Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

Characterizations of diffusion matrices in homogenization of elliptic equations in nondivergence-form

Xiaoqin Guo, Timo Sprekeler and Hung V. Tran
Calculus of Variations and Partial Differential Equations 64 (1) (2025)
https://doi.org/10.1007/s00526-024-02884-5

Multiscale Topology Optimization of modulated fluid microchannels based on asymptotic homogenization

F. Feppon
Computer Methods in Applied Mechanics and Engineering 419 116646 (2024)
https://doi.org/10.1016/j.cma.2023.116646

Effective boundary conditions for second-order homogenization

Manon Thbaut, Basile Audoly and Claire Lestringant
Journal of the Mechanics and Physics of Solids 190 105707 (2024)
https://doi.org/10.1016/j.jmps.2024.105707

Multiscale contact homogenisation: A novel perspective through the method of multiscale virtual power

António M. Couto Carneiro, Francisco M. Andrade Pires and Eduardo A. de Souza Neto
Computer Methods in Applied Mechanics and Engineering 432 117394 (2024)
https://doi.org/10.1016/j.cma.2024.117394

Sharp convergence rates for the homogenization of the Stokes equations in a perforated domain

Loïc Balazi, Grégoire Allaire and Pascal Omnes
Discrete and Continuous Dynamical Systems - B (2024)
https://doi.org/10.3934/dcdsb.2024142

Asymptotic behavior for eigenvalues and eigenfunctions associated to Stokes operator in the presence of a rapidly oscillating boundary

Ahlem Jaouabi and Abdessatar Khelifi
Mathematical Methods in the Applied Sciences 47 (4) 1915 (2024)
https://doi.org/10.1002/mma.9726

Sixty Shades of Generalized Continua

Alexander G. Kolpakov, Sergey I. Rakin and Igor V. Andrianov
Advanced Structured Materials, Sixty Shades of Generalized Continua 170 419 (2023)
https://doi.org/10.1007/978-3-031-26186-2_26

Gaussian bounds and asymptotic expansions of green function in parabolic homogenization

Jun Geng
Calculus of Variations and Partial Differential Equations 62 (6) (2023)
https://doi.org/10.1007/s00526-023-02504-8

Upscaled model for the diffusion/heterogeneous reaction in porous media: Boundary layer problem

Tien Dung Le, Christian Moyne, Mohamed Khaled Bourbatache and Olivier Millet
Advances in Water Resources 179 104500 (2023)
https://doi.org/10.1016/j.advwatres.2023.104500

Boundary layers in the vicinity of the prepreg interface in layered composites and the homogenized delamination criterion

Alexander G. Kolpakov, Sergey I. Rakin and Igor V. Andrianov
International Journal of Solids and Structures 267 112166 (2023)
https://doi.org/10.1016/j.ijsolstr.2023.112166

Hypertemperature effects in heterogeneous media and thermal flux at small-length scales

Grigor Nika and Adrian Muntean
Networks and Heterogeneous Media 18 (3) 1207 (2023)
https://doi.org/10.3934/nhm.2023052

Axisymmetric indentation of a periodically layered, viscoelastic half-space

Deepak Sachan, Ishan Sharma and T. Muthukumar
Zeitschrift für angewandte Mathematik und Physik 73 (6) (2022)
https://doi.org/10.1007/s00033-022-01859-w

Homogenization of the heat equation in a noncylindrical domain with randomly oscillating boundary

Akambadath Keerthiyil Nandakumaran and Kasinathan Sankar
Mathematical Methods in the Applied Sciences 45 (10) 6435 (2022)
https://doi.org/10.1002/mma.8179

Multiscale analysis of composite structures based on higher-order asymptotic homogenization with boundary layer correction

Mouad Fergoug, Augustin Parret-Fréaud, Nicolas Feld, Basile Marchand and Samuel Forest
European Journal of Mechanics - A/Solids 96 104754 (2022)
https://doi.org/10.1016/j.euromechsol.2022.104754

Homogenization of the Stokes System in a Domain with an Oscillating Boundary

T. Muthukumar and K. Sankar
Multiscale Modeling & Simulation 20 (4) 1361 (2022)
https://doi.org/10.1137/22M1474345

High Order Homogenization of the Stokes System in a Periodic Porous Medium

Florian Feppon
SIAM Journal on Mathematical Analysis 53 (3) 2890 (2021)
https://doi.org/10.1137/20M1348078

Stress minimization for lattice structures. Part I: Micro-structure design

A. Ferrer, P. Geoffroy-Donders and G. Allaire
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379 (2201) 20200109 (2021)
https://doi.org/10.1098/rsta.2020.0109

On a pore-scale stationary diffusion equation: Scaling effects and correctors for the homogenization limit

Vo Anh Khoa, Thi Kim Thoa Thieu and Ekeoma Rowland Ijioma
Discrete & Continuous Dynamical Systems - B 26 (5) 2451 (2021)
https://doi.org/10.3934/dcdsb.2020190

Optimal Convergence Rates for Elliptic Homogenization Problems in Nondivergence-Form: Analysis and Numerical Illustrations

Timo Sprekeler and Hung V. Tran
Multiscale Modeling & Simulation 19 (3) 1453 (2021)
https://doi.org/10.1137/20M137121X

Modelling viscoelastic wave phenomenon by homogenisation of the poroelasticity equations

Q. LI, F. SANTOSA, B. WHEELOCK and K. GOVIL
European Journal of Applied Mathematics 32 (5) 846 (2021)
https://doi.org/10.1017/S0956792520000467

Limiting boundary correctors for periodic microstructures and inverse homogenization series

Fioralba Cakoni, Shari Moskow and Tayler Pangburn
Inverse Problems 36 (6) 065009 (2020)
https://doi.org/10.1088/1361-6420/ab8bc6

Inertia and Roughness-Induced Effects on the Porous Medium Flow Through a Corrugated Channel

Eduard Marušić-Paloka and Igor Pažanin
Transport in Porous Media 134 (3) 621 (2020)
https://doi.org/10.1007/s11242-020-01460-7

Effects of boundary roughness and inertia on the fluid flow through a corrugated pipe and the formula for the Darcy–Weisbach friction coefficient

Eduard Marušić-Paloka and Igor Pažanin
International Journal of Engineering Science 152 103293 (2020)
https://doi.org/10.1016/j.ijengsci.2020.103293

Mathematical Analysis of Electromagnetic Plasmonic Metasurfaces

Habib Ammari, Bowen Li and Jun Zou
Multiscale Modeling & Simulation 18 (2) 758 (2020)
https://doi.org/10.1137/19M1275097

Uniform estimate of an iterative method for elliptic problems with rapidly oscillating coefficients

Chenlin Gu
Stochastics and Partial Differential Equations: Analysis and Computations 8 (4) 787 (2020)
https://doi.org/10.1007/s40072-019-00159-1

Calculation of Thermoelastic Stresses in a Joint Formed in Explosion Welding

A. G. Kolpakov and S. I. Rakin
Journal of Applied Mechanics and Technical Physics 61 (2) 277 (2020)
https://doi.org/10.1134/S0021894420020145

Functionally graded lattice structure topology optimization for the design of additive manufactured components with stress constraints

Lin Cheng, Jiaxi Bai and Albert C. To
Computer Methods in Applied Mechanics and Engineering 344 334 (2019)
https://doi.org/10.1016/j.cma.2018.10.010

Scattering by a Bounded Highly Oscillating Periodic Medium and the Effect of Boundary Correctors

Fioralba Cakoni, Bojan B. Guzina, Shari Moskow and Tayler Pangburn
SIAM Journal on Applied Mathematics 79 (4) 1448 (2019)
https://doi.org/10.1137/19M1237089

Effective Fluid Behavior in Domain with Rough Boundary and the Darcy--Weisbach Law

Eduard Marušić-Paloka
SIAM Journal on Applied Mathematics 79 (4) 1244 (2019)
https://doi.org/10.1137/18M1183376

An asymptotic strategy to couple homogenized elastic structures

Alexander G. Kolpakov, Igor V. Andrianov, Sergei I. Rakin and Graham A. Rogerson
International Journal of Engineering Science 131 26 (2018)
https://doi.org/10.1016/j.ijengsci.2018.04.006

Asymptotical Mechanics of Composites

Igor V. Andrianov, Jan Awrejcewicz and Vladyslav V. Danishevskyy
Advanced Structured Materials, Asymptotical Mechanics of Composites 77 1 (2018)
https://doi.org/10.1007/978-3-319-65786-8_1

Boundary Layers in Periodic Homogenization of Neumann Problems

Zhongwei Shen and Jinping Zhuge
Communications on Pure and Applied Mathematics 71 (11) 2163 (2018)
https://doi.org/10.1002/cpa.21740

On the best constant matrix approximating an oscillatory matrix-valued coefficient in divergence-form operators

Claude Le Bris, Frédéric Legoll and Simon Lemaire
ESAIM: Control, Optimisation and Calculus of Variations (2018)
https://doi.org/10.1051/cocv/2017061

Homogenization of an evolution problem with $$ L\log L$$ L log L data in a domain with oscillating boundary

Antonio Gaudiello and Olivier Guibé
Annali di Matematica Pura ed Applicata (1923 -) 197 (1) 153 (2018)
https://doi.org/10.1007/s10231-017-0673-0

Homogenization of parabolic equation in an evolving domain with an oscillating boundary

T. Muthukumar, Jean-Pierre Raymond and K. Sankar
Journal of Mathematical Analysis and Applications 463 (2) 838 (2018)
https://doi.org/10.1016/j.jmaa.2018.03.063

Quantitative Analysis of Boundary Layers in Periodic Homogenization

Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat and Christophe Prange
Archive for Rational Mechanics and Analysis 226 (2) 695 (2017)
https://doi.org/10.1007/s00205-017-1142-z

Cell Averaging Two-Scale Convergence: Applications to Periodic Homogenization

François Alouges and Giovanni Di Fratta
Multiscale Modeling & Simulation 15 (4) 1651 (2017)
https://doi.org/10.1137/16M1085309

Moment bounds on the corrector of stochastic homogenization of non-symmetric elliptic finite difference equations

Jonathan Ben-Artzi, Daniel Marahrens and Stefan Neukamm
Communications in Partial Differential Equations 42 (2) 179 (2017)
https://doi.org/10.1080/03605302.2017.1281298

Homogenization of Elastic Dielectric Composites with Rapidly Oscillating Passive and Active Source Terms

Victor Lefèvre and Oscar Lopez-Pamies
SIAM Journal on Applied Mathematics 77 (6) 1962 (2017)
https://doi.org/10.1137/17M1110432

A Mathematical and Numerical Framework for Bubble Meta-Screens

Habib Ammari, Brian Fitzpatrick, David Gontier, Hyundae Lee and Hai Zhang
SIAM Journal on Applied Mathematics 77 (5) 1827 (2017)
https://doi.org/10.1137/16M1090235

Homogenization of the Brush Problem with a Source Term in L 1

Antonio Gaudiello, Olivier Guibé and François Murat
Archive for Rational Mechanics and Analysis 225 (1) 1 (2017)
https://doi.org/10.1007/s00205-017-1079-2

Liouville Principles and a Large-Scale Regularity Theory for Random Elliptic Operators on the Half-Space

Julian Fischer and Claudia Raithel
SIAM Journal on Mathematical Analysis 49 (1) 82 (2017)
https://doi.org/10.1137/16M1070384

Macroscale modelling of multilayer diffusion: Using volume averaging to correct the boundary conditions

E.J. Carr, I.W. Turner and P. Perré
Applied Mathematical Modelling 47 600 (2017)
https://doi.org/10.1016/j.apm.2017.03.044

On the Homogenization of a Scalar Scattering Problem for Highly Oscillating Anisotropic Media

Fioralba Cakoni, Bojan B. Guzina and Shari Moskow
SIAM Journal on Mathematical Analysis 48 (4) 2532 (2016)
https://doi.org/10.1137/15M1018009

Two-scale homogenization of the Poisson equation with friction boundary condition in a perforated domain

L. Baffico
Asymptotic Analysis 96 (3-4) 331 (2016)
https://doi.org/10.3233/ASY-151346

A Multiscale Finite Element Method for Oscillating Neumann Problem on Rough Domain

Pingbing Ming and Xianmin Xu
Multiscale Modeling & Simulation 14 (4) 1276 (2016)
https://doi.org/10.1137/15M1044709

Slow Convergence in Periodic Homogenization Problems for Divergence-Type Elliptic Operators

Hayk Aleksanyan
SIAM Journal on Mathematical Analysis 48 (5) 3345 (2016)
https://doi.org/10.1137/15M1040165

Mathematical and numerical framework for metasurfaces using thin layers of periodically distributed plasmonic nanoparticles

Habib Ammari, Matias Ruiz, Wei Wu, Sanghyeon Yu and Hai Zhang
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472 (2193) 20160445 (2016)
https://doi.org/10.1098/rspa.2016.0445

Periodic Controls in an Oscillating Domain: Controls via Unfolding and Homogenization

A. K. Nandakumaran, Ravi Prakash and Bidhan Chandra Sardar
SIAM Journal on Control and Optimization 53 (5) 3245 (2015)
https://doi.org/10.1137/140994575

Scattering by a highly oscillating surface

A. Bendali and J.‐R. Poirier
Mathematical Methods in the Applied Sciences 38 (13) 2785 (2015)
https://doi.org/10.1002/mma.3261

Homogenization of Highly Oscillating Boundaries with Strongly Contrasting Diffusivity

Antonio Gaudiello and Ali Sili
SIAM Journal on Mathematical Analysis 47 (3) 1671 (2015)
https://doi.org/10.1137/140987225

Multiscale Approach for Optimal Design in Conductivity of Composite Materials

Jianjun Liu, Liqun Cao, Ningning Yan and Junzhi Cui
SIAM Journal on Numerical Analysis 53 (3) 1325 (2015)
https://doi.org/10.1137/13094904X

Rigorous upscaling of rough boundaries for reactive flows

K. Kumar, M. van Helvoort and I.S. Pop
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 94 (7-8) 623 (2014)
https://doi.org/10.1002/zamm.201200226

Upscaling of reactive flows in domains with moving oscillating boundaries

Kundan Kumar, Tycho van Noorden and Iuliu Sorin Pop
Discrete & Continuous Dynamical Systems - S 7 (1) 95 (2014)
https://doi.org/10.3934/dcdss.2014.7.95

Second-order two-scale method for bending behavior analysis of composite plate with 3-D periodic configuration and its approximation

ZiQiang Wang and JunZhi Cui
Science China Mathematics 57 (8) 1713 (2014)
https://doi.org/10.1007/s11425-014-4831-1

Stokes’ System in a Domain with Oscillating Boundary: Homogenization and Error Analysis of an Interior Optimal Control Problem

A. K. Nandakumaran, Ravi Prakash and J.-P. Raymond
Numerical Functional Analysis and Optimization 35 (3) 323 (2014)
https://doi.org/10.1080/01630563.2013.812657

Applications of Fourier Analysis in Homogenization of Dirichlet Problem III: Polygonal Domains

Hayk Aleksanyan, Henrik Shahgholian and Per Sjölin
Journal of Fourier Analysis and Applications 20 (3) 524 (2014)
https://doi.org/10.1007/s00041-014-9327-4

An optimal quantitative two-scale expansion in stochastic homogenization of discrete elliptic equations

Antoine Gloria, Stefan Neukamm and Felix Otto
ESAIM: Mathematical Modelling and Numerical Analysis 48 (2) 325 (2014)
https://doi.org/10.1051/m2an/2013110

Multiscale Finite Element approach for “weakly” random problems and related issues

Claude Le Bris, Frédéric Legoll and Florian Thomines
ESAIM: Mathematical Modelling and Numerical Analysis 48 (3) 815 (2014)
https://doi.org/10.1051/m2an/2013122

Dynamical one-dimensional models of passive piezoelectric sensors

Cédric Bellis and Sébastien Imperiale
Mathematics and Mechanics of Solids 19 (5) 451 (2014)
https://doi.org/10.1177/1081286512469980

Periodic Homogenization of Green and Neumann Functions

Carlos Kenig, Fanghua Lin and Zhongwei Shen
Communications on Pure and Applied Mathematics 67 (8) 1219 (2014)
https://doi.org/10.1002/cpa.21482

Effective slip law for general viscous flows over an oscillating surface

Andro Mikelić, Šárka Nečasová and Maria Neuss‐Radu
Mathematical Methods in the Applied Sciences 36 (15) 2086 (2013)
https://doi.org/10.1002/mma.2923

Second order corrector in the homogenization of a conductive-radiative heat transfer problem

Grégoire Allaire and Zakaria Habibi
Discrete & Continuous Dynamical Systems - B 18 (1) 1 (2013)
https://doi.org/10.3934/dcdsb.2013.18.1

Modeling of thermophysical properties in heterogeneous periodic media according to a multi-scale approach: Effective conductivity tensor and edge effects

A. Matine, N. Boyard, P. Cartraud, G. Legrain and Y. Jarny
International Journal of Heat and Mass Transfer 62 586 (2013)
https://doi.org/10.1016/j.ijheatmasstransfer.2013.03.036

Applications of Fourier analysis in homogenization of Dirichlet problem I. Pointwise estimates

Hayk Aleksanyan, Henrik Shahgholian and Per Sjölin
Journal of Differential Equations 254 (6) 2626 (2013)
https://doi.org/10.1016/j.jde.2012.12.017

Multiscale Asymptotic Analysis and Computation of Optimal Control for Elliptic Systems with Constraints

Jianjun Liu, Liqun Cao and Ningning Yan
SIAM Journal on Numerical Analysis 51 (4) 1978 (2013)
https://doi.org/10.1137/120869614

Effective boundary condition for Stokes flow over a very rough surface

Youcef Amirat, Olivier Bodart, Umberto De Maio and Antonio Gaudiello
Journal of Differential Equations 254 (8) 3395 (2013)
https://doi.org/10.1016/j.jde.2013.01.024

Asymptotic Analysis of Boundary Layer Correctors in Periodic Homogenization

Christophe Prange
SIAM Journal on Mathematical Analysis 45 (1) 345 (2013)
https://doi.org/10.1137/120876502

Asymptotic analysis and error estimates for an optimal control problem with oscillating boundaries

A. K. Nandakumaran, Ravi Prakash and J.-P. Raymond
ANNALI DELL'UNIVERSITA' DI FERRARA 58 (1) 143 (2012)
https://doi.org/10.1007/s11565-011-0135-3

Boundary effects on effective conductivity of random heterogeneous media with spherical inclusions

A. Rabinovich, G. Dagan and T. Miloh
Physical Review E 86 (4) (2012)
https://doi.org/10.1103/PhysRevE.86.046601

Thermal properties of composite materials :effective conductivity tensor and edge effects

A Matine, N Boyard, P Cartraud, G Legrain and Y Jarny
Journal of Physics: Conference Series 395 012014 (2012)
https://doi.org/10.1088/1742-6596/395/1/012014

On multiscale homogenization problems in boundary layer theory

Youcef Amirat, Gregory A. Chechkin and Maxim Romanov
Zeitschrift für angewandte Mathematik und Physik 63 (3) 475 (2012)
https://doi.org/10.1007/s00033-011-0167-7

Two-scale analysis for very rough thin layers. An explicit characterization of the polarization tensor

Ionel Sorin Ciuperca, Ronan Perrussel and Clair Poignard
Journal de Mathématiques Pures et Appliquées 95 (3) 277 (2011)
https://doi.org/10.1016/j.matpur.2010.12.001

Periodic homogenization with an interface: The multi-dimensional case

Martin Hairer and Charles Manson
The Annals of Probability 39 (2) (2011)
https://doi.org/10.1214/10-AOP564

Scattering, Homogenization, and Interface Effects for Oscillatory Potentials with Strong Singularities

Vincent Duchêne and Michael I. Weinstein
Multiscale Modeling & Simulation 9 (3) 1017 (2011)
https://doi.org/10.1137/100811672

Approximate transmission conditions through a rough thin layer: The case of periodic roughness

I. S. CIUPERCA, M. JAI and C. POIGNARD
European Journal of Applied Mathematics 21 (1) 51 (2010)
https://doi.org/10.1017/S095679250999012X

Homogenization of a Conductive and Radiative Heat Transfer Problem

Grégoire Allaire and Karima El Ganaoui
Multiscale Modeling & Simulation 7 (3) 1148 (2009)
https://doi.org/10.1137/080714737

Diffractive behavior of the wave equation in periodic media: weak convergence analysis

Grégoire Allaire, Mariapia Palombaro and Jeffrey Rauch
Annali di Matematica Pura ed Applicata 188 (4) (2009)
https://doi.org/10.1007/s10231-008-0089-y

Asymptotic Homogenization of Composite Materials and Structures

Alexander L. Kalamkarov, Igor V. Andrianov and Vladyslav V. Danishevs’kyy
Applied Mechanics Reviews 62 (3) (2009)
https://doi.org/10.1115/1.3090830

Convergence Analysis for The Numerical Boundary Corrector for Elliptic Equations with Rapidly Oscillating Coefficients

Marcus Sarkis and Henrique Versieux
SIAM Journal on Numerical Analysis 46 (2) 545 (2008)
https://doi.org/10.1137/060654773

Effective laws for the Poisson equation on domains with curved oscillating boundaries

N. Neuss, M. Neuss-Radu and A. Mikelić
Applicable Analysis 85 (5) 479 (2006)
https://doi.org/10.1080/00036810500340476

Homogenization of a Nonlinear Elliptic Boundary Value Problem Modeling Galvanic Currents

Y. S. Bhat and S. Moskow
Multiscale Modeling & Simulation 5 (1) 149 (2006)
https://doi.org/10.1137/050637042

Localization for the Schrödinger Equation in a Locally Periodic Medium

Grégoire Allaire and Mariapia Palombaro
SIAM Journal on Mathematical Analysis 38 (1) 127 (2006)
https://doi.org/10.1137/050635572

Asymptotics of simple eigenvalues and eigenfunctions for the Laplace operator in a domain with an oscillating boundary

Y. Amirat, G. A. Chechkin and R. R. Gadyl’shin
Computational Mathematics and Mathematical Physics 46 (1) 97 (2006)
https://doi.org/10.1134/S0965542506010118

Asymptotic Expansions of Eigenelements of the Laplace Operator in a Domain with Many “Light” Concentrated Masses Closely Located on the Boundary. Multi-Dimensional Case

G. A. Chechkin
Journal of Mathematical Sciences 128 (5) 3263 (2005)
https://doi.org/10.1007/s10958-005-0268-y

Numerical approximation of laminar flows over rough walls with sharp asperities

Youcef Amirat and Olivier Bodart
Journal of Computational and Applied Mathematics 164-165 25 (2004)
https://doi.org/10.1016/S0377-0427(03)00639-3

Asymptotic Approximation of the Solution of the Laplace Equation in a Domain with Highly Oscillating Boundary

Y. Amirat, O. Bodart, U. De Maio and A. Gaudiello
SIAM Journal on Mathematical Analysis 35 (6) 1598 (2004)
https://doi.org/10.1137/S0036141003414877