119 citations · 535 across the 49 of their papers we have counts for
60 papers
Numerical homogenization of a linear multiscale conservation law
Claude Le Bris, Frédéric Legoll, Giulia Merlini
We address the numerical approximation of a scalar conservation law with a highly oscillatory flux, in the linear setting. Taking advantage of the intrinsic numerical viscosity of…
A Multiscale Finite Element Method for reaction-diffusion eigenproblems arising from neutronics
Claude Le Bris, Albéric Lefort, Frédéric Legoll
We consider reaction-diffusion eigenproblems with oscillatory diffusion and reaction coefficients. The reaction coefficient magnitude is large: the corrector equation identified by…
Certification of PGD reduced-order models with separated spatial variables
Jean Ruel, Ludovic Chamoin, Frédéric Legoll +1
Model order reduction techniques have become an attractive approach for obtaining fast approximations of multidimensional problems. Besides computational efficiency, ensuring the r…
Three short tales on the parity operator
Robert Fulsche
In this paper, we discuss three short topics related to the parity operator and his role in quantum harmonic analysis. We derive results for the Fredholm index of even and odd oper…
Effective approximations of solutions to highly oscillatory diffusion equations from coarse measurements
Claude Le Bris, Frédéric Legoll, Simon Ruget
We approximate a diffusion equation with highly oscillatory coefficients with a diffusion equation with constant coefficients. The approach is put in action in contexts where only…
Convergence of two-scale expansions for elastic heterogeneous plates
Virginie Ehrlacher, Arthur Lebée, Frédéric Legoll +1
The aim of this article is to prove strong convergence results on the difference between the solution to highly oscillatory problems posed in thin domains and its two-scale expansi…
MsFEM for advection-dominated problems in heterogeneous media: Stabilization via nonconforming variants
Rutger A. Biezemans, Claude Le Bris, Frédéric Legoll +1
We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite E…
Survival probability of structures under fatigue: a data-based approach
Francois-Baptiste Cartiaux, Frederic Legoll, Alex Libal +1
This article addresses the probabilistic nature of fatigue life in structures subjected to cyclic loading with variable amplitude. Drawing on the formalisation of Miner's cumulativ…
Embedded corrector problems for homogenization in linear elasticity
Virginie Ehrlacher, Frederic Legoll, Benjamin Stamm +1
In this article, we extend the study of embedded corrector problems, that we have previously introduced in the context of the homogenization of scalar diffusive equations, to the c…
A variance reduction strategy for numerical random homogenization based on the equivalent inclusion method
Sebastien Brisard, Michael Bertin, Frederic Legoll
Using the equivalent inclusion method (a method strongly related to the Hashin-Shtrikman variational principle) as a surrogate model, we propose a variance reduction strategy for t…
Probabilistic formulation of Miner's rule and application to structural fatigue
Francois-Baptiste Cartiaux, Alain Ehrlacher, Frederic Legoll +2
The standard stress-based approach to fatigue is based on the use of S-N curves. They are obtained by applying cyclic loading of constant amplitude to identical and standardise…
Combining machine-learned and empirical force fields with the parareal algorithm: application to the diffusion of atomistic defects
Olga Gorynina, Frederic Legoll, Tony Lelievre +1
We numerically investigate an adaptive version of the parareal algorithm in the context of molecular dynamics. This adaptive variant has been originally introduced in [F. Legoll, T…
Non-intrusive implementation of a wide variety of Multiscale Finite Element Methods
Rutger A. Biezemans, Claude Le Bris, Frédéric Legoll +1
Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-…
Non-intrusive implementation of Multiscale Finite Element Methods: an illustrative example
Rutger A. Biezemans, Claude Le Bris, Frederic Legoll +1
Multiscale Finite Element Methods (MsFEM) are finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functi…
A pedagogical review on a posteriori error estimation in Finite Element computations
Ludovic Chamoin, Frederic Legoll
This article is a review on basic concepts and tools devoted to a posteriori error estimation for problems solved with the Finite Element Method. For the sake of simplicity and cla…
An MsFEM approach enriched using Legendre polynomials
Frederic Legoll, Pierre-Loik Rothe, Claude Le Bris +1
We consider a variant of the conventional MsFEM approach with enrichments based on Legendre polynomials, both in the bulk of mesh elements and on their interfaces. A convergence an…
Mathematical analysis of a coupling method for the practical computation of homogenized coefficients
Olga Gorynina, Claude Le Bris, Frederic Legoll
We present the mathematical study of a computational approach originally introduced by R. Cottereau in [R. Cottereau, IJNME 2013]. The approach aims at evaluating the effective (a.…
Some remarks on a coupling method for the practical computation of homogenized coefficients
Olga Gorynina, Claude Le Bris, Frédéric Legoll
We numerically investigate, and improve upon, a computational approach originally introduced in [Cottereau, IJNME 2013] which aims at evaluating the effective coefficient of a medi…
Parareal computation of stochastic differential equations with time-scale separation: a numerical study
Tony Lelièvre, Frédéric Legoll, Keith Myerscough +1
The parareal algorithm is known to allow for a significant reduction in wall clock time for accurate numerical solutions by parallelising across the time dimension. We present and…
Goal-oriented error estimation and adaptivity in MsFEM computations
Ludovic Chamoin, Frederic Legoll
We introduce a goal-oriented strategy for multiscale computations performed using the Multiscale Finite Element Method (MsFEM). In a previous work, we have shown how to use, in the…
An embedded corrector problem for homogenization. Part II: Algorithms and discretization
Eric Cancès, Virginie Ehrlacher, Frederic Legoll +2
This contribution is the numerically oriented companion article of the work [E. Cancès, V. Ehrlacher, F. Legoll, B. Stamm and S. Xiang, arxiv preprint 1807.05131]. We focus here on…
Effective dynamics for non-reversible stochastic differential equations: a quantitative study
Frédéric Legoll, Tony Lelièvre, Upanshu Sharma
Coarse-graining is central to reducing dimensionality in molecular dynamics, and is typically characterized by a mapping which projects the full state of the system to a smaller cl…
An embedded corrector problem for homogenization. Part I: Theory
Eric Cancès, Virginie Ehrlacher, Frederic Legoll +2
This article is the first part of a two-fold study, the objective of which is the theoretical analysis and numerical investigation of new approximate corrector problems in the cont…
Stochastic homogenization of a scalar viscoelastic model exhibiting stress-strain hysteresis
Thomas Hudson, Frédéric Legoll, Tony Lelièvre
Motivated by rate-independent stress-strain hysteresis observed in filled rubber, this article considers a scalar viscoelastic model in which the constitutive law is random and var…