Effective models for the multidimensional wave equation in 806 heterogeneous media over long time and numerical homogenization, Mathematical Models 807 and Methods in Applied Sciences, vol.26, pp.2651-2684, 2016. ,
Effective models and numerical homogenization for wave prop-809 agation in heterogeneous media on arbitrary timescales, Foundations of Computational 810 Mathematics, pp.1-43, 2020. ,
An extension theorem from 812 connected sets, and homogenization in general periodic domains, Nonlinear Analysis: The-813 ory, vol.18, pp.481-496, 1992. ,
Homogénéisation deséquations de Stokes et de Navier-Stokes, 1989. ,
Homogenization of the Stokes flow in a connected porous medium, Asymptotic, vol.817, pp.203-222, 1989. ,
Continuity of the Darcy's law in the low-volume fraction limit, Annali della Scuola, vol.819 ,
, Classe di Scienze. Serie IV, vol.18, pp.475-499, 1991.
Homogenization of the Navier-Stokes equations in open sets perforated with tiny 821 holes I. Abstract framework, a volume distribution of holes, Archive for Rational Mechanics 822 and Analysis, vol.113, pp.209-259, 1991. ,
Homogenization of the Navier-Stokes equations with a slip boundary condition, 824 Communications on pure and applied mathematics, vol.44, pp.605-641, 1991. ,
Homogenization and two-scale convergence, SIAM Journal on Mathematical, vol.826, pp.1482-1518, 1992. ,
URL : https://hal.archives-ouvertes.fr/hal-01111805
Shape optimization by the homogenization method, vol.146, 2012. ,
Boundary layer tails in periodic homogenization, ESAIM: Control, 830 Optimisation and Calculus of Variations, vol.4, pp.209-243, 1999. ,
A comparison between two-scale asymp-832 totic expansions and Bloch wave expansions for the homogenization of periodic structures, 833 SEMA journal, vol.73, pp.237-259, 2016. ,
Bloch wave homogenization and spectral asymptotic analysis, 835 Journal de mathématiques pures et appliquées, vol.77, pp.153-208, 1998. ,
Topology optimization of modulated and 837 oriented periodic microstructures by the homogenization method, Computers & Mathemat-838 ics with Applications, 2018. ,
, Crime Pays; Homogenized Wave Equations for Long 840 Times, 2018.
Optimization of dispersive coefficients in the homogenization of 842 the wave equation in periodic structures, Numerische Mathematik, vol.140, pp.265-326, 2018. ,
On the domain of validity of Brinkman's equation, Transp. Porous Media, vol.79, pp.215-223, 2009. ,
Darcy's law, Brinkman's law and poor sepa-846 ration of scales, Proceedings of the 3rd 847 Biot Conference on Poromechanics, pp.553-558, 1905. ,
Homogenisation: averaging processes in periodic media, of Mathematics and its Applications (Soviet Series), vol.849, 1989. ,
Shape optimization of periodic structures, Computational Mechanics, vol.30, pp.235-246, 2003. ,
Generating optimal topologies in structural design using 854 a homogenization method, Computer methods in applied mechanics and engineering, vol.71, pp.197-224, 1988. ,
Asymptotics of solutions to the Poisson problem in a perforated 857 domain with corners, Journal de mathématiques pures et appliquées, vol.76, p.911, 1997. ,
Local profiles for elliptic problems at different scales: 860 defects in, and interfaces between periodic structures, Communications in Partial Differ-861 ential Equations, vol.40, pp.2173-2236, 2015. ,
Large-scale topology optimization in 3D using parallel com-863 puting, Computer methods in applied mechanics and engineering, vol.190, p.6229, 2001. ,
Topology optimization of fluids in Stokes flow, International 866 Journal for Numerical Methods in Fluids, vol.41, pp.77-107, 2003. ,
Weak nonlinear corrections for Darcy's 868 law, Mathematical Models and Methods in Applied Sciences, vol.6, pp.1143-1155, 1996. ,
Full Two-Scale Asymptotic Expansion and Higher-870 ,
, Order Constitutive Laws in the Homogenization of the System of Quasi-static Maxwell 871 Equations, Multiscale Modeling & Simulation, vol.14, pp.1513-1539, 2016.
On full two-scale expansion of the solutions of 873 nonlinear periodic rapidly oscillating problems and higher-order homogenised variational 874 problems, Archive for rational mechanics and analysis, vol.174, pp.385-442, 2004. ,
The Stokes and Navier-Stokes equations with 876 boundary conditions involving the pressure, Japanese journal of mathematics. New series, vol.877, issue.20, pp.279-318, 1994. ,
Density 879 based topology optimization of turbulent flow heat transfer systems, Structural and Multi-880 disciplinary Optimization, vol.57, pp.1905-1918, 2018. ,
, Theory and practice of finite elements, vol.159, 2013.
Homogenization of stationary Navier-Stokes equations in domains 884 with tiny holes, Journal of Mathematical Fluid Mechanics, vol.17, pp.381-392, 2015. ,
Shape and topology optimization of multiphysics systems, 2019. ,
URL : https://hal.archives-ouvertes.fr/tel-02441844
High order homogenization of the Poisson equation in a perforated periodic domain, Radon Series on Computational and Applied Mathematics, p.889, 2020. ,
URL : https://hal.archives-ouvertes.fr/hal-02518528
Nonlinear corrections to Darcy's law at 890 low Reynolds numbers, Journal of Fluid Mechanics, vol.343, pp.331-350, 1997. ,
Steady Stokes Flow in Exterior Domains, pp.244-303, 1994. ,
3-d topology optimization of modulated 894 and oriented periodic microstructures by the homogenization method, Journal of Compu-895 tational Physics, vol.401, p.108994, 2020. ,
Finite element approximation of the Navier-Stokes equations, vol.897, 1979. ,
Homogenization-based topology optimization for high-resolution 899 manufacturable microstructures, International Journal for Numerical Methods in Engineer-900 ing, vol.113, pp.1148-1163, 2018. ,
De-homogenization 902 of optimal multi-scale 3d topologies, Computer Methods in Applied Mechanics and Engi-903 neering, vol.364, p.112979, 2020. ,
, A unified homogenization approach for the Dirichlet problem in Perforated Domains, 905 arXiv preprint, 2019.
, The mathematical theory of viscous incompressible flow, vol.2, 1969.
, Perturbations singulières dans les problèmes aux limites et en contrôle optimal, p.909
, Lecture Notes in Mathematics, vol.323, 1973.
Some methods in the mathematical analysis of systems and their control, 1981. ,
, Homogenization of stokes equations in perforated domains: a unified approach, 2019.
Asymptotic expansion for a flow in a periodic porous medium, Comptes, vol.915 ,
, Rendus de l'Academie des Sciences-Series IIB-Mechanics-Physics-Chemistry-Astronomy, vol.916, pp.369-374, 1997.
Sur le contrôle par un domaine géométrique, Publication du Labo-918 ratoire d'Analyse Numérique de l, 1976. ,
Acoustic and electromagnetic equations: integral representations for harmonic 920 problems, 2001. ,
Non-homogeneous media and vibration theory, Lecture Notes in Physics, vol.127, p.922, 1980. ,
A post-treatment of the homogenization method for shape opti-924 mization, SIAM Journal on Control and Optimization, vol.47, pp.1380-1398, 2008. ,
A "poor man's" approach 926 for high-resolution three-dimensional topology design for natural convection problems, Ad-927 vances in Engineering Software, vol.140, p.102736, 2020. ,
Fluid flow in porous media, Non-homogeneous media and vibration 929 theory, pp.129-157, 1980. ,
On rigorous derivation of strain gradient effects 931 in the overall behaviour of periodic heterogeneous media, Journal of the Mechanics, vol.932, pp.1325-1357, 2000. ,
, Topics in nonlinear analysis, Publications mathématiques d'Orsay, p.78, 1978.
, Navier stokes equations: Theory and numerical analysis, vol.45, 1977.
A "poor man's approach" to topology 937 optimization of cooling channels based on a Darcy flow model, International Journal of 938 Heat and Mass Transfer, vol.116, pp.1108-1123, 2018. ,