Legoll, Frédéric
Overview
Works:  12 works in 13 publications in 2 languages and 22 library holdings 

Roles:  Author, Opponent, Thesis advisor, Contributor, Other 
Publication Timeline
.
Most widely held works by
Frédéric Legoll
Méthodes moléculaires et multiéchelles pour la simulation numérique des matériaux by
Frédéric Legoll(
Book
)
2 editions published in 2004 in French and held by 6 WorldCat member libraries worldwide
2 editions published in 2004 in French and held by 6 WorldCat member libraries worldwide
Stress Gradient Elasticity Theory: Existence and Uniqueness of Solution by
Karam Sab(
)
1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2015 in English and held by 2 WorldCat member libraries worldwide
Longtime averaging for integrable Hamiltonian dynamics by
Eric Cancès(
)
1 edition published in 2005 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 2 WorldCat member libraries worldwide
NonErgodicity of the NoséHoover Thermostatted Harmonic Oscillator by
Frédéric Legoll(
)
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 2 WorldCat member libraries worldwide
MsFEM à la CrouzeixRaviart for Highly Oscillatory Elliptic Problems by
Claude Le Bris(
)
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
Quelques problèmes liés à l'erreur statistique en homogénéisation stochastique by
William Minvielle(
)
1 edition published in 2015 in French and held by 2 WorldCat member libraries worldwide
Le travail de cette thèse a porté sur le développement de techniques numériques pour l'homogénéisation d'équations dont les coefficients présentent des hétérogénéités aléatoires à petite échelle. Les difficultés liées à la résolution de telles équations aux dérivées partielles peuvent être résolues grâce à la théorie de l'homogénéisation stochastique. On substitue alors la résolution d'une équation dont les coefficients sont aléatoires et oscillants à l'échelle la plus fine du problème par la résolution d'une équation à coefficients constants. Cependant, une difficulté subsiste : le calcul de ces coefficients dits homogénéisés sont définis par une moyenne ergodique, que l'on ne peut atteindre en pratique. Seuls des approximations aléatoires de ces quantités déterministes sont calculables, et l'erreur commise lors de l'approximation est importante. Ces questions sont développées en détail dans le Chapitre 1 qui tient lieu d'introduction. L'objet du Chapitre 2 de cette thèse est de réduire l'erreur de cette approximation dans un cas nonlinéaire, en réduisant la variance de l'estimateur par la méthode des variables antithétiques. Dans le Chapitre 3, on montre comment obtenir une meilleure réduction de variance par la méthode des vari ables de contrôle. Cette approche repose sur un modèle approché, disponible dans le cas étudié. Elle est plus invasive et moins générique, on l'étudie dans un cas linéaire. Dans le Chapitre 4, à nouveau dans un cas linéaire, on introduit une méthode de sélection pour réduire l'erreur commise. Enfin, le Chapitre 5 porte sur l'analyse d'un problème in verse, où l'on recherche des paramètres à l'échelle la plus fine, ne connaissant que quelques quantités macroscopiques, par exemple les coefficients homogénéisés du modèle
1 edition published in 2015 in French and held by 2 WorldCat member libraries worldwide
Le travail de cette thèse a porté sur le développement de techniques numériques pour l'homogénéisation d'équations dont les coefficients présentent des hétérogénéités aléatoires à petite échelle. Les difficultés liées à la résolution de telles équations aux dérivées partielles peuvent être résolues grâce à la théorie de l'homogénéisation stochastique. On substitue alors la résolution d'une équation dont les coefficients sont aléatoires et oscillants à l'échelle la plus fine du problème par la résolution d'une équation à coefficients constants. Cependant, une difficulté subsiste : le calcul de ces coefficients dits homogénéisés sont définis par une moyenne ergodique, que l'on ne peut atteindre en pratique. Seuls des approximations aléatoires de ces quantités déterministes sont calculables, et l'erreur commise lors de l'approximation est importante. Ces questions sont développées en détail dans le Chapitre 1 qui tient lieu d'introduction. L'objet du Chapitre 2 de cette thèse est de réduire l'erreur de cette approximation dans un cas nonlinéaire, en réduisant la variance de l'estimateur par la méthode des variables antithétiques. Dans le Chapitre 3, on montre comment obtenir une meilleure réduction de variance par la méthode des vari ables de contrôle. Cette approche repose sur un modèle approché, disponible dans le cas étudié. Elle est plus invasive et moins générique, on l'étudie dans un cas linéaire. Dans le Chapitre 4, à nouveau dans un cas linéaire, on introduit une méthode de sélection pour réduire l'erreur commise. Enfin, le Chapitre 5 porte sur l'analyse d'un problème in verse, où l'on recherche des paramètres à l'échelle la plus fine, ne connaissant que quelques quantités macroscopiques, par exemple les coefficients homogénéisés du modèle
Effective Dynamics for a Kinetic MonteCarlo Model with Slow and Fast Time Scales by
Salma Lahbabi(
)
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2013 in English and held by 2 WorldCat member libraries worldwide
Simulation des matériaux magnétiques à base Cobalt par Dynamique Moléculaire Magnétique by
David Beaujouan(
)
1 edition published in 2012 in French and held by 1 WorldCat member library worldwide
The magnetic properties of materials are strongly connected to their crystallographic structure. An atomistic model of the magnetization dynamics is developed which takes into account magnetoelasticity. Although this study is valid for all magnetic materials under temperatures, this study focuses only on Cobalt. In our effective model, atoms are described by three classical vectors as position, momentum and spin, which interact via an ad hoc magnetomechanical potential.The atomistic spin dynamics is first considered. This method allows us to write the evolution equations of an atomic system of spins in which positions and impulsions are first frozen. However, a spin temperature is introduced to develop a natural connection with a thermal bath. Showing the limits of the stochastic approach, a genuine deterministic approach is followed to control the canonical temperature in this spin system.In a second step, several geometrical integrators are developed and analyzed to couple together both the molecular dynamics and atomic spin dynamics schemes. The connection between the spins and the lattice is provided by the atomic positions dependence of the magnetic potential. The novelty of this potential lies in the parameterization of the magnetic anisotropy which originates in the spinorbit coupling. Using a dedicated pair model of anisotropy, the magnetostrictive constants of hcpCo are restored. In a canonical system where pressure and temperature are controlled simultaneously, the transition of rotational magnetization of Co is found.Finally the magnetization reversals of superparamagnetic Co nanodots is studied to quantify the impact of spinlattice coupling respectively to recent measurements
1 edition published in 2012 in French and held by 1 WorldCat member library worldwide
The magnetic properties of materials are strongly connected to their crystallographic structure. An atomistic model of the magnetization dynamics is developed which takes into account magnetoelasticity. Although this study is valid for all magnetic materials under temperatures, this study focuses only on Cobalt. In our effective model, atoms are described by three classical vectors as position, momentum and spin, which interact via an ad hoc magnetomechanical potential.The atomistic spin dynamics is first considered. This method allows us to write the evolution equations of an atomic system of spins in which positions and impulsions are first frozen. However, a spin temperature is introduced to develop a natural connection with a thermal bath. Showing the limits of the stochastic approach, a genuine deterministic approach is followed to control the canonical temperature in this spin system.In a second step, several geometrical integrators are developed and analyzed to couple together both the molecular dynamics and atomic spin dynamics schemes. The connection between the spins and the lattice is provided by the atomic positions dependence of the magnetic potential. The novelty of this potential lies in the parameterization of the magnetic anisotropy which originates in the spinorbit coupling. Using a dedicated pair model of anisotropy, the magnetostrictive constants of hcpCo are restored. In a canonical system where pressure and temperature are controlled simultaneously, the transition of rotational magnetization of Co is found.Finally the magnetization reversals of superparamagnetic Co nanodots is studied to quantify the impact of spinlattice coupling respectively to recent measurements
Multiscale Problems in Materials Science: A Mathematical Approach to the Role of Uncertainty(
Book
)
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
The bottom line of this work is to develop affordable numerical methods in the context of stochastic homogenization. Many partial differential equations of materials science indeed involve highly oscillatory coefficients and small lengthscales. Homogenization theory is concerned with the derivation of averaged equations from the original oscillatory equations, and their treatment by adequate numerical approaches. Stationary ergodic random problems (and the associated stochastic homogenization theory) are one instance for modelling uncertainty in continuous media. The theoretical aspects of these problems are now wellunderstood, at least for a large variety of situations. On the other hand, the numerical aspects have received less attention from the mathematics community. Standard methods available in the literature often lead to very, and sometimes prohibitively, costly computations. In this report, we first review an approach popular in particular in the computational mechanics community, which is to try and obtain bounds on the homogenized matrix, rather than computing it. Only computations of moderate difficulty are then required. However, we will show that, not unexpectedly, this method has strong limitations. We will next introduce a class of materials of significant practical relevance, that of random materials where the amount of randomness is small. They can be considered as stochastic perturbations of deterministic materials, in a sense made precise below. We will adapt to such a case the wellknown Multiscale Finite Element Method (MsFEM), and design a method which is much more affordable than, and as accurate as, the original method
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
The bottom line of this work is to develop affordable numerical methods in the context of stochastic homogenization. Many partial differential equations of materials science indeed involve highly oscillatory coefficients and small lengthscales. Homogenization theory is concerned with the derivation of averaged equations from the original oscillatory equations, and their treatment by adequate numerical approaches. Stationary ergodic random problems (and the associated stochastic homogenization theory) are one instance for modelling uncertainty in continuous media. The theoretical aspects of these problems are now wellunderstood, at least for a large variety of situations. On the other hand, the numerical aspects have received less attention from the mathematics community. Standard methods available in the literature often lead to very, and sometimes prohibitively, costly computations. In this report, we first review an approach popular in particular in the computational mechanics community, which is to try and obtain bounds on the homogenized matrix, rather than computing it. Only computations of moderate difficulty are then required. However, we will show that, not unexpectedly, this method has strong limitations. We will next introduce a class of materials of significant practical relevance, that of random materials where the amount of randomness is small. They can be considered as stochastic perturbations of deterministic materials, in a sense made precise below. We will adapt to such a case the wellknown Multiscale Finite Element Method (MsFEM), and design a method which is much more affordable than, and as accurate as, the original method
Méthodes éléments finis de type MsFEM pour des problèmes d'advectiondiffusion by
François Madiot(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
This work essentially deals with the development and the study of multiscale finite element methods for multiscale advectiondiffusion problems in the advectiondominated regime. Two types of approaches are investigated: Take into account the advection in the construction of the approximation space, or apply a stabilization method. We begin with advectiondominated advectiondiffusion problems in heterogeneous media. We carry on with advectiondominated advectiondiffusion problems posed in perforated domains.Here, we focus on the CrouzeixRaviart type boundary condition for the construction of the multiscale finite elements. We consider two different situations depending on the condition prescribed on the boundary of the perforations: the homogeneous Dirichlet condition or the homogeneous Neumann condition. This study relies on a coercivity assumption.Lastly, we consider a general framework where the advectiondiffusion operator is not coercive, possibly in the advectiondominated regime. We propose a Finite Element approach based on the use of an invariant measure associated to the adjoint operator. This approach is unconditionally wellposed in the mesh size. We compare it numerically to a standard stabilization method
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
This work essentially deals with the development and the study of multiscale finite element methods for multiscale advectiondiffusion problems in the advectiondominated regime. Two types of approaches are investigated: Take into account the advection in the construction of the approximation space, or apply a stabilization method. We begin with advectiondominated advectiondiffusion problems in heterogeneous media. We carry on with advectiondominated advectiondiffusion problems posed in perforated domains.Here, we focus on the CrouzeixRaviart type boundary condition for the construction of the multiscale finite elements. We consider two different situations depending on the condition prescribed on the boundary of the perforations: the homogeneous Dirichlet condition or the homogeneous Neumann condition. This study relies on a coercivity assumption.Lastly, we consider a general framework where the advectiondiffusion operator is not coercive, possibly in the advectiondominated regime. We propose a Finite Element approach based on the use of an invariant measure associated to the adjoint operator. This approach is unconditionally wellposed in the mesh size. We compare it numerically to a standard stabilization method
Méthodes numériques pour l'estimation des fluctuations dans les matériaux multiéchelles et problèmes reliés by
PierreLoïk Rothé(
)
1 edition published in 2019 in French and held by 1 WorldCat member library worldwide
This thesis is about the numerical approximation of multiscale materials. We consider heterogeneous materials whose physical or mechanical (thermal conductivity, elasticity tensor, ...) vary on a small scale compared to the material length. This thesis is composed of two parts describing two different aspects of multiscale problems.In the first part, we consider the stochastic homogenization framework. The aim here is to go beyond the identification of an effective behavior, and to characterize the fluctuations of the response. Generally speaking we strive to understand: (i) what parameters of the distribution of the material coefficient affect the distribution of the response and (ii) if it is possible to approximate this distribution without resorting to a costly MonteCarlo method. On the theoretical standpoint, we consider a weakly random material (the microstructure is periodic and presents some small random defects).We show that we are able to compute a tensor Q that governs completely the fluctuations of the response, thanks to the use of standard corrector functions from the stochastic homogenization theory. This tensor is defined by an explicit formula and allows us to estimate the fluctuation of the response without solving the fine problem for many realizations. A numerical approximation of this tensor has been proposed and numerical experiments have been performed in broader random frameworks to assess the effectiveness of the approach.In the second part, we consider a heterogeneous deterministic material where classical homogenization (periodicity, ...) assumptions are not satisfied. Standard methods such as Finite Elements give bad approximations. In order to solve this issue the Multiscale Finite Element Method (MsFEM) can be used.This approach proceeds in two steps: (i) design a coarse approximation space spanned by solutions to wellchosen local problems; (ii) approximate the solution by an inexpensive Galerkin approach on the space designed in (i). On this topic, we first implemented the main variants of the MsFEM methods in the Finite Element software FreeFem++ on template form.Second, many MsFEM approaches suffer from resonance error: when the size of the heterogeneities is close to the coarse mesh size the accuracy decreases. In order to circumvent this issue, we designed an enriched MsFEM method: to the classical MsFEM basis, we add solutions to local problems with high degree polynomial boundary conditions. The use of polynomials allows us to obtain a converging approach for a limited computational cost
1 edition published in 2019 in French and held by 1 WorldCat member library worldwide
This thesis is about the numerical approximation of multiscale materials. We consider heterogeneous materials whose physical or mechanical (thermal conductivity, elasticity tensor, ...) vary on a small scale compared to the material length. This thesis is composed of two parts describing two different aspects of multiscale problems.In the first part, we consider the stochastic homogenization framework. The aim here is to go beyond the identification of an effective behavior, and to characterize the fluctuations of the response. Generally speaking we strive to understand: (i) what parameters of the distribution of the material coefficient affect the distribution of the response and (ii) if it is possible to approximate this distribution without resorting to a costly MonteCarlo method. On the theoretical standpoint, we consider a weakly random material (the microstructure is periodic and presents some small random defects).We show that we are able to compute a tensor Q that governs completely the fluctuations of the response, thanks to the use of standard corrector functions from the stochastic homogenization theory. This tensor is defined by an explicit formula and allows us to estimate the fluctuation of the response without solving the fine problem for many realizations. A numerical approximation of this tensor has been proposed and numerical experiments have been performed in broader random frameworks to assess the effectiveness of the approach.In the second part, we consider a heterogeneous deterministic material where classical homogenization (periodicity, ...) assumptions are not satisfied. Standard methods such as Finite Elements give bad approximations. In order to solve this issue the Multiscale Finite Element Method (MsFEM) can be used.This approach proceeds in two steps: (i) design a coarse approximation space spanned by solutions to wellchosen local problems; (ii) approximate the solution by an inexpensive Galerkin approach on the space designed in (i). On this topic, we first implemented the main variants of the MsFEM methods in the Finite Element software FreeFem++ on template form.Second, many MsFEM approaches suffer from resonance error: when the size of the heterogeneities is close to the coarse mesh size the accuracy decreases. In order to circumvent this issue, we designed an enriched MsFEM method: to the classical MsFEM basis, we add solutions to local problems with high degree polynomial boundary conditions. The use of polynomials allows us to obtain a converging approach for a limited computational cost
Stochastic analysis, simulation and identification of hyperelastic constitutive equations by
Brian Staber(
)
1 edition published in 2018 in English and held by 0 WorldCat member libraries worldwide
Le projet de thèse concerne la construction, la génération et l'identification de modèles continus stochastiques, pour des milieux hétérogènes exhibant des comportements non linéaires. Le domaine d'application principal visé est la biomécanique, notamment au travers du développement d'outils de modélisation multiéchelles et stochastiques, afin de quantifier les grandes incertitudes exhibées par les tissus mous. Deux aspects sont particulièrement mis en exergue. Le premier point a trait à la prise en compte des incertitudes en mécanique non linéaire, et leurs incidences sur les prédictions des quantités d'intérêt. Le second aspect concerne la construction, la génération (en grandes dimensions) et l'identification multiéchelle de représentations continues à partir de résultats expérimentaux limités
1 edition published in 2018 in English and held by 0 WorldCat member libraries worldwide
Le projet de thèse concerne la construction, la génération et l'identification de modèles continus stochastiques, pour des milieux hétérogènes exhibant des comportements non linéaires. Le domaine d'application principal visé est la biomécanique, notamment au travers du développement d'outils de modélisation multiéchelles et stochastiques, afin de quantifier les grandes incertitudes exhibées par les tissus mous. Deux aspects sont particulièrement mis en exergue. Le premier point a trait à la prise en compte des incertitudes en mécanique non linéaire, et leurs incidences sur les prédictions des quantités d'intérêt. Le second aspect concerne la construction, la génération (en grandes dimensions) et l'identification multiéchelle de représentations continues à partir de résultats expérimentaux limités
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Related Identities
 Le Bris, Claude Opponent Thesis advisor Author
 SpringerLink (Online service) Other
 Maday, Yvon (1957....). Thesis advisor
 Université Pierre et Marie Curie (Paris / 19712017) Degree grantor
 Université ParisEst (2015....). Degree grantor
 Centre d'enseignement et de recherche en mathématiques et calcul scientifique (ChampssurMarne, SeineetMarne) Other
 École doctorale Mathématiques, Sciences et Technologies de l'Information et de la Communication (ChampssurMarne, SeineetMarne / 2015....). Other
 Forest, Samuel Contributor
 Lozinski, Alexei
 Minvielle, William (1990....). Author