List of publications

Grégoire Allaire


LIST OF PUBLICATIONS




To appear

  • A. Maury, G. Allaire, F. Jouve, Elasto-plastic shape optimization using the level set method, submitted to SICON. HAL preprint: hal-01519017 (May 2017).
  • A. Maury, G. Allaire, F. Jouve, Shape optimisation with the level set method for contact problems in linearised elasticity, to appear in SMAI Journal of Computational Mathematics. HAL preprint: hal-01435325 (January 2017).
  • G. Allaire, G. Michailidis, Modal basis approaches in shape and topology optimization of frequency response problems, to appear in IJNME. HAL preprint: hal-01354162 (August 2016).
  • G. Allaire, T. Yamada, Optimization of dispersive coefficients in the homogenization of the wave equation in periodic structures, submitted to Numerische Mathematik. HAL preprint: hal-01341082 (July 2016).
  • G. Allaire, A. Piatnitski, On the asymptotic behaviour of the kernel of an adjoint convection-diffusion operator in a long cylinder, to appear in Revista Matematica Iberoamericana. HAL preprint: hal-01258747 (January 2016).

  • 2017

  • G. Allaire, C. Dapogny, R. Estevez, A. Faure and G. Michailidis, Structural optimization under overhang constraints imposed by additive manufacturing technologies, Journal of Computational Physics, 351, pp.295-328 (2017). HAL preprint: hal-01523009 (May 2017).
  • G. Allaire, T. Ghosh, M. Vanninathan, Homogenization of Stokes System using Bloch Waves, Networks and Heterogeneous Media, 12(4), pp.525-550 (2017). HAL preprint: hal-01522262 (May 2017).
  • G. Allaire, C. Dapogny, R. Estevez, A. Faure and G. Michailidis, Structural optimization under overhang constraints imposed by additive manufacturing processes: an overview of some recent results, Applied Mathematics and Nonlinear Science, Volume 2 - Issue 2, pp.385-403 (2017). HAL preprint: hal-01589906 (September 2017).
  • G. Allaire, O. Bernard, J.-F. Dufrêche, A. Mikelic Ion transport through deformable porous media: derivation of the macroscopic equations using upscaling, COAM, 36(3), 1431-1462 (2017). HAL preprint: hal-01215457 (October 2015).
  • C. Dapogny, A. Faure, G. Michailidis, G. Allaire, A. Couvelas, R. Estevez, Geometric constraints for shape and topology optimization in architectural design, Computational Mechanics, 59, no. 6, 933-965 (2017). HAL preprint: hal-01354004 (August 2016).
  • P. Geoffroy-Donders, G. Allaire, J. Cortial, O. Pantz, Optimization of oriented and parametric cellular structures by the homogenization method, paper 502, proceedings of the 12th World Congress on Structural and Multidisciplinary Optimization, 5-9 June 2017, Braunschweig, Germany. HAL preprint: hal-01537841v1 (June 2017).
  • G. Allaire, C. Dapogny, A. Faure, G. Michailidis, A model of layer by layer mechanical constraint for additive manufacturing in shape and topology optimization, paper 255, proceedings of the 12th World Congress on Structural and Multidisciplinary Optimization, 5-9 June 2017, Braunschweig, Germany. HAL preprint: hal-01536668 (June 2017).
  • G. Allaire, C. Dapogny, A. Faure, G. Michailidis, Shape optimization of a layer by layer mechanical constraint for additive manufacturing, C. R. Math. Acad. Sci. Paris, 355, no. 6, 699-717 (2017). HAL preprint: hal-01398877 (November 2016). Open Access manuscript: CRAS Série I.
  • F. Feppon, G. Michailidis, M.S. Sidebottom, G. Allaire, B.A. Krick, N. Vermaak, Introducing a level-set based shape and topology optimization method for the wear of composite materials with geometric constraints, SMO, 55, no. 2, 547-568 (2017). HAL preprint: hal-01336301 (June 2016).
  • G. Allaire, J. Rauch, Instability of dielectrics and conductors in electrostatic fields, Arch. Rat. Mech. Anal., 124, pp.233-268 (2017). HAL preprint: hal-01321566 (May 2016).

  • 2016

  • G. Allaire, F. Jouve, G. Michailidis, Molding direction constraints in structural optimization via a level-set method, in Variational Analysis and Aerospace Engineering, Mathematical Challenges for the Aerospace of the Future, Frediani, A., Mohammadi, B., Pironneau, O., Cipolla, V. (Eds.), Springer Optimization and Its Applications 116, pp.1-39, Springer (2016). HAL preprint: hal-01242945 (December 2015).
  • G. Allaire, E. Cancès, J.-L. Vié, Second-order shape derivatives along normal trajectories, governed by Hamilton-Jacobi equations, SMO, 54, pp.1245-1266 (2016). HAL preprint: hal-01326805 (June 2016).
  • G. Allaire, H. Hutridurga, Upscaling nonlinear adsorption in periodic porous media - Homogenization approach, Applicable Analysis, 96(10), 2126-2161 (2016). Preprint on arXiv (December 2014).
  • G. Allaire, G. Delgado, Stacking sequence and shape optimization of laminated composite plates via a level-set method, Journal of the Mechanics and Physics of Solids, 97, pp.168-196 (2016). HAL preprint: hal-01164929 (June 2015).
  • G. Allaire, M. Briane, M. Vanninathan A comparison between two-scale asymptotic expansions and Bloch wave expansions for the homogenization of periodic structures, SEMA journal, 73(3), 237-259 (2016). HAL preprint: hal-01215580 (October 2015).
  • G. Allaire, F. Jouve, G. Michailidis, Thickness control in structural optimization via a level set method, SMO 53, 1349-1382 (2016). HAL preprint: hal-00985000 (April 2014).

  • 2015

  • G. Allaire, Ch. Dapogny, A deterministic approximation method in shape optimization under random uncertainties, HAL preprint: hal-01160256v1 (June 2015). SMAI J. Computational Mathematics, 1, 83-143 (2015).
  • G. Allaire, M. Palombaro, J. Rauch, A bound on group velocity for Bloch wave packets, Preprint on arXiv (March 2012). Portugaliae Mathematica, 72, 119-123 (2015).
  • Th. Abballe, M. Albertelli, G. Allaire, A. Caron, Ph. Conraux, L. Dall'Olio, Ch. Dapogny, C. Dobrzynski, B. Jeannin, F. Jouve, D. Lachouette, Th. Le Sommer, K.Maquin, G. Michailidis, M. Siavelis, V. Srithammavanh, RODIN project, topology optimization 2.0 ?, Actes du congrès "Simulation" de la Société des Ingénieurs de l'Automobile (SIA), Montigny le Bretonneux, 18-19 mars 2015. Preprint here. HAL preprint: hal-01237051 (December 2015).
  • G. Allaire, A review of adjoint methods for sensitivity analysis, uncertainty quantification and optimization in numerical codes, Actes du congrès "Simulation" de la Société des Ingénieurs de l'Automobile (SIA), Montigny le Bretonneux, 18-19 mars 2015. Preprint here. Reprinted in the journal "Ingénieurs de l'automobile", no. 836, pp.33-36, July 2015. HAL preprint: hal-01242950 (December 2015).
  • F. Ouaki, G. Allaire, S. Desroziers, G. Enchéry, A priori error estimate of a multiscale finite element method for transport modeling, SEMA Journal, 67, no. 1, 1-37 (2015). HAL preprint: hal-01071637 (October 2014).
  • G. Allaire, H. Hutridurga, On the homogenization of multicomponent transport, DCDS-B, 20, 2527-2551 (2015). Preprint on arXiv (November 2014).

  • 2014

  • G. Allaire, Ch. Dapogny, P. Frey, Shape optimization with a level set based mesh evolution method, CMAME 282, 22-53 (2014). HAL preprint: hal-00801704, version 1 (January 2014).
  • N. Vermaak, G. Michailidis, G. Parry, R. Estevez, G. Allaire, Y. Bréchet, Material Interface Effects on the Topology Optimization of Multi-Phase Structures Using A Level Set Method, SMO Vol. 50, no. 4, 623-644 (2014). HAL preprint: hal-01072223, version 1 (October 2014).
  • G. Allaire, Ch. Dapogny, A linearized approach to worst-case design in parametric and geometric shape optimization, M3AS Vol. 24, No. 11 (2014) 2199-2257. HAL preprint: hal-00918896, version 1 (December 2013).
  • G. Allaire, Ch. Dapogny, G. Delgado, G. Michailidis, Multi-phase structural optimization via a level set method, COCV 20, pp.576-611 (2014). HAL preprint: hal-00839464, version 1 (June 2013).
  • G. Allaire, R. Brizzi, J.-F. Dufrêche, A. Mikelic, A. Piatnitski, Role of non-ideality for the ion transport in porous media: derivation of the macroscopic equations using upscaling, Physica D, 282, pp.39-60 (2014). arXiv:1309.3679.
  • D. Schmitt, G. Allaire, O. Pantz, N. Pozin, Shape Optimization of a sodium cooled fast reactor, SNA + MC 2013, 02206 (2014). Electronic version.

  • 2013

  • G. Allaire, F. Jouve, G. Michailidis, Casting constraints in structural optimization via a level set method, proceedings of the 10th World Congress on Structural and Multidisciplinary Optimization, paper 4873 (May 2013).
  • G. Allaire, M. Palombaro, J. Rauch, Diffraction of Bloch Wave Packets for Maxwell's Equations, Communications in Contemporary Mathematics, 15(6), 1350040 (2013). Preprint on arXiv.
  • G. Allaire, R. Brizzi, J.-F. Dufrêche, A. Mikelic, A. Piatnitski, Ion transport in porous media: derivation of the macroscopic equations using upscaling and properties of the effective coefficients, Comp. Geosci. 17, Issue 3, pp.479-495 (2013). Internal report, n. 767, CMAP, Ecole Polytechnique (January 2013). 767.pdf.
  • G. Allaire, Ch. Dapogny, P. Frey, A mesh evolution algorithm based on the level set method for geometry and topology optimization, SMO 48 (2013), no. 4, 711-715. HAL preprint: hal-00801704, version 1 (March 2013).
  • G. Allaire, Z. Habibi, Homogenization of a Conductive, Convective and Radiative Heat Transfer Problem in a Heterogeneous Domain, SIAM J. Math. Anal. 45 (2013), no. 3, 1136-1178. Internal report, n. 746, CMAP, Ecole Polytechnique (March 2012). 746.pdf.
  • G. Allaire, J.-F. Dufrêche, A. Mikelic, A. Piatnitski, Asymptotic analysis of the Poisson-Boltzmann equation describing electrokinetics in porous media, Nonlinearity 26 (2013) 881-910. Preprint on arXiv. Internal report, n. 766, CMAP, Ecole Polytechnique (January 2013). 766.pdf.
  • G. Allaire, Z. Habibi, Second order corrector in the homogenization of a conductive-radiative heat transfer problem, DCDS-B, 18, pp.1-36 (2013). Internal report, n. 758, CMAP, Ecole Polytechnique (August 2012). 758.pdf.

  • 2012

  • G. Allaire, A brief introduction to homogenization and miscellaneous applications, Mathematical and numerical approaches for multiscale problem, ESAIM Proceedings, 37, 1-49 (2012). Article.
  • E. Dombre, G. Allaire, O. Pantz, D. Schmitt, Shape Optimization of a sodium fast reactor core, ESAIM Proceedings, 38, 319-334 (2012). Internal report, n. 750, CMAP, Ecole Polytechnique (January 2012). 750.pdf.
  • G. Allaire, S. Desroziers, G. Enchéry, F. Ouaki, A multiscale finite element method for transport modeling, CD-ROM Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), September 10-14, 2012, Vienna, Austria, Eds.: Eberhardsteiner, J.; Böhm, H.J.; Rammerstorfer, F.G., Publisher: Vienna University of Technology, Austria, ISBN: 978-3-9502481-9-7. Preprint
  • G. Allaire, H. Hutridurga, Homogenization of reactive flows in porous media and competition between bulk and surface diffusion, IMA Journal of Applied Mathematics (2012). Internal report, n. 721, CMAP, Ecole Polytechnique (July 2011). 721.pdf.
  • G. Allaire, A la recherche de l'inégalité perdue, Matapli, 98, pp.52-64 (2012). HAL preprint: hal-01111806.  poincare-GAv3.pdf
  • G. Faccanoni, S. Kokh, G. Allaire, Modelling and simulation of liquid-vapor phase transition in compressible flows based on thermodynamical equilibrium, M2AN, 46, pp.1029-1054 (2012).
  • G. Allaire, Y. Capdeboscq, M. Puel, Homogenization of a One-Dimensional Spectral Problem for a Singularly Perturbed Elliptic Operator with Neumann Boundary Conditions, DCDS-B, 17, pp.1-31 (2012). Internal report, n. 724, CMAP, Ecole Polytechnique (September 2011). 724.pdf.
  • G. Allaire, I. Pankratova, A. Piatnitski, Homogenization and concentration for a diffusion equation with large convection in a bounded domain, Journal of Functional Analysis, 262, pp.300-330 (2012). Internal report, n. 713, CMAP, Ecole Polytechnique (May 2011). 713.pdf.
  • G. Allaire, I. Pankratova, A. Piatnitski, Homogenization of a nonstationary convection-diffusion equation in a thin rod and in a layer, SeMA Journal, 58, pp.53-95 (2012). Internal report, n. 745, CMAP, Ecole Polytechnique (March 2012). 745.pdf.

  • 2011

  • G. Allaire, M. Palombaro, J. Rauch, Diffractive Geometric Optics for Bloch Wave Packets, Archive Rat. Mech. Anal. 202, pp.373-426 (2011). Internal report, n. 710, CMAP, Ecole Polytechnique (March 2011). 710.pdf.
  • G. Allaire, Ch. Dapogny, P. Frey, Topology and geometry optimization of elastic structures by exact deformation of simplicial mesh, C. R. Acad. Sci. Paris, Série I, 349, pp.999-1003 (2011). Internal report, n. 723, CMAP, Ecole Polytechnique (August 2011). 723.pdf.
  • G. Allaire, A. Kelly, Optimal Design of Low-Contrast Two Phase Structures for the Wave Equation, M3AS, 21, No. 7, pp.1499-1538 (2011). Internal report, n. 692, CMAP, Ecole Polytechnique (August 2010). 692.pdf.
  • G. Allaire, F. Jouve, N. Van Goethem, Damage and fracture evolution in brittle materials by shape optimization methods, Journal of Computational Physics 230, pp.5010-5044 (2011). Internal report, n. 676, CMAP, Ecole Polytechnique (March 2010). 676.pdf.

  • 2010

  • G. Allaire, A. Münch, F. Periago, Long time behavior of a two-phase optimal design for the heat equation, SIAM Journal on Control and Optimization, 48(8), pp.5333-5356 (2010). Internal report, n. 690, CMAP, Ecole Polytechnique (August 2010). 690.pdf.
  • G. Allaire, A. Mikelic, A. Piatnitski, Homogenization of The Linearized Ionic Transport Equations in Rigid Periodic Porous Media, Journal of Mathematical Physics 51, 123103 (2010). Erratum in the same journal, 52, 063701 (2011). Internal report, n. 698, CMAP, Ecole Polytechnique (November 2010). 698.pdf.
  • G. Allaire, L. Friz, Localization of high frequency waves propagating in a locally periodic medium, Proc. Roy. Soc. Edinburgh, 140A, pp.897-926 (2010). Internal report, n. 668, CMAP, Ecole Polytechnique (November 2009). 668.pdf.
  • Th. Abballe, G. Allaire, E. Laucoin, Ph. Montarnal, Application of a coupled FV/FE multiscale method to cement media, Networks and Heterogeneous Media, 5 (3), pp.603-615 (2010).  Reprint available here
  • G. Allaire, A. Piatnitski, Homogenization of nonlinear reaction-diffusion equation with a large reaction term, Annali dell'Universita di Ferrara, 56, pp.141-161 (2010). Internal report, n. 672, CMAP, Ecole Polytechnique (February 2010). 672.pdf.
  • G. Allaire, A. Mikelic, A. Piatnitski, Homogenization approach to the dispersion theory for reactive transport through porous media, SIAM J. Math. Anal. 42, pp.125-144 (2010). Internal report, n. 671, CMAP, Ecole Polytechnique (February 2010). 671.pdf.
  • G. Allaire, R. Brizzi, A. Mikelic, A. Piatnitski, Two-scale expansion with drift approach to the Taylor dispersion for reactive transport through porous media, Chemical Engineering Science, 65, pp.2292-2300 (2010). Internal report, n. 660, CMAP, Ecole Polytechnique (May 2009). 660.pdf.
  • G. Faccanoni, S. Kokh, G. Allaire, Approximation of Liquid-Vapor Phase Transition for Compressible Fluids with Tabulated EOS, C. R. Acad. Sci. Paris, Série I, 348, pp.473-478 (2010). Preprint

  • 2009

  • G. Allaire, F. Jouve, Design et formes optimales I, II, III, Image des mathématiques, CNRS (2009). Partie I. Partie II. Partie III.
  • G. Allaire, M. Briane, R. Brizzi, Y. Capdeboscq, Two Asymptotic Models for Arrays of Underground Waste Containers, Applicable Analysis, 88, pp.1445-1467 (2009). Internal report, n. 657, CMAP, Ecole Polytechnique (January 2009). 657.pdf.
  • G. Allaire, M. Palombaro, J. Rauch, Diffractive behavior of the wave equation in periodic media: weak convergence analysis, Annali di Matematica Pura ed Applicata, 188, Issue 4, pp.561-590 (2009). Internal report, n. 628, CMAP, Ecole Polytechnique (November 2007). 628.pdf.
  • G. Allaire, F. Jouve, N. Van Goethem A level set method for the numerical simulation of damage evolution, Proceedings of ICIAM 2007 Zürich, R. Jeltsch and G. Wanner eds., pp.3-22, EMS, Zürich (2009). Internal report, n. 629, CMAP, Ecole Polytechnique (December 2007). 629.pdf.
  • J. Chetboun, G. Allaire, Flow Control of Curved Air Ducts using Topological Derivatives, Proceedings of the 8th World Congress on Structural and Multidisciplinary Optimization, H.C. Rodrigues et al. eds., ISSMO (2009). ISBN:978-989-20-1554-5. 1104.pdf
  • G. Allaire, F. de Gournay, F. Jouve, Stress minimization and robust compliance optimization of structures by the level set method, Proceedings of the 8th World Congress on Structural and Multidisciplinary Optimization, H.C. Rodrigues et al. eds., ISSMO (2009). ISBN:978-989-20-1554-5. 1064.pdf
  • G. Allaire, F. Golse, Transport et diffusion, polycopié de cours de troisième année à l'Ecole Polytechnique (2009).
  • G. Allaire, K. El Ganaoui, Homogenization of a conductive and radiative heat transfer problem, SIAM MMS, 7, pp.1148-1170 (2009). Internal report, n. 639, CMAP, Ecole Polytechnique (September 2008). 639.pdf.

  • 2008

  • G. Allaire, F. Jouve, Minimum stress optimal design with the level set method, Engineering Analysis with Boundary Elements 32, pp.909-918 (2008). Internal report, n. 618, CMAP, Ecole Polytechnique (June 2007). 618.pdf
  • G. Allaire, Periodic homogenization and effective mass theorems for the Schrödinger equation, in Quantum transport. Modelling, analysis and asymptotics. N. Ben Abdallah and G. Frosali eds., pp.1-44, Lecture Notes in Mathematics 1946,   Springer (2008).
  • G. Faccanoni, S. Kokh, G. Allaire, Numerical simulation with finite volume of a dynamic liquid-vapour phase transition, in Finite volumes for complex applications V, Problems and perspectives, R. Eymard et al. eds., pp.391-398, ISTE Wiley (2008). Preprint
  • F. de Gournay, G. Allaire, F. Jouve, Shape and topology optimization of the robust compliance via the level set method, COCV, 14, pp.43-70 (2008). Internal report, n. 593, CMAP, Ecole Polytechnique (2006). 593.pdf.
  • G. Allaire, A. Ferriero, Homogenization and long time asymptotic of a fluid-structure interaction problem, DCDS series B, 9, pp.199-220 (2008). Internal report, n. 627, CMAP, Ecole Polytechnique (November 2007). 627.pdf.
  • G. Allaire, S. M. Kaber, Numerical Linear Algebra, Texts in Applied Mathematics, 55, Springer (2008). (Traduction et adaptation de la version française de 2002.)

  • 2007

  • G. Allaire, R. Orive, Homogenization of periodic non self-adjoint problems with large drift and potential, COCV, 13, pp.735-749 (2007). Internal report, n. 599, CMAP, Ecole Polytechnique (July 2006). 599.pdf
  • G. Allaire, S. Gutierrez, Optimal Design in Small Amplitude Homogenization, M2AN, 41, pp.543-574 (2007). Internal report, n. 576, CMAP, Ecole Polytechnique (June 2005). 576.pdf
  • G. Allaire, Numerical Analysis and Optimization. An Introduction to Mathematical Modelling and Numerical Simulation, translated by Alan Craig, Oxford University Press, (2007). (Traduction de la version française de 2005.)
  • G. Allaire, A. Raphael, Homogenization of a convection-diffusion model with reaction in a porous medium, C. R. Acad. Sci. Paris, Série I, 344, pp.523-528 (2007). Preprint
  • G. Allaire, G. Faccanoni, S. Kokh, A strictly hyperbolic equilibrium phase transition model, C. R. Acad. Sci. Paris, Série I, 344, pp.135-140 (2007). Reprint
  • G. Allaire, Conception optimale de structures, Collection: Mathématiques et Applications, Vol. 58, Springer (2007).
  • G. Allaire, C. Conca, L. Friz, J. Ortega, On Bloch waves for the Stokes equations, DCDS series B, 7, pp.1-28 (2007). Reprint
  • E. Munoz, G. Allaire, M. P. Bendsoe, On two formulations of an optimal insulation problem, SMO, 33, pp.363-373 (2007). Reprint.

  • 2006

  • G. Allaire, A. Raphael, Homogénéisation d'un modèle de convection-diffusion avec chimie/adsorption en milieu poreux, rapport interne n. 604, CMAP, Ecole Polytechnique (2006). 604.pdf
  • G. Allaire, O. Pantz, Structural Optimization with FreeFem++, SMO, 32, pp.173-181 (2006). 586.pdf
  • G. Allaire, M. Palombaro, Localization for the Schrödinger equation in a locally periodic medium, SIAM J. Math. Anal. 38, pp.127-142 (2006). 588.pdf
  • G. Allaire, M. Vanninathan, Homogenization of the Schrödinger equation with a time oscillating potential, DCDS-B, 6, pp.1-16 (2006). Internal report, n. 582, CMAP, Ecole Polytechnique (August 2005). 582.pdf
  • G. Allaire, F. Jouve, Coupling the level set method and the topological gradient in structural optimization, in IUTAM symposium on topological design optimization of structures, machines and materials, M. Bendsoe et al. eds., pp3-12, Springer (2006). Preprint available here
  • G. Allaire, S. Gutierrez, Optimal Design with Small Contrast, in IUTAM symposium on topological design optimization of structures, machines and materials, M. Bendsoe et al. eds., pp137-146, Springer (2006). Preprint available here

  • 2005

  • G. Allaire, F. de Gournay, F. Jouve, A.-M. Toader, Structural optimization using topological and shape sensitivity via a level set method, Control and Cybernetics 34, pp.59-80 (2005). Internal report, n. 555, CMAP, Ecole Polytechnique (October 2004). 555.pdf
  • G. Allaire, R. Brizzi, A multiscale finite element method for numerical homogenization, SIAM MMS 4, pp.790-812 (2005). Preliminary version: internal report, n. 545, CMAP, Ecole Polytechnique (July 2004). 545.pdf
  • K. El Ganaoui, G. Allaire, Homogenization of a Conductive and Radiative Heat Transfer Problem, Simulation with Cast3m, Proceedings of the 2005 ASME Summer heat transfer conference, July 17-22, 2005, San Francisco.  elganaoui.allaire.pdf
  • G. Allaire, Analyse numérique et optimisation,  Editions de l'Ecole Polytechnique, Palaiseau (2005).
  • G. Allaire, A. Piatnistki, Homogenization of the Schrodinger equation and effective mass theorems , Comm. Math. Phys. 258, pp.1-22 (2005). Internal report, n. 540, CMAP, Ecole Polytechnique (June 2004). schrod.rev.pdf
  • G. Allaire, R. Orive, On the band gap structure of Hill's equation , J. Math. Anal. Appl. 306, pp.462-480 (2005). Internal report, n. 541, CMAP, Ecole Polytechnique (June 2004). 541.pdf
  • G. Allaire, F. Jouve, A level-set method for vibration and multiple loads structural optimization , Comput. Methods Appl. Mech. Engrg. 194, pp.3269-3290 (2005). Internal report, n. 542, CMAP, Ecole Polytechnique (June 2004).  cmame.pdf
  • G. Allaire, F. de Gournay, F. Jouve, Optimisation de forme de micro-mécanismes compliants par la méthode des courbes de niveaux, Actes du 7ème colloque national en calcul des structures, Giens, Mai 2005, Vol 2, pp.229-234. (2005). Preprint available here

  • 2004

  • G. Allaire, F. Jouve, A.-M. Toader, Structural optimization using sensitivity analysis and a level-set method , J. Comp. Phys. Vol 194/1, pp.363-393 (2004). Internal report, n. 508, CMAP, Ecole Polytechnique (July 2003). level-ri.pdf
  • G. Allaire, Topology optimization with the homogenization and the level-set method, in Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials, P. Ponte Castaneda et al. eds., pp.1-13, Kluwer (2004). Preprint available here
  • G. Allaire, F. Jouve, H. Maillot, Topology optimization for minimum stress design with the homogenization method, Structural and Multidisciplinary Optmization, 28, pp.87-98 (2004). Internal report, n. 509, CMAP, Ecole Polytechnique (July 2003). stress.pdf
  • G. Allaire, Y. Capdeboscq, A. Piatnistki, V. Siess, M. Vanninathan, Homogenization of periodic systems with large potentials, Arch. Rat. Mech. Anal. 174, pp.179-220 (2004). Internal report, n. 521, CMAP, Ecole Polytechnique (January 2004). acpsv.pdf
  • G. Allaire, D. Silva, O. Pantz, Sur un problème inverse de détermination de coefficients de diffusion, Rapport interne, n. 560, CMAP, Ecole Polytechnique (Novembre 2004).  rapport560

  • 2003

  • G. Allaire, H. Maillot, H-measures and bounds on the effective properties of composite materials, Portugalia Matematicae 60, pp.161-192 (2003). Reprint available here.
  • G. Allaire, Y. Capdeboscq, A. Piatnistki, Homogenization and localization with an interface , Indiana University Mathematics Journal, 52, pp.1413-1446 (2003). Internal report, n. 488, CMAP, Ecole Polytechnique (May 2002). Reprint available here
  • G. Allaire, F. Jouve, A.-M. Toader, Structural optimization by the level-set method, in International Series of Numerical Mathematics, vol. 147, pp.1-15, Birkhauser, Basel (2003). Preprint available here
  • G. Allaire, Dispersive limits in the homogenization of the wave equation , Annales de la Faculté des Sciences de Toulouse, vol. XII, pp.415-431 (2003). Preliminary version: internal report, n. 510, CMAP, Ecole Polytechnique.  onde-ri.pdf

  • 2002

  • G. Allaire, Shape optimization by the homogenization method , Springer Verlag, New York (2002).
  • G. Allaire, S. M. Kaber, Algèbre linéaire numérique. Cours et exercices , Editions Ellipses (2002).
  • G. Allaire, S. M. Kaber, Introduction à Scilab. Exercices pratiques corrigés d'algèbre linéaire , Editions Ellipses (2002).
  • G. Allaire, A. Piatnistki, Uniform Spectral Asymptotics for Singularly Perturbed Locally Periodic Operators , Com. in PDE 27, pp.705-725 (2002). Preprint available here
  • G. Allaire, Homogénéisation et limite de diffusion pour une équation de transport , Séminaire: Équations aux Dérivées Partielles, 2001--2002, Exp. No. XIV, 12 pp., Sémin. Équ. Dériv. Partielles, École Polytech., Palaiseau (2002). Preprint available here
  • G. Allaire, F. Jouve, Optimal design of micro-mechanisms by the homogenization method, European Journal of Finite Elements, 11, pp.405-416 (2002). Reprint available here
  • G. Allaire, F. Jouve, A.-M. Toader, A level-set method for shape optimization, C. R. Acad. Sci. Paris, Série I, 334, pp.1125-1130 (2002). Reprint available here.
  • G. Allaire, G. Bal, V. Siess, Homogenization and localization in locally periodic transport, ESAIM/COCV, 8, pp.1-30 (2002). Preprint available here
  • G. Allaire, Y. Capdeboscq, Homogenization and localization for a 1-D eigenvalue problem in a periodic medium with an interface, Annali di Matematica 181, pp.247-282 (2002).  Reprint available here
  • G. Allaire, S. Castro, Optimization of nuclear fuel reloading by the homogenization method, Structural and Multidisciplinary Optimization, 24, pp.1-22 (2002). Reprint available here.
  • G. Allaire, S. Clerc, S. Kokh, A five-equation model for the simulation of interfaces between compressible fluids J. Comp. Phys. 181, pp.577-616 (2002). Reprint available here
  • G. Allaire, Numerical methods of homogenization, Lecture Series 2002-06, 32nd Computational fluid dynamics - Multiscale methods, H. Deconinck ed., Von Karman Institute, Rhode Saint Genèse, Belgique (2002).

  • 2001

  • G. Allaire, S. Aubry, F. Jouve, Eigenfrequency optimization in optimal design , Comput. Methods Appl. Mech. Engrg. 190, pp.3565-3579 (2001). Reprint available here
  • G. Allaire, F. Jouve, Optimisation de structures par homogénéisation pour des fonctions-cout générales. Application à l'optimisation de mécanismes , Actes du 5ème colloque national en calcul des structures, pp.853-860, CSMA ed., Teknea, Toulouse (2001). Preprint
  • G. Allaire, A. Henrot, On some recent advances in shape optimization C. R. Acad. Sci. Paris, Série IIb, t. 329, pp.383-396 (2001). Reprint available here.
  • G. Allaire, S. Castro, A new approach for the optimal distribution of assemblies in a nuclear reactor, Numerische Mathematik, 89, pp.1-29 (2001). Reprint available here.
  • S. Kokh, G. Allaire, Numerical simulation of 2-D two-phase flows with interface, in Godunov Methods: Theory and Applications, E.F. Toro ed., Kluwer Academic/Plenum Publishers (2001). Preprint available here

  • 2000

  • G. Allaire, S. Kokh, Simulating interfaces in two-phase flows , in the Proceedings of AMIF-ESF Workshop "Computing Methods for Two-Phase Flow", Aussois, France, 12-14 January 2000 (CD-ROM).  Preprint
  • G. Allaire, Y. Capdeboscq, Homogenization of a spectral problem in neutronic multigroup diffusion , Comput. Methods Appl. Mech. Engrg. 187, pp.91-117 (2000). Reprint available here.
  • G. Allaire, S. Aubry, F. Jouve, Shape optimization with general objective functions using partial relaxation, in Topology optimization of structures and composite continua, G.I.N. Rozvany and N. Olhoff eds., pp.239-249, Kluwer Academic Publishers (2000). Preprint available here
  • G. Allaire, S. Clerc, S. Kokh, A five-equation model for the numerical simulation of interfaces in two-phase flows , C. R. Acad. Sci. Paris, Série I, t. 331, pp.1017-1022 (2000). Preprint available here

  • 1999

  • G. Allaire, F. Jouve, Structural optimization by the homogenization method, in the Proceedings of IUTAM Symposium "Variations of domains and free-boundary problems in solid mechanics", P. Argoul et al. eds., Kluwer Academic Publishers, Dordrecht, pp.293-300 (1999).
  • G. Allaire, S. Aubry, On optimal microstructures for a plane shape optimization problem, Structural Optimization 17, pp.86-94 (1999). Reprint available here.
  • G. Allaire, M. Amar, Boundary layer tails in periodic homogenization , ESAIM COCV 4, pp.209-243 (1999).  lien
  • G. Allaire, V. Lods, Minimizers for a double-well problem with affine boundary conditions, Proc. Roy. Soc. Edinburgh 129A, pp.439-466 (1999).  Preprint.
  • G. Allaire, G. Bal Homogenization of the criticality spectral equation in neutron transport, M2AN 33, pp.721-746 (1999). Preprint available here.
  • G. Allaire, C. Conca, M. Vanninathan, Spectral asymptotics of the Helmholtz model in fluid-solid structures, Int. J. Numer. Meth. Engng. 46, pp.1463-1504 (1999). Reprint available here.
  • S. Kokh, G. Allaire, S. Clerc, Towards boiling crisis simulation: the level set method, in the Proceedings of the Ninth International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-9), San Francisco, California, October 3-8, 1999 (CD-ROM edited by the American Nuclear Society).  Preprint
  • G. Allaire, Homogenization and applications to material sciences, Notes de cours au Newton Institute de Cambridge, Septembre 1999.

  • 1998

  • G. Allaire, C. Conca, Bloch wave homogenization and spectral asymptotic analysis, J. Math. Pures et Appli. 77, pp.153-208 (1998). Reprint available here.
  • G. Allaire, C. Conca, Boundary layers in the homogenization of a spectral problem in fluid-solid structures, SIAM J. Math. Anal. 29, pp.343-379 (1998). Reprint available here.
  • G. Allaire, G. Francfort, Existence of minimizers for non-quasiconvex functionals arising in optimal design, Annales de l'Institut Henri Poincaré, Analyse Non-Linéaire, 155, pp.301-339 (1998).  Reprint available here
  • G. Allaire, S. Aubry, F. Jouve, Simulation numérique de l'endommagement à l'aide du modèle Francfort-Marigo, Actes du 29ème congrès d'analyse numérique, ESAIM Proceedings, vol. 3, pp.1-9 (1998).  lien
  • G. Allaire, C. Conca, M. Vanninathan, The Bloch transform and applications, Actes du 29ème congrès d'analyse numérique, ESAIM Proceedings, vol. 3, pp.65-84 (1998).  lien
  • G. Allaire, C. Conca, J. Planchard, Homogenization and Bloch wave method for fluid tube bundle interaction , Comput. Methods Appl. Mech. Engrg. 164, pp.333-361 (1998). Reprint available here.
  • G. Allaire, La méthode d'homogénéisation pour l'optimisation topologique de structures élastiques, article de vulgarisation paru dans le numéro 53 de MATAPLI, bulletin de la SMAI, en janvier 1998.

  • 1997

  • G. Allaire, E. Bonnetier, G. Francfort, F. Jouve, Shape optimization by the homogenization method, Numerische Mathematik 76, pp.27-68 (1997).  Reprint available here
  • G. Allaire, M. Avellaneda, J.L. Auriault, A. Bourgeat, H. Ene, K. Golden, U. Hornung, A. Mikelic, R. Showalter, Homogenization and porous media, Interdisciplinary Applied Mathematics Series, vol. 6, U. Hornung ed., pp.45-68, pp.225-250, Springer Verlag (1997).
  • G. Allaire, A. Zelmanse, Kinetic schemes for gas dynamics of real gases or two-phase mixtures, dans Numerical methods in mechanics, C. Conca, G. Gatica eds., Pitman Research Notes in Mathematics 371, pp.13-24, Longman, Harlow (1997). Preprint available here.
  • G. Allaire, The homogenization method for topology and shape optimization, dans "Topology optimization in structural mechanics", G. Rozvany ed., pp.101-134, CISM Courses and Lectures 374, Springer, Wien (1997).
  • G. Allaire, F. Malige, Analyse asymptotique spectrale d'un problème de diffusion neutronique, C. R. Acad. Sci. Paris, Série I, t.324, pp.939-944 (1997). Reprint available here.
  • G. Allaire, F. Jouve, Optimisation topologique de structures élastiques, Actes du 3ème colloque national en calcul des structures, B. Peseux et al. eds., pp.49-58, Presses Académiques de l'Ouest, Nantes (1997). Preprint available here.
  • G. Allaire, G. Bal Homogénéisation d'une équation spectrale du transport neutronique, C. R. Acad. Sci. Paris, Série I, 325, pp.1043-1048 (1997).  Reprint available here

  • 1996

  • G. Allaire, M. Briane, Multiscale convergence and reiterated homogenization, Proc. Roy. Soc. Edinburgh 126A, pp.297-342 (1996).  Reprint available here
  • G. Allaire, C. Conca, Bloch wave homogenization for a spectral problem in fluid-solid structures, Arch. Rat. Mech. Anal. 135, pp.197-257 (1996). Reprint available here.
  • G. Allaire, A. Damlamian, U. Hornung, Two-scale convergence on periodic surfaces and applications, In Proceedings of the International Conference on Mathematical Modelling of Flow through Porous Media (May 1995), A. Bourgeat et al. eds., pp.15-25, World Scientific Pub., Singapore (1996). Preprint available here.
  • G. Allaire, E. Bonnetier, G. Francfort, F. Jouve, A topological approach to shape optimization, in Applied Stochastics and Optimization, O. Mahrenholtz et al. eds., ICIAM 95 special issue of ZAMM, Z. angew. Math. Mech. 76, S3, pp.255-258 (1996). Preprint available here.
  • G. Allaire, Z. Belhachmi, F. Jouve, The homogenization method for topology and shape optimization. Single and multiple loads case, Revue Européenne des Eléments Finis, 5, pp.649-672 (1996). Reprint available here.

  • 1995

  • G. Allaire, Solving linear systems in FLICA-4, a thermohydraulic code for 3-D transient computations, "Proceedings of the International Conference on Mathematics and Computations, Reactor Physics, and Environmental Analysis", Portland Oregon, American Nuclear Society (1995).
  • P. Raymond, G. Allaire, G. Boudsocq, D. Caruge, T. de Gramont, I. Toumi, FLICA-4 (Version 1) a computer code for three dimensional thermal analysis of nuclear reactor cores, "Proceedings of the International Conference on Mathematics and Computations, Reactor Physics, and Environmental Analysis", Portland Oregon, American Nuclear Society (1995).
  • G. Allaire, Relaxation of structural optimization problems by homogenization, "Trends in Applications of Mathematics to Mechanics", M.M.Marques and J.F.Rodrigues Eds., Pitman monographs and surveys in pure and applied mathematics 77, pp.237-251, Longman, Harlow (1995).
  • G. Allaire, C. Conca, Analyse asymptotique spectrale de l'équation des ondes. Homogénéisation par ondes de Bloch, C. R. Acad. Sci. Paris t. 321, Série I, pp.293-298 (1995).
  • G. Allaire, C. Conca, Analyse asymptotique spectrale de l'équation des ondes. Complétude du spectre de Bloch, C. R. Acad. Sci. Paris t. 321, Série I, pp.557-562 (1995).

  • 1994

  • G. Allaire, R.V. Kohn, Optimal lower bound on the elastic energy of a composite made from two non well-ordered isotropic materials, Quat. Appl. Math. 52, pp.311-333 (1994).
  • G. Allaire, Two-scale convergence : a new method in periodic homogenization, dans "Nonlinear partial differential equations and their applications, Collège de France Seminar", pp.1-14, vol. XII, H. Brézis and J.L. Lions Eds., Pitman Research Notes in Mathematical Sciences 302, Longman (1994).  Preprint available here
  • G. Allaire, A remark on trace bounds for elastic composite materials, dans "Calculus of Variations, Homogenization and Continuum Mechanics", Series on Advances in Mathematics for Applied Sciences, pp.19-28, vol. 18, P. Suquet et al. Eds., World Scientific, Singapore (1994).  Preprint available here
  • G. Allaire, Explicit lamination parameters for three-dimensional shape optimization, Control and Cybernetics, vol. 23, pp.309-326 (1994).  Reprint available here

  • 1993

  • G. Allaire, F. Murat, Homogenization of the Neumann problem with non-isolated holes, Asymptotic Analysis, 7, pp.81-95 (1993).  Copy available here
  • G. Allaire, R.V. Kohn, Optimal bounds on the effective behavior of a mixture of two well-ordered elastic materials, Quat. Appl. Math. 51, pp.643-674 (1993).  Reprint available here
  • G. Allaire, R.V. Kohn, Explicit optimal bounds on the elastic energy of a two-phase composite in two space dimensions, Quat. Appl. Math. 51, pp.675-699 (1993).
  • G. Allaire, R.V. Kohn, Optimal design for minimum weight and compliance in plane stress using extremal microstructures, Europ. J. Mech. A/Solids 12, 6, pp.839-878 (1993).  Reprint available here
  • G. Allaire, G. Francfort, A numerical algorithm for topology and shape optimization, "Topology design of structures" Nato ASI Series E, pp.239-248, vol.227, M. Bendsoe et al. eds., Kluwer, Dordrecht (1993).  Preprint available here
  • G. Allaire, R.V. Kohn, Topology optimization and optimal shape design using homogenization , "Topology design of structures" Nato ASI Series E, pp.207-218,vol.227, M. Bendsoe et al. eds., Kluwer, Dordrecht (1993).  Preprint available here
  • G. Allaire, Structural optimization using optimal microstructures, dans "MECAMAT 93 International Seminar on Micromechanics of Materials", Collection de la Direction des Etudes et Recherches d'Electricité de France, pp.106-114, Eyrolles, Paris (1993).  Reprint available here
  • G. Allaire, Two-scale convergence and homogenization of periodic structures. An introduction to homogenization and bounds on effective properties applied to optimal shape design, dans "School on Homogenization", SISSA preprint 140/93/M (1993).

  • 1992

  • G. Allaire, Homogenization and two-scale convergence, SIAM J. Math. Anal. 23, 6, pp.1482-1518 (1992).  Reprint available here
  • G. Allaire, Homogenization of the unsteady Stokes equations in porous media, dans "Progress in partial differential equations: calculus of variations, applications" Pitman Research Notes in Mathematics Series 267, pp.109-123, C. Bandle et al. eds, Longman Higher Education, New York (1992).  Preprint available here

  • 1991

  • G. Allaire, Homogenization of the Navier-Stokes equations in open set perforated with tiny holes, Part I: Abstract framework, a volume distribution of holes, Arch. Rat. Mech. Anal., 113, pp.209-259 (1991).  Reprint available here
  • G. Allaire, Homogenization of the Navier-Stokes equations in open set perforated with tiny holes, Part II: Non-critical size of the holes for a volume distribution and a surface distribution of holes, Arch. Rat. Mech. Anal., 113, pp.261-298 (1991).  Reprint available here
  • G. Allaire, Homogenization of the Navier-Stokes equations and derivation of Brinkman's law, in Applied Mathematics for Engineering Sciences, C. Carasso et al. eds., pp.7-20, Cépaduès Editions, Toulouse (1991).  Copy available here
  • G. Allaire, Homogenization of the Navier-Stokes equations with a slip boundary condition, Comm. Pure Appl. Math., 44, pp.605-641 (1991).  Reprint available here
  • G. Allaire, Continuity of the Darcy's law in the low-volume fraction limit, Ann. Scuola Norm. Sup. Pisa, 18, pp.475-499 (1991).  Reprint available here
  • G. Allaire, Homogénéisation et convergence à deux échelles, application à un problème de convection-diffusion, C. R. Acad. Sci. Paris, 312, pp.581-586 (1991).  Reprint available here

  • 1989

  • G. Allaire, Prolongement de la pression et homogénéisation des équations de Stokes dans un milieu poreux connexe, C. R. Acad. Sci. Paris, 309, pp.717-722 (1989).  Reprint available here
  • G. Allaire, Homogénéisation des équations de Stokes dans un domaine perforé de petits trous répartis périodiquement, C. R. Acad. Sci. Paris, 309, pp.741-746 (1989).
  • G. Allaire, Homogenization of the Stokes flow in a connected porous medium, Asymptotic Analysis, 2, pp.203-222 (1989).  Reprint available here