G.; Briane, M. 107 1996 Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. I: Abstract framework, a volume distribution of holes. Zbl 0724.76020Allaire, Grégoire 103 1991 A level-set method for shape optimization. Zbl 1115.49306Allaire, Grégoire; Jouve, François; Toader, Anca-Maria 97 2002 Optimal treatment of structures. (Conception optimale de structures.) Zbl 1132.49033Allaire, Grégoire 79 2007 Shape optimization by the homogenization method. Zbl 0889.73051Allaire, Grégoire; Bonnetier, Eric; Francfort, Gilles; Jouve, François 73 1997 Optimal design for minimum weight and compliance in plane stress using extremal microstructures. Zbl 0794.73044Allaire, G.; Kohn, Robert V. 65 1993 Boundary layer tails in periodic homogenization. Zbl 0922.35014Allaire, Grégoire; Amar, Micol 62 1999 Homogenization of the Stokes flow in a connected porous medium. Zbl 0682.76077Allaire, Grégoire 62 1989 A level-set method for vibration and multiple loads structural optimization. Zbl 1091.74038Allaire, Grégoire; Jouve, François 60 2005 Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. II: Non-critical sizes of the holes for a volume distribution and a surface distribution of holes. Zbl 0724.76021Allaire, Grégoire 60 1991 Bloch wave homogenization and spectral asymptotic analysis. Zbl 0901.35005Allaire, Grégoire; Conca, Carlos 52 1998 A multiscale finite element method for numerical homogenization. Zbl 1093.35007Allaire, Grégoire; Brizzi, Robert 48 2005 Numerical analysis and optimization. An introduction to mathematical modelling and numerical simulation. Translation from the French by Alan Craig. Zbl 1120.65001Allaire, Grégoire 44 2007 Homogenization of the Schrödinger equation and effective mass theorems. Zbl 1081.35092Allaire, Grégoire; Piatnitski, Andrey 39 2005 Minimum stress optimal design with the level set method. Zbl 1244.74104Allaire, Grégoire; Jouve, François 39 2008 Optimal bounds on the effective behavior of a mixture of two well-ordered elastic materials. Zbl 0805.73043Allaire, Grégoire; Kohn, Robert V. 38 1993 Topology optimization for minimum stress design with the homogenization method. Zbl 1243.74148Allaire, Grégoire; Jouve, François; Maillot, Hervé 37 2004 Damage and fracture evolution in brittle materials by shape optimization methods. Zbl 1356.74178Allaire, Grégoire; Jouve, François; Van Goethem, Nicolas 36 2011 Shape optimization with a level set based mesh evolution method. Zbl 1423.74739Allaire, G.; Dapogny, C.; Frey, P. 35 2014 Multi-phase structural optimization via a level set method. Zbl 1287.49045Allaire, G.; Dapogny, C.; Delgado, G.; Michailidis, G. 33 2014 Shape and topology optimization of the robust compliance via the level set method. Zbl 1245.49054De Gournay, Frédéric; Allaire, Grégoire; Jouve, François 33 2008 Homogenization of the Neumann problem with nonisolated holes. Zbl 0823.35014Allaire, Grégoire; Murat, François 32 1993 A comparison between two-scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures. Zbl 1364.35029Allaire, Gregoire; Briane, M.; Vanninathan, M. 28 2016 Structural optimization with FreeFem++. Zbl 1245.74049Allaire, Grégoire; Pantz, Olivier 28 2006 Structural optimization under overhang constraints imposed by additive manufacturing technologies. Zbl 1375.74076Allaire, G.; Dapogny, C.; Estevez, R.; Faure, A.; Michailidis, G. 25 2017 Homogenization of the Navier-Stokes equations with a slip boundary condition. Zbl 0738.35059Allaire, Grégoire 24 1991 Explicit optimal bounds on the elastic energy of a two-phase composite in two space dimensions. Zbl 0805.73042Allaire, Grégoire; Kohn, Robert V. 23 1993 Numerical linear algebra. Zbl 1135.65014Allaire, Grégoire; Kaber, Sidi Mahmoud 23 2008 Homogenization of a conductive and radiative heat transfer problem. Zbl 1180.35062Allaire, Grégoire; El Ganaoui, Karima 22 2009 Homogenization of the criticality spectral equation in neutron transport. Zbl 0931.35010Allaire, Grégoire; Bal, Guillaume 22 1999 Homogenization of periodic systems with large potentials. Zbl 1072.35023Allaire, Grégoire; Capdeboscq, Yves; Piatnitski, Andrey; Siess, Vincent; Vanninathan, M. 21 2004 Second order corrector in the homogenization of a conductive-radiative heat transfer problem. Zbl 1270.35053Allaire, Grégoire; Habibi, Zakaria 21 2013 Homogenization of the unsteady Stokes equations in porous media. Zbl 0801.35103Allaire, G. 20 1993 Homogenization of a spectral problem in neutronic multigroup diffusion. Zbl 1126.82346Allaire, Grégoire; Capdeboscq, Yves 20 2000 Homogenization of a convection-diffusion model with reaction in a porous medium. Zbl 1114.35007Allaire, Grégoire; Raphael, Anne-Lise 20 2007 Continuity of Darcy’s law in thelow-volume fraction limit. Zbl 0755.35084Allaire, Grégoire 19 1991 Shape optimization of a coupled thermal fluid-structure problem in a level set mesh evolution framework. Zbl 1422.49038Feppon, F.; Allaire, G.; Bordeu, F.; Cortial, J.; Dapogny, C. 19 2019 Homogenization approach to the dispersion theory for reactive transport through porous media. Zbl 1213.35057Allaire, Grégoire; Mikelić, Andro; Piatnitski, Andrey 18 2010 Eigenfrequency optimization in optimal design. Zbl 1004.74063Allaire, Grégoire; Aubry, Sylvie; Jouve, François 18 2001 A five-equation model for the numerical simulation of interfaces in two-phase flows. Zbl 1010.76055Allaire, Grégoire; Clerc, Sébastien; Kokh, Samuel 17 2000 A linearized approach to worst-case design in parametric and geometric shape optimization. Zbl 1297.49075Allaire, Grégoire; Dapogny, Charles 17 2014 Long time behavior of a two-phase optimal design for the heat equation. Zbl 1298.35015Allaire, Grégoire; Münch, Arnaud; Periago, Francisco 15 2010 Homogenization of the linearized ionic transport equations in rigid periodic porous media. Zbl 1314.76039Allaire, Grégoire; Mikelić, Andro; Piatnitski, Andrey 15 2010 Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium. Zbl 1267.76110Faccanoni, Gloria; Kokh, Samuel; Allaire, Grégoire 15 2012 Homogenization of a conductive, convective, and radiative heat transfer problem in a heterogeneous domain. Zbl 1276.35019Allaire, Grégoire; Habibi, Zakaria 15 2013 Diffractive geometric optics for Bloch wave packets. Zbl 1269.78004Allaire, Grégoire; Palombaro, Mariapia; Rauch, Jeffrey 15 2011 Topology optimization of modulated and oriented periodic microstructures by the homogenization method. Zbl 1443.74246Allaire, Grégoire; Geoffroy-Donders, Perle; Pantz, Olivier 15 2019 Optimal lower bounds on the elastic energy of a composite made from two non-well-ordered isotropic materials. Zbl 0806.73038Allaire, Grégoire; Kohn, Robert V. 14 1994 Minimizers for a double-well problem with affine boundary conditions. Zbl 0958.49008Allaire, Grégoire; Lods, Véronique 14 1999 Boundary layers in the homogenization of a spectral problem in fluid-solid structures. Zbl 0918.35018Allaire, Grégoire; Conca, Carlos 14 1998 Taking into account thermal residual stresses in topology optimization of structures built by additive manufacturing. Zbl 1411.49028Allaire, Grégoire; Jakabčin, Lukas 14 2018 Bloch-wave homogenization for a spectral problem in fluid-solid structures. Zbl 0857.73008Allaire, Grégoire; Conca, Carlos 13 1996 Spectral asymptotic analysis of a neutronic diffusion problem. (Analyse asymptotique spectrale d’un problème de diffusion neutronique.) Zbl 0879.35153Allaire, Grégoire; Malige, François 13 1997 Optimal design in small amplitude homogenization. Zbl 1148.65048Allaire, Grégoire; Gutiérrez, Sergio 13 2007 Homogenization of nonlinear reaction-diffusion equation with a large reaction term. Zbl 1205.35019Allaire, Grégoire; Piatnitski, Andrey 12 2010 Dispersive limits in the homogenization of the wave equation. Zbl 1070.35006Allaire, Grégoire 12 2003 Diffractive behavior of the wave equation in periodic media: weak convergence analysis. Zbl 1200.35019Allaire, Grégoire; Palombaro, Mariapia; Rauch, Jeffrey 12 2009 Existence of minimizers for non-quasiconvex functionals arising in optimal design. Zbl 0913.49008Allaire, Grégire; Francfort, Gilles 12 1998 Homogenization of periodic non self-adjoint problems with large drift and potential. Zbl 1130.35307Allaire, Grégoire; Orive, Rafael 12 2007 Ion transport in porous media: derivation of the macroscopic equations using upscaling and properties of the effective coefficients. Zbl 1392.76071Allaire, Grégoire; Brizzi, Robert; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 12 2013 Uniform spectral asymptotics for singularly perturbed locally periodic operators. Zbl 1026.35012Allaire, Grégoire; Piatnitski, Andrey 11 2002 On some recent advances in shape optimization. Zbl 0986.49023Allaire, Grégoire; Henrot, Antoine 11 2001 The homogenization method for topology and shape optimization. Zbl 0885.73049Allaire, G. 11 1997 3-d topology optimization of modulated and oriented periodic microstructures by the homogenization method. Zbl 1453.74072Geoffroy-Donders, Perle; Allaire, Grégoire; Pantz, Olivier 11 2020 Shape optimization of a layer by layer mechanical constraint for additive manufacturing. (Optimisation de forme pour une contrainte mécanique associée aux procédés de fabrication additive.) Zbl 1370.49037Allaire, Grégoire; Dapogny, Charles; Faure, Alexis; Michailidis, Georgios 9 2017 A level set method for the numerical simulation of damage evolution. Zbl 1419.74250Allaire, Grégoire; Jouve, François; Van Goethem, Nicolas 9 2008 Geometric constraints for shape and topology optimization in architectural design. Zbl 1398.74256Dapogny, Charles; Faure, Alexis; Michailidis, Georgios; Allaire, Grégoire; Couvelas, Agnes; Estevez, Rafael 9 2017 Optimal design of low-contrast two-phase structures for the wave equation. Zbl 1219.74039Allaire, Grégoire; Kelly, Alex 9 2011 Topology and geometry optimization of elastic structures by exact deformation of simplicial mesh. Zbl 1368.74045Allaire, Grégoire; Dapogny, Charles; Frey, Pascal 9 2011 Homogenization of reactive flows in porous media and competition between bulk and surface diffusion. Zbl 1341.76017Allaire, G.; Hutridurga, H. 9 2012 Homogénéisation et convergence à deux échelles. Application à un problème de convection diffusion. (Homogenization and two-scale convergence. Application to a problem of advection-diffusion). Zbl 0724.46033Allaire, Grégoire 9 1991 Upscaling nonlinear adsorption in periodic porous media – homogenization approach. Zbl 1379.35010Allaire, Grégoire; Hutridurga, Harsha 8 2016 Homogenization of the Navier-Stokes equations and derivation of Brinkman’s law. Zbl 0759.76072Allaire, G. 7 1991 A brief introduction to homogenization and miscellaneous applications. Zbl 1339.35001Allaire, Grégoire 7 2012 A strictly hyperbolic equilibrium phase transition model. Zbl 1109.35066Allaire, Grégoire; Faccanoni, Gloria; Kokh, Samuel 7 2007 Asymptotic analysis of the Poisson-Boltzmann equation describing electrokinetics in porous media. Zbl 1264.35159Allaire, Grégoire; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 7 2013 A deterministic approximation method in shape optimization under random uncertainties. Zbl 1416.74080Allaire, Grégoire; Dapogny, Charles 7 2015 Homogenization and localization for a 1D eigenvalue problem in a periodic medium with an interface. Zbl 1072.35026Allaire, Grégoire; Capdeboscq, Yves 6 2002 Homogenization and concentration for a diffusion equation with large convection in a bounded domain. Zbl 1233.35013Allaire, G.; Pankratova, I.; Piatnitski, A. 6 2012 Shape optimisation with the level set method for contact problems in linearised elasticity. Zbl 1416.74079Maury, Aymeric; Allaire, Grégoire; Jouve, François 6 2017 Topology optimization of thermal fluid-structure systems using body-fitted meshes and parallel computing. Zbl 1437.74021Feppon, F.; Allaire, G.; Dapogny, C.; Jolivet, P. 6 2020 Two-scale convergence: A new method in periodic homogenization. Zbl 0822.35011Allaire, G. 5 1994 Spectral asymptotic analysis of the wave equation. Bloch wave homogenization. (Analyse asymptotique spectrale de l’équation des ondes. Homogénéisation par ondes de Bloch.) Zbl 0844.35075Allaire, Grégoire; Conca, Carlos 5 1995 Topology optimization with the homogenization and the level-set methods. Zbl 1320.74089Allaire, G. 5 2005 Localization of high-frequency waves propagating in a locally periodic medium. Zbl 1204.35034Allaire, G.; Friz, L. 5 2010 Optimal design of micro-mechanisms by the homogenization method. Zbl 1120.74710Allaire, Grégoire; Jouve, François 5 2002 Shape and topology optimization. Zbl 1475.49048Allaire, Grégoire; Dapogny, Charles; Jouve, François 4 2021 On the band gap structure of Hill’s equation. Zbl 1095.34014Allaire, G.; Orive, R. 4 2005 Asymptotic spectral analysis of the wave equation. Completeness of the Bloch spectrum. (Analyse asymptotique spectrale de l’équation des ondes. Complétude du spectre de Bloch.) Zbl 0844.35076Allaire, Grégoire; Conca, Carlos 4 1995 Role of non-ideality for the ion transport in porous media: derivation of the macroscopic equations using upscaling. Zbl 1349.76803Allaire, Grégoire; Brizzi, Robert; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 4 2014 Homogenization and localization with an interface. Zbl 1073.35018Allaire, Grégoire; Capdeboscq, Yves; Piatnitski, Andrey 4 2003 Localization for the Schrödinger equation in a locally periodic medium. Zbl 1302.35034Allaire, Grégoire; Palombaro, Mariapia 4 2006 The homogenization method for topology and shape optimization. Single and multiple loads case. Zbl 0924.73163Allaire, Grégoire; Belhachmi, Zakaria; Jouve, François 4 1996 Two asymptotic models for arrays of underground waste containers. Zbl 1180.35061Allaire, Grégoire; Briane, Marc; Brizzi, Robert; Capdeboscq, Yves 4 2009 Optimization of dispersive coefficients in the homogenization of the wave equation in periodic structures. Zbl 1404.35021Allaire, G.; Yamada, T. 4 2018 Shape and topology optimization. Zbl 1475.49048Allaire, Grégoire; Dapogny, Charles; Jouve, François 4 2021 Body-fitted topology optimization of 2D and 3D fluid-to-fluid heat exchangers. Zbl 07340417Feppon, F.; Allaire, G.; Dapogny, C.; Jolivet, P. 1 2021 3-d topology optimization of modulated and oriented periodic microstructures by the homogenization method. Zbl 1453.74072Geoffroy-Donders, Perle; Allaire, Grégoire; Pantz, Olivier 11 2020 Topology optimization of thermal fluid-structure systems using body-fitted meshes and parallel computing. Zbl 1437.74021Feppon, F.; Allaire, G.; Dapogny, C.; Jolivet, P. 6 2020 A variational formulation for computing shape derivatives of geometric constraints along rays. Zbl 07201581Feppon, Florian; Allaire, Grégoire; Dapogny, Charles 4 2020 Null space gradient flows for constrained optimization with applications to shape optimization. Zbl 1464.65064Feppon, Florian; Allaire, Grégoire; Dapogny, Charles 1 2020 Shape optimization of a coupled thermal fluid-structure problem in a level set mesh evolution framework. Zbl 1422.49038Feppon, F.; Allaire, G.; Bordeu, F.; Cortial, J.; Dapogny, C. 19 2019 Topology optimization of modulated and oriented periodic microstructures by the homogenization method. Zbl 1443.74246Allaire, Grégoire; Geoffroy-Donders, Perle; Pantz, Olivier 15 2019 Structural optimization under internal porosity constraints using topological derivatives. Zbl 1440.74273Martínez-Frutos, J.; Allaire, G.; Dapogny, C.; Periago, F. 2 2019 The homogenization method for topology optimization of structures: old and new. Zbl 1452.74096Allaire, Grégoire; Cavallina, Lorenzo; Miyake, Nobuhito; Oka, Tomoyuki; Yachimura, Toshiaki 1 2019 Taking into account thermal residual stresses in topology optimization of structures built by additive manufacturing. Zbl 1411.49028Allaire, Grégoire; Jakabčin, Lukas 14 2018 Optimization of dispersive coefficients in the homogenization of the wave equation in periodic structures. Zbl 1404.35021Allaire, G.; Yamada, T. 4 2018 Elasto-plastic shape optimization using the level set method. Zbl 1387.35247Maury, Aymeric; Allaire, Grégoire; Jouve, François 2 2018 Transport and diffusion. (Transport et diffusion.) Zbl 1432.82002Allaire, Grégoire; Blanc, Xavier; Després, Bruno; Golse, François 1 2018 Structural optimization under overhang constraints imposed by additive manufacturing technologies. Zbl 1375.74076Allaire, G.; Dapogny, C.; Estevez, R.; Faure, A.; Michailidis, G. 25 2017 Shape optimization of a layer by layer mechanical constraint for additive manufacturing. (Optimisation de forme pour une contrainte mécanique associée aux procédés de fabrication additive.) Zbl 1370.49037Allaire, Grégoire; Dapogny, Charles; Faure, Alexis; Michailidis, Georgios 9 2017 Geometric constraints for shape and topology optimization in architectural design. Zbl 1398.74256Dapogny, Charles; Faure, Alexis; Michailidis, Georgios; Allaire, Grégoire; Couvelas, Agnes; Estevez, Rafael 9 2017 Shape optimisation with the level set method for contact problems in linearised elasticity. Zbl 1416.74079Maury, Aymeric; Allaire, Grégoire; Jouve, François 6 2017 Homogenization of Stokes system using Bloch waves. Zbl 1375.35355Allaire, Grégoire; Ghosh, Tuhin; Vanninathan, Muthusamy 3 2017 Ion transport through deformable porous media: derivation of the macroscopic equations using upscaling. Zbl 1476.76074Allaire, Grégoire; Bernard, Olivier; Dufrêche, Jean-François; Mikelić, Andro 2 2017 On the asymptotic behaviour of the kernel of an adjoint convection-diffusion operator in a long cylinder. Zbl 1382.35020Allaire, Grégoire; Piatnitski, Andrey 1 2017 A comparison between two-scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures. Zbl 1364.35029Allaire, Gregoire; Briane, M.; Vanninathan, M. 28 2016 Upscaling nonlinear adsorption in periodic porous media – homogenization approach. Zbl 1379.35010Allaire, Grégoire; Hutridurga, Harsha 8 2016 Stacking sequence and shape optimization of laminated composite plates via a level-set method. Zbl 1445.74040Allaire, G.; Delgado, G. 1 2016 A deterministic approximation method in shape optimization under random uncertainties. Zbl 1416.74080Allaire, Grégoire; Dapogny, Charles 7 2015 On the homogenization of multicomponent transport. Zbl 1339.35026Hutridurga, Harsha; Allaire, Grégoire 3 2015 A priori error estimate of a multiscale finite element method for transport modeling. Zbl 1320.74106Ouaki, Franck; Allaire, Grégoire; Desroziers, Sylvain; Enchéry, Guillaume 2 2015 Shape optimization with a level set based mesh evolution method. Zbl 1423.74739Allaire, G.; Dapogny, C.; Frey, P. 35 2014 Multi-phase structural optimization via a level set method. Zbl 1287.49045Allaire, G.; Dapogny, C.; Delgado, G.; Michailidis, G. 33 2014 A linearized approach to worst-case design in parametric and geometric shape optimization. Zbl 1297.49075Allaire, Grégoire; Dapogny, Charles 17 2014 Role of non-ideality for the ion transport in porous media: derivation of the macroscopic equations using upscaling. Zbl 1349.76803Allaire, Grégoire; Brizzi, Robert; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 4 2014 Second order corrector in the homogenization of a conductive-radiative heat transfer problem. Zbl 1270.35053Allaire, Grégoire; Habibi, Zakaria 21 2013 Homogenization of a conductive, convective, and radiative heat transfer problem in a heterogeneous domain. Zbl 1276.35019Allaire, Grégoire; Habibi, Zakaria 15 2013 Ion transport in porous media: derivation of the macroscopic equations using upscaling and properties of the effective coefficients. Zbl 1392.76071Allaire, Grégoire; Brizzi, Robert; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 12 2013 Asymptotic analysis of the Poisson-Boltzmann equation describing electrokinetics in porous media. Zbl 1264.35159Allaire, Grégoire; Dufrêche, Jean-François; Mikelić, Andro; Piatnitski, Andrey 7 2013 Diffraction of Bloch wave packets for Maxwell’s equations. Zbl 1281.35083Allaire, Grégoire; Palombaro, Mariapia; Rauch, Jeffrey 2 2013 Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium. Zbl 1267.76110Faccanoni, Gloria; Kokh, Samuel; Allaire, Grégoire 15 2012 Homogenization of reactive flows in porous media and competition between bulk and surface diffusion. Zbl 1341.76017Allaire, G.; Hutridurga, H. 9 2012 A brief introduction to homogenization and miscellaneous applications. Zbl 1339.35001Allaire, Grégoire 7 2012 Homogenization and concentration for a diffusion equation with large convection in a bounded domain. Zbl 1233.35013Allaire, G.; Pankratova, I.; Piatnitski, A. 6 2012 Homogenization of a nonstationary convection-diffusion equation in a thin rod and in a layer. Zbl 1310.35026Allaire, G.; Pankratova, I.; Piatnitski, A. 3 2012 Shape optimization of a sodium fast reactor core. Zbl 1329.74228Dombre, Emmanuel; Allaire, Grégoire; Pantz, Olivier; Schmitt, Damien 2 2012 In search of the lost inequality. (À la recherche de l’inégalité perdue.) Zbl 1365.35002Allaire, Grégoire 1 2012 Homogenization of a one-dimensional spectral problem for a singularly perturbed elliptic operator with Neumann boundary conditions. Zbl 1235.35024Allaire, Grégoire; Capdeboscq, Yves; Puel, Marjolaine 1 2012 Damage and fracture evolution in brittle materials by shape optimization methods. Zbl 1356.74178Allaire, Grégoire; Jouve, François; Van Goethem, Nicolas 36 2011 Diffractive geometric optics for Bloch wave packets. Zbl 1269.78004Allaire, Grégoire; Palombaro, Mariapia; Rauch, Jeffrey 15 2011 Optimal design of low-contrast two-phase structures for the wave equation. Zbl 1219.74039Allaire, Grégoire; Kelly, Alex 9 2011 Topology and geometry optimization of elastic structures by exact deformation of simplicial mesh. Zbl 1368.74045Allaire, Grégoire; Dapogny, Charles; Frey, Pascal 9 2011 Erratum: “Homogenization of the linearized ionic transport equations in rigid periodic porous media” [J. Math. Phys. 51, 123103, 18 p. (2010)]. Zbl 1317.76075Allaire, Grégoire; Mikelić, Andro; Piatnitski, Andrey 1 2011 Homogenization approach to the dispersion theory for reactive transport through porous media. Zbl 1213.35057Allaire, Grégoire; Mikelić, Andro; Piatnitski, Andrey 18 2010 Long time behavior of a two-phase optimal design for the heat equation. Zbl 1298.35015Allaire, Grégoire; Münch, Arnaud; Periago, Francisco 15 2010 Homogenization of the linearized ionic transport equations in rigid periodic porous media. Zbl 1314.76039Allaire, Grégoire; Mikelić, Andro; Piatnitski, Andrey 15 2010 Homogenization of nonlinear reaction-diffusion equation with a large reaction term. Zbl 1205.35019Allaire, Grégoire; Piatnitski, Andrey 12 2010 Localization of high-frequency waves propagating in a locally periodic medium. Zbl 1204.35034Allaire, G.; Friz, L. 5 2010 Approximation of liquid-vapor phase transition for compressible fluids with tabulated EOS. Zbl 1258.76162Faccanoni, Gloria; Kokh, Samuel; Allaire, Grégoire 1 2010 Homogenization of a conductive and radiative heat transfer problem. Zbl 1180.35062Allaire, Grégoire; El Ganaoui, Karima 22 2009 Diffractive behavior of the wave equation in periodic media: weak convergence analysis. Zbl 1200.35019Allaire, Grégoire; Palombaro, Mariapia; Rauch, Jeffrey 12 2009 Two asymptotic models for arrays of underground waste containers. Zbl 1180.35061Allaire, Grégoire; Briane, Marc; Brizzi, Robert; Capdeboscq, Yves 4 2009 Minimum stress optimal design with the level set method. Zbl 1244.74104Allaire, Grégoire; Jouve, François 39 2008 Shape and topology optimization of the robust compliance via the level set method. Zbl 1245.49054De Gournay, Frédéric; Allaire, Grégoire; Jouve, François 33 2008 Numerical linear algebra. Zbl 1135.65014Allaire, Grégoire; Kaber, Sidi Mahmoud 23 2008 A level set method for the numerical simulation of damage evolution. Zbl 1419.74250Allaire, Grégoire; Jouve, François; Van Goethem, Nicolas 9 2008 Periodic homogenization and effective mass theorems for the Schrödinger equation. Zbl 1173.82330Allaire, Grégoire 4 2008 Numerical simulation with finite volume of dynamic liquid-vapor phase transition. Zbl 1374.76137Faccanoni, G.; Kokh, S.; Allaire, G. 1 2008 Optimal treatment of structures. (Conception optimale de structures.) Zbl 1132.49033Allaire, Grégoire 79 2007 Numerical analysis and optimization. An introduction to mathematical modelling and numerical simulation. Translation from the French by Alan Craig. Zbl 1120.65001Allaire, Grégoire 44 2007 Homogenization of a convection-diffusion model with reaction in a porous medium. Zbl 1114.35007Allaire, Grégoire; Raphael, Anne-Lise 20 2007 Optimal design in small amplitude homogenization. Zbl 1148.65048Allaire, Grégoire; Gutiérrez, Sergio 13 2007 Homogenization of periodic non self-adjoint problems with large drift and potential. Zbl 1130.35307Allaire, Grégoire; Orive, Rafael 12 2007 A strictly hyperbolic equilibrium phase transition model. Zbl 1109.35066Allaire, Grégoire; Faccanoni, Gloria; Kokh, Samuel 7 2007 On two formulations of an optimal insulation problem. Zbl 1245.74067Munoz, E.; Allaire, Grégoire; Bendsøe, Martin Philip 3 2007 On Bloch waves for the Stokes equations. Zbl 1124.35050Allaire, Grégoire; Conca, Carlos; Friz, Luis; Ortega, Jaime H. 2 2007 Structural optimization with FreeFem++. Zbl 1245.74049Allaire, Grégoire; Pantz, Olivier 28 2006 Localization for the Schrödinger equation in a locally periodic medium. Zbl 1302.35034Allaire, Grégoire; Palombaro, Mariapia 4 2006 Homogenization of the Schrödinger equation with a time oscillating potential. Zbl 1096.35009Allaire, Grégoire; Vanninathan, M. 2 2006 Structural optimization using topological and shape sensitivity via a level set method. Zbl 1167.49324Allaire, Grégoire; de Gournay, Frédéric; Jouve, François; Toader, Anca-Maria 110 2005 A level-set method for vibration and multiple loads structural optimization. Zbl 1091.74038Allaire, Grégoire; Jouve, François 60 2005 A multiscale finite element method for numerical homogenization. Zbl 1093.35007Allaire, Grégoire; Brizzi, Robert 48 2005 Homogenization of the Schrödinger equation and effective mass theorems. Zbl 1081.35092Allaire, Grégoire; Piatnitski, Andrey 39 2005 Topology optimization with the homogenization and the level-set methods. Zbl 1320.74089Allaire, G. 5 2005 On the band gap structure of Hill’s equation. Zbl 1095.34014Allaire, G.; Orive, R. 4 2005 Numerical analysis and optimisation. (Analyse numérique et optimisation.) Zbl 1190.65001Allaire, Grégoire 3 2005 Structural optimization using sensitivity analysis and a level-set method. Zbl 1136.74368Allaire, Grégoire; Jouve, François; Toader, Anca-Maria 475 2004 Topology optimization for minimum stress design with the homogenization method. Zbl 1243.74148Allaire, Grégoire; Jouve, François; Maillot, Hervé 37 2004 Homogenization of periodic systems with large potentials. Zbl 1072.35023Allaire, Grégoire; Capdeboscq, Yves; Piatnitski, Andrey; Siess, Vincent; Vanninathan, M. 21 2004 Dispersive limits in the homogenization of the wave equation. Zbl 1070.35006Allaire, Grégoire 12 2003 Homogenization and localization with an interface. Zbl 1073.35018Allaire, Grégoire; Capdeboscq, Yves; Piatnitski, Andrey 4 2003 \(H\)-measures and bounds on the effective properties of composite materials. Zbl 1075.74068Allaire, Grégoire; Maillot, Hervé 3 2003 Structural optimization by the level-set method. Zbl 1051.49028Allaire, Grégoire; Jouve, François; Toader, Anca-Maria 2 2003 Shape optimization by the homogenization method. Zbl 0990.35001Allaire, Grégoire 327 2002 A five-equation model for the simulation of interfaces between compressible fluids. Zbl 1169.76407Allaire, Grégoire; Clerc, Sébastien; Kokh, Samuel 146 2002 A level-set method for shape optimization. Zbl 1115.49306Allaire, Grégoire; Jouve, François; Toader, Anca-Maria 97 2002 Uniform spectral asymptotics for singularly perturbed locally periodic operators. Zbl 1026.35012Allaire, Grégoire; Piatnitski, Andrey 11 2002 Homogenization and localization for a 1D eigenvalue problem in a periodic medium with an interface. Zbl 1072.35026Allaire, Grégoire; Capdeboscq, Yves 6 2002 Optimal design of micro-mechanisms by the homogenization method. Zbl 1120.74710Allaire, Grégoire; Jouve, François 5 2002 Homogenization and localization in locally periodic transport. Zbl 1065.35042Allaire, Grégoire; Bal, Guillaume; Siess, Vincent 2 2002 Eigenfrequency optimization in optimal design. Zbl 1004.74063Allaire, Grégoire; Aubry, Sylvie; Jouve, François 18 2001 On some recent advances in shape optimization. Zbl 0986.49023Allaire, Grégoire; Henrot, Antoine 11 2001 A new approach for the optimal distribution of assemblies in a nuclear reactor. Zbl 0985.65074Allaire, Grégoire; Castro, Carlos 2 2001 Numerical simulation of 2-D two-phase flows with interface. Zbl 1064.76548Kokh, S.; Allaire, G. 2 2001 ...and 39 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,117 Authors 79 Allaire, Grégoire 30 Piatnitski, Andrey L. 28 Wang, Michael Yu 26 Casado-Díaz, Juan 24 Dapogny, Charles 23 Cui, Junzhi 23 Luo, Zhen 20 Amstutz, Samuel 20 Mikelić, Andro 20 Novotny, Antonio André 19 Guo, Xu 18 Pedregal, Pablo 18 Suárez-Grau, Francisco Javier 18 Zhang, Weihong 17 Kang, Zhan 17 Nishiwaki, Shinji 17 Schweizer, Ben 16 Abdulle, Assyr 16 Briane, Marc 16 Yamada, Takayuki 16 Yang, Zhiqiang 15 Conca, Carlos 15 Pastukhova, Svetlana Evgenievna 15 Xia, Qi 14 Efendiev, Yalchin R. 14 Izui, Kazuhiro 14 Maute, Kurt 14 Sigmund, Ole 14 Tortorelli, Daniel A. 14 Zhang, Weisheng 13 Gao, Liang 13 Milton, Graeme Walter 13 Zhu, Shengfeng 12 Amaziane, Brahim 12 Cao, Liqun 12 Gruais, Isabelle 12 Hoang, Viet Ha 12 Muntean, Adrian 12 Neukamm, Stefan 12 Pankratov, Leonid S. 12 Rohan, Eduard 12 Shi, Tielin 12 Velčić, Igor 11 Bouchitté, Guy 11 Cherednichenko, Kirill D. 11 Jouve, François 11 Kovtunenko, Viktor Anatolievich 11 Pažanin, Igor 11 Ptashnyk, Mariya 11 Sokołowski, Jan 11 Sun, Yi 11 Visintin, Augusto 11 Woukeng, Jean Louis 11 Xia, Liang 11 Yeh, Li-Ming 11 Zhu, Jihong 11 Zuazua, Enrique 10 Chung, Tsz Shun Eric 10 Dambrine, Marc 10 Evgrafov, Anton 10 Frénod, Emmanuel 10 Henning, Patrick 10 Neuss-Radu, Maria 10 Osmolovskij, V. G. 10 Periago, Francisco 10 Poliševski, Dan A. 10 Sili, Ali 10 Vanninathan, Muthusamy 10 Wang, Yiqiang 10 Zhikov, Vasiliĭ Vasil’evich 9 Amar, Micol 9 Boughammoura, Ahmed 9 Luna-Laynez, Manuel 9 Masmoudi, Nader 9 Nnang, Hubert 9 Shumilova, Vladlena Valerievna 9 Toader, Anca-Maria 9 Tong, Liyong 9 Van Goethem, Nicolas 9 Wei, Peng 8 Barbarosie, Cristian 8 Chen, Shikui 8 Dong, Hao 8 Hassine, Maatoug 8 Holmbom, Anders 8 Lamacz, Agnes 8 Lewiński, Tomasz 8 Lipton, Robert P. 8 Martínez-Frutos, Jesús 8 Marušić-Paloka, Eduard 8 Münch, Arnaud 8 Nomura, Tsuyoshi 8 Ohlberger, Mario 8 Rabczuk, Timon 8 Rozvany, George I. N. 8 Rumpf, Martin 8 Wheeler, Mary Fanett 8 Yamasaki, Shintaro 7 Anguiano, María 7 Bal, Guillaume ...and 3,017 more Authors all top 5 Cited in 318 Serials 276 Computer Methods in Applied Mechanics and Engineering 148 Journal of Computational Physics 92 Structural and Multidisciplinary Optimization 58 Applicable Analysis 57 M\(^3\)AS. 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Académie des Sciences, Paris 28 Journal de Mathématiques Pures et Appliquées. Neuvième Série 27 Journal of the Mechanics and Physics of Solids 25 Journal of Optimization Theory and Applications 25 SIAM Journal on Control and Optimization 25 Applied Mathematical Modelling 21 Networks and Heterogeneous Media 20 Journal of Scientific Computing 20 Journal of Elasticity 19 Applied Mathematics and Computation 19 Asymptotic Analysis 19 Applications of Mathematics 18 SIAM Journal on Applied Mathematics 18 Discrete and Continuous Dynamical Systems. Series S 17 Communications in Partial Differential Equations 16 International Journal of Engineering Science 16 SIAM Journal on Scientific Computing 16 Engineering Analysis with Boundary Elements 16 Nonlinear Analysis. Real World Applications 15 ZAMP. Zeitschrift für angewandte Mathematik und Physik 15 Numerische Mathematik 15 Computational Geosciences 14 Annales de l’Institut Henri Poincaré. 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Mathematical, Physical and Engineering Sciences 8 Quarterly of Applied Mathematics 8 European Journal of Applied Mathematics 8 Computational Optimization and Applications 8 NoDEA. Nonlinear Differential Equations and Applications 8 Communications in Computational Physics 7 Mathematics of Computation 7 Applied Mathematics and Optimization 7 Zeitschrift für Analysis und ihre Anwendungen 7 Advances in Computational Mathematics 7 Journal of Mathematical Fluid Mechanics 7 Acta Mechanica Sinica 6 Communications on Pure and Applied Mathematics 6 International Journal of Solids and Structures 6 Mathematical Notes 6 Chinese Annals of Mathematics. Series B 6 RAIRO. Modélisation Mathématique et Analyse Numérique 6 Mathematical and Computer Modelling 6 International Journal of Computer Mathematics 6 Mediterranean Journal of Mathematics 6 Inverse Problems in Science and Engineering 6 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 5 International Journal for Numerical Methods in Fluids 5 Journal of Engineering Mathematics 5 Journal of Statistical Physics 5 Ricerche di Matematica 5 Physica D 5 Computational Mathematics and Mathematical Physics 5 St. Petersburg Mathematical Journal 5 Computational and Applied Mathematics 5 Discrete and Continuous Dynamical Systems 5 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 5 Optimization Methods & Software 5 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 5 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 5 International Journal of Computational Methods 5 Mathematical Control and Related Fields ...and 218 more Serials all top 5 Cited in 49 Fields 1,209 Partial differential equations (35-XX) 1,113 Mechanics of deformable solids (74-XX) 630 Fluid mechanics (76-XX) 561 Numerical analysis (65-XX) 506 Calculus of variations and optimal control; optimization (49-XX) 130 Optics, electromagnetic theory (78-XX) 93 Classical thermodynamics, heat transfer (80-XX) 92 Statistical mechanics, structure of matter (82-XX) 90 Operations research, mathematical programming (90-XX) 65 Biology and other natural sciences (92-XX) 61 Probability theory and stochastic processes (60-XX) 53 Operator theory (47-XX) 45 Systems theory; control (93-XX) 39 Functional analysis (46-XX) 25 Ordinary differential equations (34-XX) 25 Quantum theory (81-XX) 22 Computer science (68-XX) 17 Dynamical systems and ergodic theory (37-XX) 16 Integral equations (45-XX) 16 Information and communication theory, circuits (94-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 13 Global analysis, analysis on manifolds (58-XX) 13 Geophysics (86-XX) 11 Harmonic analysis on Euclidean spaces (42-XX) 11 Statistics (62-XX) 10 Approximations and expansions (41-XX) 10 General topology (54-XX) 10 Mechanics of particles and systems (70-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Differential geometry (53-XX) 8 Measure and integration (28-XX) 8 Potential theory (31-XX) 7 General and overarching topics; collections (00-XX) 6 Real functions (26-XX) 5 Functions of a complex variable (30-XX) 4 Difference and functional equations (39-XX) 4 Manifolds and cell complexes (57-XX) 3 Relativity and gravitational theory (83-XX) 2 History and biography (01-XX) 2 Combinatorics (05-XX) 2 Sequences, series, summability (40-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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