Frédéric LEGOLL
 Organization: ENPC
 Research Unit: Laboratoire
Navier, Multiscale team
 Phone: 33 1 64 15 37 81
 Fax: 33 1 64 15 37 41
 Email: legoll at lami.enpc.fr
 Office: V 014
 Mail:
LAMI  ENPC
6 et 8 avenue Blaise Pascal
Cité
Descartes  Champs sur Marne
77455 Marne la Vallée Cedex 2 (FRANCE)
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I am currently a researcher at Laboratoire Navier and
Professor at Ecole Nationale des Ponts et Chaussées.
I am a member of the MATHERIALS
projectteam, at INRIA (I was a
member of the MICMAC projectteam).
I defended my habilitation thesis on October 17th, 2011
(abstract, manuscript; see also
here).
Title: Mathematical and numerical study of some models in multiscale
simulation of materials.
During the year 20042005, I was a postdoctoral fellow at the Institute for
Mathematics and its Applications (IMA, part of the University of
Minnesota, Minneapolis). I participated in the thematic year on Mathematics of Materials and
Macromolecules: Multiple Scales, Disorder, and Singularities.
I defended my PhD thesis on August 31st, 2004
(abstract, ps.gz (862 Ko) or pdf (2.5 Mo) file.
Title: Molecular and multiscale methods for the numerical
simulation of materials.
Supervisors: Claude Le
Bris (CERMICS) and Yvon
Maday (Laboratoire
JacquesLouis Lions, University Paris 6).
My resume (pdf file).
Open position:
We are looking for a Postdoctoral student to work on domain decomposition methods for the computation of the effective elastic tensor of random materials. See here for a complete description. This project, funded by the Labex MMCD, will be supervised by Eric Cances, Virginie Ehrlacher and Frederic Legoll. The work, in between PDEs, scientific computing and computational mechanics, can start as soon as possible. Please email me for more information.
Research themes:
 Numerical methods for stochastic homogenization (variance
reduction, weakly stochastic problems), numerical
homogenization (MsFEM approach).
 Methods and algorithms for molecular dynamics (effective
dynamics, reduction of dimension, multiscaleintime problems, parareal algorithms, highly
oscillatory Hamiltonians, sampling).
 Numerical analysis of micromacro models for solids, coupling
an atomistic model with a continuum mechanics model (variational
problems, coarsegraining, finite temperature).
Collaborations with the Molecular and
Multiscale Modelling team of the CERMICS.
See also the Action Concertée Incitative Simulation
moléculaire webpage.
Editorial activity:
Journal articles:
 F. Legoll, T. Lelievre and S. Olla,
Pathwise estimates for an effective dynamics,
arxiv preprint
1605.02644
and HAL preprint
01314221.
 C. Le Bris and F. Legoll,
Examples of computational approaches to accommodate randomness in elliptic PDEs,
arxiv preprint
1604.05061
and HAL preprint
01304040.
 C. Le Bris, F. Legoll and F. Madiot,
Stabilisation de problemes non coercifs via une methode numerique utilisant la mesure invariante (Stabilization of noncoercive problems using the invariant measure),
C. R. Acad. Sci. Paris, Serie I, accepted for publication.
 T. Jourdan, G. Stoltz, F. Legoll and L. Monasse,
An accurate scheme to solve cluster dynamics equations using a FokkerPlanck approach,
Computer Physics Communications,
accepted for publication,
HAL preprint
01302986.
 C. Le Bris, F. Legoll and F. Madiot,
A numerical comparison of some Multiscale Finite Element approaches for convectiondominated problems in heterogeneous media,
arxiv preprint
1511.08453
and HAL preprint
01235642.
 X. Blanc, C. Le Bris and F. Legoll,
Some variance reduction methods for numerical stochastic homogenization,
Philosophical Transactions of the Royal Society A,
vol. 374 (2066), 20150168 (2016).
 C. Le Bris, F. Legoll and W. Minvielle,
Special Quasirandom Structures: a selection approach for stochastic homogenization,
Monte Carlo Methods and Applications,
vol. 22 (1), 2554 (2016).
 I.G. Tejada, L. Brochard, T. Lelièvre, G. Stoltz, F. Legoll and E. Cancès,
Coupling a reactive potential with a harmonic approximation for atomistic simulations of material failure,
Computer Methods in Applied Mechanics and Engineering,
vol. 305, 422440 (2016).
 K. Sab, F. Legoll and S. Forest,
Stress Gradient elasticity theory: existence and uniqueness of solution,
J. of Elasticity,
vol. 123 (2), 179201 (2016).
 E. Cancès, V. Ehrlacher, F. Legoll and B. Stamm,
An embedded corrector problem to approximate the homogenized
coefficients of an elliptic equation,
C. R. Acad. Sci. Paris, Série I,
vol. 353 (9), 801806 (2015).
 S. Brisard and F. Legoll,
Periodic homogenization using the LippmannSchwinger formalism,
arxiv preprint
1411.0330
and HAL preprint
01080251.
 I.G. Tejada, L. Brochard, G. Stoltz, F. Legoll, T. Lelièvre and
E. Cancès, Combining a reactive potential with a harmonic
approximation for molecular dynamics simulation of
failure: construction of a reduced potential, Proceedings of the
2014 ICMSQUARE conference, Journal of Physics: Conference Series, vol. 574, 012041 (2015).
 F. Legoll and W. Minvielle,
A control variate approach based on a defecttype theory for variance reduction in stochastic homogenization,
SIAM Multiscale Modeling and Simulation,
vol. 13 (2), 519550 (2015).
 F. Legoll, W. Minvielle, A. Obliger and M. Simon,
A parameter identification problem in stochastic homogenization,
ESAIM Proceedings,
vol. 48, 190214 (2015).
 C. Le Bris, F. Legoll and A. Lozinski,
An MsFEM type approach for perforated domains,
SIAM Multiscale Modeling and Simulation,
vol. 12 (3), 10461077 (2014).
 C. Le Bris, F. Legoll and K. Li,
Approximation grossière d'un problème elliptique à coefficients
hautement oscillants (Coarse approximation of an elliptic problem with
highly oscillatory coefficients),
C. R. Acad. Sci. Paris, Série I,
vol. 351 (78), 265270 (2013).
 F. Legoll and W. Minvielle,
Variance reduction using antithetic variables for a nonlinear convex
stochastic homogenization problem,
Discrete and Continuous Dynamical Systems  S,
vol. 8 (1), 127 (2015).
 Y. Efendiev, C. Kronsbein and F. Legoll,
MultiLevel Monte Carlo approaches for numerical homogenization,
SIAM Multiscale Modeling and Simulation,
vol. 13 (4), 11071135 (2015).
 S. Lahbabi and F. Legoll,
Effective dynamics for a kinetic MonteCarlo model with slow and
fast time scales,
Journal of Statistical Physics, vol. 153 (6), 931966 (2013).
 F. Legoll and F. Thomines,
On a variant of random homogenization theory: convergence of the residual process and approximation of the homogenized coefficients,
Mathematical Modelling and Numerical Analysis,
vol. 48 (2), 347386 (2014).
 C. Le Bris, F. Legoll and A. Lozinski,
MsFEM à la CrouzeixRaviart for highly oscillatory elliptic
problems,
Chinese Annals of Mathematics, Series B,
vol. 34 (1), 113138 (2013).
This article has been also published as:
C. Le Bris, F. Legoll and A. Lozinski,
MsFEM à la CrouzeixRaviart for highly oscillatory elliptic
problems, in Partial Differential Equations: Theory, Control and
Approximation, P. G. Ciarlet, T. Li, Y. Maday eds., Springer, 265294
(2014).
 E. B. Tadmor, F. Legoll, W. K. Kim, L. M. Dupuy and R. E. Miller,
FiniteTemperature QuasiContinuum, Applied Mechanics Reviews, vol. 65 (1), 010803 (2013).
 F. Legoll, T. Lelièvre and G. Samaey,
A micromacro parareal algorithm: application to singularly
perturbed ordinary differential equations,
SIAM Journal on Scientific Computing,
vol. 35 (4), A1951A1986 (2013).
 M. Dobson, F. Legoll, T. Lelièvre and G. Stoltz,
Derivation of Langevin Dynamics in a nonzero Background Flow
Field,
Mathematical Modelling and Numerical Analysis,
vol. 47 (6), 15831626 (2013).
 C. Le Bris, F. Legoll and F. Thomines,
Multiscale Finite Element approach for "weakly" random problems
and related issues,
Mathematical Modelling and Numerical Analysis,
vol. 48 (3), 815858 (2014).
 C. Le Bris, F. Legoll and F. Thomines,
Rate of convergence of a twoscale expansion for some "weakly" stochastic homogenization problems,
Asymptotic Analysis, vol. 80 (34), 237267 (2012).
 X. Blanc, F. Legoll and A. Anantharaman,
Asymptotic behaviour of Green functions of divergence form operators
with periodic coefficients,
Applied Mathematics Research Express, vol. 2013 (1), 79101 (2013).
 X. Blanc and F. Legoll,
A numerical strategy for coarsegraining twodimensional atomistic
models at finite temperature: the membrane case,
Computational Materials Science, vol. 66, 8495 (2013).
 A. Iacobucci, F. Legoll, S. Olla and G. Stoltz,
Negative thermal conductivity of chains of rotors with mechanical
forcing, Phys. Rev. E, vol. 84 (6), 061108 (2011).
 X. Dai, C. Le Bris, F. Legoll and Y. Maday,
Symmetric parareal algorithms for Hamiltonian systems,
Mathematical Modelling and Numerical Analysis, vol. 47 (3), 717742 (2013).
 F. Legoll and T. Lelièvre, Some remarks on free energy and
coarsegraining,
in
Numerical Analysis of Multiscale Computations,
B. Engquist, O. Runborg, R. Tsai eds.,
Lect. Notes Comput. Sci. Eng., vol. 82, Springer, 279329 (2012).
 F. Legoll and T. Lelièvre, Effective dynamics using conditional
expectations,
Nonlinearity, vol. 23 (9), 21312163 (2010).
 M. Dobson, C. Le Bris and F. Legoll, Symplectic schemes
for highly oscillatory Hamiltonian systems: the homogenization approach
beyond the constant frequency case,
IMA Journal of Numerical Analysis, vol. 33 (1), 3056 (2013)
(earlier extended version: arxiv preprint 1008.1030 and HAL
00524814).
 A. Anantharaman, R. Costaouec, C. Le Bris, F. Legoll and F. Thomines,
Introduction to numerical stochastic homogenization and the related
computational challenges: some recent developments,
W. Bao and Q. Du eds.,
Lecture Notes
Series, Institute for Mathematical Sciences, National University of
Singapore,
volume
22, 197272 (2011).
 X. Blanc, R. Costaouec, C. Le Bris and F. Legoll,
Variance reduction in
stochastic homogenization using antithetic variables,
Markov Processes and Related Fields, vol. 18 (1), 3166 (2012)
(link).
 X. Blanc, R. Costaouec, C. Le Bris and F. Legoll,
Variance reduction in
stochastic homogenization: the technique of antithetic variables,
in
Numerical Analysis of Multiscale Computations,
B. Engquist, O. Runborg, R. Tsai eds.,
Lect. Notes Comput. Sci. Eng., vol. 82, Springer, 4770 (2012).
 M. Dobson, C. Le Bris and F. Legoll, Symplectic schemes for highly
oscillatory Hamiltonian systems with varying fast frequencies (Intégrateurs
symplectiques pour des systèmes Hamiltoniens hautement oscillants avec fréquences
rapides variables), C. R. Acad. Sci. Paris, Série I, vol. 348 (1718), 10331038 (2010).
 C. Le Bris and F. Legoll, Integrators for highly oscillatory Hamiltonian systems: an homogenization approach,
Discrete and Continuous Dynamical Systems  B, vol. 13 (2), 347373
(2010) (earlier extended version: HAL preprint
00165293).
 X. Blanc, C. Le Bris, F. Legoll and C. Patz, Finitetemperature
coarsegraining of onedimensional models: mathematical analysis and
computational approaches,
Journal of Nonlinear Science, vol. 20 (2), 241275 (2010).
 R. Costaouec, C. Le Bris and F. Legoll, Variance reduction
in stochastic homogenization: proof of concept, using antithetic
variables,
Boletin Soc. Esp. Mat. Apl., vol. 50, 927 (2010).
 A. Iacobucci, F. Legoll, S. Olla and G. Stoltz, Thermal
conductivity of the Toda lattice with conservative noise,
Journal of Statistical Physics, vol. 140 (2), 336348 (2010).
 X. Blanc, C. Le Bris, F. Legoll and T. Lelièvre, Beyond
multiscale and multiphysics: multimaths for model coupling, Networks
and Heterogeneous Media, vol. 5 (3), 423460 (2010).
 B. Dickson, F. Legoll, T. Lelièvre, G. Stoltz and
P. FleuratLessard, Free energy calculations: An efficient adaptive
biasing potential method,
Journal of Physical Chemistry B, vol. 114 (17), 58235830 (2010).
 R. Costaouec, C. Le Bris and F. Legoll, Approximation
numérique d'une classe de problèmes en
homogénéisation stochastique (Numerical approximation of a class of problems in stochastic
homogenization), C. R. Acad. Sci. Paris, Série I, vol. 348 (12), 99103 (2010).
 F. Legoll, Multiscale methods coupling atomistic and continuum mechanics:
some examples of mathematical analysis,
in Analytical and Numerical Aspects of Partial Differential Equations,
E. Emmrich and P. Wittbold eds.,
de
Gruyter Proceedings in Mathematics, 193245 (2009).
 F. Legoll, M. Luskin and R. Moeckel, Nonergodicity of
NoséHoover dynamics,
Nonlinearity, vol. 22 (7), 16731694 (2009).
 M. Hammoud, D. Duhamel, K. Sab and F. Legoll, Coupled Discrete
and Continuum Approach to the Behavior of Ballast, Ninth
International Conference on Computational Structures Technology
proceeding, Athens (september 2008).
 E. Cancès, F. Legoll, M.C. Marinica, K. Minoukadeh and F. Willaime,
Some improvements of the activationrelaxation technique method for finding
transition pathways on potential energy surfaces,
Journal of Chemical Physics, vol. 130 (11), 114711 (2009).
 B. Leimkuhler, F. Legoll and E. Noorizadeh, A temperature control
technique for nonequilibrium molecular simulation,
Journal of Chemical Physics, vol. 128 (7), 074105 (2008).
 F. Legoll, T. Lelièvre and G. Stoltz, Some remarks on sampling
methods in molecular dynamics, ESAIM Proceedings, vol. 22, 217233
(2008).
 C. Le Bris and F. Legoll, Dérivation de schémas numériques
symplectiques pour des systèmes hamiltoniens hautement oscillants
(derivation of symplectic numerical schemes for highly oscillatory
hamiltonian systems),
C. R. Acad. Sci. Paris, Série I, vol. 344 (4), 277282 (2007).
 F. Legoll, M. Luskin and R. Moeckel, Nonergodicity of the
NoséHoover Thermostatted Harmonic Oscillator, Archive for
Rational Mechanics and Analysis, vol. 184 (3), 449463 (2007).
 E. Cancès, F. Legoll and G. Stoltz, Theoretical and numerical
comparison of some sampling methods for molecular dynamics,
Mathematical Modelling and Numerical Analysis, vol. 41 (2), 351389
(2007).
 X. Blanc, C. Le Bris and F. Legoll,
Analysis of a prototypical multiscale method coupling atomistic and
continuum mechanics: the convex case, Acta Mathematicae Applicatae
Sinica, vol. 23 (2), 209216 (2007).
 X. Blanc, C. Le Bris and F. Legoll,
Analysis of a prototypical multiscale method coupling atomistic and
continuum mechanics, Mathematical Modelling and Numerical
Analysis, vol. 39 (4), 797826 (2005).
 Numerical homogenization of nonlinear viscoplastic
twodimensional polycrystals, Computational and Applied Mathematics,
vol. 23 (23), 309325 (2004).
 E. Cancès, F. Castella, Ph. Chartier, E. Faou, C. Le Bris, F. Legoll and G. Turinici,
Highorder averaging schemes with error bounds for thermodynamical
properties calculations by molecular dynamics simulations, Journal
of Chemical Physics, vol. 121 (21), 1034610355 (2004).
 E. Cancès, F. Castella, Ph. Chartier, E. Faou, C. Le Bris, F. Legoll and G. Turinici, Longtime averaging for integrable Hamiltonian
dynamics, Numerische Mathematik, vol. 100 (2), 211232 (2005).
 F. Legoll and R. Monneau, Designing reversible measure invariant algorithms
with applications to molecular dynamics, Journal of Chemical
Physics, vol. 117 (23), 1045210464 (2002).
Conferences and minisymposium organization:
 Member of the scientific committee SciCADE 2017.
 Member of the scientific committee SciCADE 2015.

Workshop Stochastic
and multiscale inverse problems (ENPC, 23 october 2014),
organized with Virginie Ehrlacher, Tony Lelièvre and Karam Sab.
 SciCADE 2013
conference, September 1620, 2013: with Yvon Maday (Paris 6),
we have coorganized a minisymposium on "Recent advances on parareal
algorithms".
 12th U.S. National Congress
on Computational Mechanics (12th USNCCM), July 2225, 2013:
with Régis Cottereau (Centrale Paris), Lori GrahamBrady (Johns Hopkins) and Martin OstojaStarzewski (U. of Illinois),
we coorganized a minisymposium on "Multiscale methods for heterogeneous materials".
 12th U.S. National Congress
on Computational Mechanics (12th USNCCM), July 2225, 2013:
with Brent Kraczek (US Army Research Laboratory), Reese Jones (Sandia
National Laboratories) and Kranthi Mandadapu (Sandia National
Laboratories), we coorganized a minisymposium on "The atomistic basis
of nonequilibrium thermal processes in materials".
 22nd International
Workshop on Computational Mechanics of Materials (IWCMM XXII),
September 2426, 2012:
with Brent Kraczek (US Army Research Laboratory), Reese Jones (Sandia National Laboratories) and Kranthi Mandadapu (Sandia National Laboratories),
we coorganized a minisymposium on "Atomistic basis of thermal
processes in driven systems".

with E. Faou,
T. Lelièvre and
G. Stoltz,
we coorganized a
CEAEDFINRIA school on
Simulation of hybrid dynamical systems and applications to molecular
dynamics, September 2730, 2010 (see also here
for the program).

Dynamics Days
Europe 2010, September 610, 2010: with
B. Leimkuhler,
we coorganized a minisymposium on
"Molecular Dynamics".

Multiscale
Molecular Modelling conference, June 30  July 3, 2010: with
T. Lelièvre,
we coorganized a minisymposium on
"Coarsegraining and effective dynamics in molecular simulation".

4th European Conference on
Computational Mechanics, May 1621, 2010: with
H. Ben Dhia (Centrale Paris),
F. Feyel (Onera and ENSMP)
and
V. Kouznetsova (TU Eindhoven),
we coorganized a minisymposium on
"Arlequin, FE2 and other embedded domains methods for multimodel and
multiscale mechanical problems: advances, analyses and computation of
challenging fine scales applications".

Minisymposium
Numerical methods and their applications in molecular simulation
(ICNAAM 2009 conference, Crete,
September 1822, 2009), organized with E. Cancès.

Minisymposium "Multimodel and Multiscale Approaches in Solid Mechanics: Algorithms and
Applications Advances" (10th US National
Congress on Computational Mechanics, Columbus, July 1619, 2009),
organized with H. Ben Dhia.

Workshop Numerical
methods in molecular simulation (HIM, Bonn, April 711, 2008),
organised with Tony
Lelièvre, Mathias
Rousset and Gabriel
Stoltz.

Workshop on Models and numerical methods
for granular materials (ENPC, November 1921, 2007),
organized with François
Castella (this workshop is part of the GdR CHANT activities).

Minisymposium Molecular dynamics (SciCADE 2007 conference,
SaintMalo, July 913, 2007), organised with Eric Darve.

Conference on Molecular
simulation: algorithmic and mathematical aspects (IHP, Paris, 13 december 2004).

Workshop PRESTISSIMO
(IHP, Paris, 1112 december 2003), on Molecular dynamics and long
term integration.
Short term visits:
 IPAM Los Angeles, december 2012: 3 weeks (core participant within
the ``Materials Defects'' program, Sept.Dec. 2012).
 Texas A & M University, december 2011: 2 weeks (collaboration with
Y. Efendiev).
 Minneapolis, may 2009: 3 weeks at the IMA (Institute for Mathematics and its Applications).
 Berlin, july 2008: 3 weeks at the Technische Universität, with
participation in the program
Analytical and numerical aspects of partial differential equations.
 Bonn, spring 2008: 3 weeks with the HIM
Junior Trimester Program on Computational Mathematics (Numerical
methods in molecular simulation, organised with Tony Lelièvre, Mathias Rousset and Gabriel Stoltz).
 Minneapolis, april 2006: 3 weeks at the IMA (Institute for Mathematics and
its Applications).
Teaching activities:
 since sept. 2015: in charge of the course Partial Differential Equations and the Finite Element Method (15h in the first year).
 The course webpage (lecture notes in english, practical informations in french).
 since sept. 2015: Mathematical Tools for Engineers (9h in the first year), managed by Eric Cances.
 since sept. 2008: Multiscale problems: theoretical and numerical aspects (M2
Mathématiques et Applications, Université Pierre et Marie Curie Paris 6).
 since sept. 2006: in charge of the course Mathematics of multiscale models (39h in the
second year).
 sept. 2002  june 2015: Analysis course (36h in the first year), managed
by Eric Cancès.
More details on the cursus at the ENPC.
Links
Last update: june 2016.