33 citations · 95 across the 8 of their papers we have counts for
10 papers
The homogenization method for topology optimization of structures: old and new
Grégoire Allaire, Lorenzo Cavallina, Nobuhito Miyake +2
These are the lecture notes of a short course on the homogenization method for topology optimization of structures, given by Grégoire Allaire, during the "GSIS International Summer…
Crime Pays; Homogenized Wave Equations for Long Times
Grégoire Allaire, Agnes Lamacz, Jeffrey Rauch
This article examines the accuracy for large times of asymptotic expansions from periodic homogenization of wave equations. As usual, denotes the small period of the coefficien…
Homogenization of Stokes System using Bloch Waves
Grégoire Allaire, Tuhin Ghosh, Muthusamy Vanninathan
In this work, we study the Bloch wave homogenization for the Stokes system with periodic viscosity coefficient. In particular, we obtain the spectral interpretation of the homogeni…
Localization for the Schrödinger equation in a locally periodic medium
Grégoire Allaire, Mariapia Palombaro
We study the homogenization of a Schrödinger equation in a locally periodic medium. For the time and space scaling of semi-classical analysis we consider well-prepared initial data…
Upscaling nonlinear adsorption in periodic porous media - Homogenization approach
Grégoire Allaire, Harsha Hutridurga
We consider the homogenization of a model of reactive flows through periodic porous media involving a single solute which can be absorbed and desorbed on the pore boundaries. This…
On the homogenization of multicomponent transport
Gregoire Allaire, Harsha Hutridurga
This paper is devoted to the homogenization of weakly coupled cooperative parabolic systems in strong convection regime with purely periodic coefficients. Our approach is to factor…
Role of non-ideality for the ion transport in porous media: derivation of the macroscopic equations using upscaling
Gregoire Allaire, Robert Brizzi, Jean-Francois Dufreche +2
This paper is devoted to the homogenization (or upscaling) of a system of partial differential equations describing the non-ideal transport of a N-component electrolyte in a dilute…
Asymptotic analysis of the Poisson-Boltzmann equation describing electrokinetics in porous media
Gregoire Allaire, Jean-Francois Dufreche, Andro Mikelic +1
We consider the Poisson-Boltzmann equation in a periodic cell, representative of a porous medium. It is a model for the electrostatic distribution of chemical species diluted i…
A bound on group velocity for Bloch wave packets
Grégoire Allaire, Mariapia Palombaro, Jeffrey Rauch
This short note is a sequel to our previous papers on the asymptotic behavior of Bloch wave packet solutions of the wave equation in periodic media. The purpose is to prove that th…
Diffraction of Bloch Wave Packets for Maxwell's Equations
Grégoire Allaire, Mariapia Palombaro, Jeffrey Rauch
We study, for times of order 1/h, solutions of Maxwell's equations in an O(h^2) modulation of an h-periodic medium. The solutions are of slowly varying amplitude type built on Bloc…