Frédéric LEGOLL

Organization: ENPC
Research Unit: Laboratoire Navier, Multiscale team
Phone: 33 1 64 15 37 81
Fax: 33 1 64 15 37 41
E-mail: 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)

I am currently a researcher at Laboratoire Navier and Professor at Ecole Nationale des Ponts et Chaussées.

I am a member of the MICMAC project-team, at INRIA.

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 2004-2005, 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 Jacques-Louis Lions, University Paris 6).

My resume (pdf file).

Forthcoming events:

with Yvon Maday (Paris 6), we co-organize a mini-symposium on "Recent advances on parareal algorithms", within the SciCADE 2013 conference, September 16-20, 2013.

with Régis Cottereau (Centrale Paris), Lori Graham-Brady (Johns Hopkins) and Martin Ostoja-Starzewski (U. of Illinois), we co-organize a mini-symposium on "Multi-scale methods for heterogeneous materials", within the 12th U.S. National Congress on Computational Mechanics (12th USNCCM), July 22-25, 2013.

with Brent Kraczek (US Army Research Laboratory), Reese Jones (Sandia National Laboratories) and Kranthi Mandadapu (Sandia National Laboratories), we co-organize a mini-symposium on "The atomistic basis of non-equilibrium thermal processes in materials", within the 12th U.S. National Congress on Computational Mechanics (12th USNCCM), July 22-25, 2013.

Research themes:

Methods and algorithms for molecular dynamics (see the website of the Action de Recherche Collaborative INRIA PRESTISSIMO).
Numerical analysis of micro-macro models for solids, coupling an atomistic model with a continuum mechanics model.
Numerical methods for stochastic homogenization.

Collaborations with the Molecular and Multiscale Modelling team of the CERMICS.

See also the Action Concertée Incitative Simulation moléculaire webpage.

Editorial activity:

Journal articles:

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, accepted for publication.
F. Legoll and W. Minvielle, Variance reduction using antithetic variables for a nonlinear convex stochastic homogenization problem, arxiv preprint 1302.0038 and HAL preprint 00784187.
Y. Efendiev, C. Kronsbein and F. Legoll, Multi-Level Monte Carlo approaches for numerical homogenization, arxiv preprint 1301.2798 and HAL preprint 00776287.
S. Lahbabi and F. Legoll, Effective dynamics for a kinetic Monte-Carlo model with slow and fast time scales, arxiv preprint 1301.0266 and HAL preprint 00772489.
F. Legoll and F. Thomines, On a variant of random homogenization theory: convergence of the residual process and approximation of the homogenized coefficients, arxiv preprint 1211.4252 and HAL preprint 00755230.
C. Le Bris, F. Legoll and A. Lozinski, MsFEM à la Crouzeix-Raviart for highly oscillatory elliptic problems, Chinese Annals of Mathematics, Series B, vol. 34 (1), 113-138 (2013).
E. B. Tadmor, F. Legoll, W. K. Kim, L. M. Dupuy and R. E. Miller, Finite-Temperature Quasicontinuum, Applied Mechanics Reviews, accepted for publication.
F. Legoll, T. Lelièvre and G. Samaey, A micro-macro parareal algorithm: application to singularly perturbed ordinary differential equations, SIAM Journal on Scientific Computing, accepted for publication, arxiv preprint 1204.5926 and HAL 00691939.
M. Dobson, F. Legoll, T. Lelièvre and G. Stoltz, Derivation of Langevin Dynamics in a nonzero Background Flow Field, Mathematical Modelling and Numerical Analysis, accepted for publication, arxiv preprint 1203.3773 and HAL 00680278.
C. Le Bris, F. Legoll and F. Thomines, Multiscale Finite Element approach for "weakly" random problems and related issues, arxiv preprint 1111.1524 and HAL 00639349.
C. Le Bris, F. Legoll and F. Thomines, Rate of convergence of a two-scale expansion for some "weakly" stochastic homogenization problems, Asymptotic Analysis, vol. 80 (3-4), 237-267 (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), 79-101 (2013).
X. Blanc and F. Legoll, A numerical strategy for coarse-graining two-dimensional atomistic models at finite temperature: the membrane case, Computational Materials Science, vol. 66, 84-95 (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), 717-742 (2013).
F. Legoll and T. Lelièvre, Some remarks on free energy and coarse-graining, in Numerical Analysis and Multiscale Computations, B. Engquist, O. Runborg, R. Tsai eds., Lect. Notes Comput. Sci. Eng., vol. 82, Springer, 279-329 (2012).
F. Legoll and T. Lelièvre, Effective dynamics using conditional expectations, Nonlinearity, vol. 23 (9), 2131-2163 (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), 30-56 (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, 197-272 (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), 31-66 (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 and Multiscale Computations, B. Engquist, O. Runborg, R. Tsai eds., Lect. Notes Comput. Sci. Eng., vol. 82, Springer, 47-70 (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 (17-18), 1033-1038 (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), 347-373 (2010) (earlier extended version: HAL preprint 00165293).
X. Blanc, C. Le Bris, F. Legoll and C. Patz, Finite-temperature coarse-graining of one-dimensional models: mathematical analysis and computational approaches, Journal of Nonlinear Science, vol. 20 (2), 241-275 (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, 9-27 (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), 336-348 (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), 423-460 (2010).
B. Dickson, F. Legoll, T. Lelièvre, G. Stoltz and P. Fleurat-Lessard, Free energy calculations: An efficient adaptive biasing potential method, Journal of Physical Chemistry B, vol. 114 (17), 5823-5830 (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 (1-2), 99-103 (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, 193-245 (2009).
F. Legoll, M. Luskin and R. Moeckel, Non-ergodicity of Nosé-Hoover dynamics, Nonlinearity, vol. 22 (7), 1673-1694 (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 activation-relaxation 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, 217-233 (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), 277-282 (2007).
F. Legoll, M. Luskin and R. Moeckel, Non-ergodicity of the Nosé-Hoover Thermostatted Harmonic Oscillator, Archive for Rational Mechanics and Analysis, vol. 184 (3), 449-463 (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), 351-389 (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), 209-216 (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), 797-826 (2005).
Numerical homogenization of nonlinear viscoplastic two-dimensional polycrystals, Computational and Applied Mathematics, vol. 23 (2-3), 309-325 (2004).
E. Cancès, F. Castella, Ph. Chartier, E. Faou, C. Le Bris, F. Legoll and G. Turinici, High-order averaging schemes with error bounds for thermodynamical properties calculations by molecular dynamics simulations, Journal of Chemical Physics, vol. 121 (21), 10346-10355 (2004).
E. Cancès, F. Castella, Ph. Chartier, E. Faou, C. Le Bris, F. Legoll and G. Turinici, Long-time averaging for integrable Hamiltonian dynamics, Numerische Mathematik, vol. 100 (2), 211-232 (2005).
F. Legoll and R. Monneau, Designing reversible measure invariant algorithms with applications to molecular dynamics, Journal of Chemical Physics, vol. 117 (23), 10452-10464 (2002).

Conferences and mini-symposium organization:

22nd International Workshop on Computational Mechanics of Materials (IWCMM XXII), September 24-26, 2012: with Brent Kraczek (US Army Research Laboratory), Reese Jones (Sandia National Laboratories) and Kranthi Mandadapu (Sandia National Laboratories), we co-organized a mini-symposium on "Atomistic basis of thermal processes in driven systems".

with E. Faou, T. Lelièvre and G. Stoltz, we co-organized a CEA-EDF-INRIA school on Simulation of hybrid dynamical systems and applications to molecular dynamics, September 27-30, 2010 (see also here for the program).

Dynamics Days Europe 2010, September 6-10, 2010: with B. Leimkuhler, we co-organized a mini-symposium on "Molecular Dynamics".

Multiscale Molecular Modelling conference, June 30 - July 3, 2010: with T. Lelièvre, we co-organized a mini-symposium on "Coarse-graining and effective dynamics in molecular simulation".

4th European Conference on Computational Mechanics, May 16-21, 2010: with H. Ben Dhia (Centrale Paris), F. Feyel (Onera and ENSMP) and V. Kouznetsova (TU Eindhoven), we co-organized a mini-symposium on "Arlequin, FE2 and other embedded domains methods for multimodel and multiscale mechanical problems: advances, analyses and computation of challenging fine scales applications".

Mini-symposium Numerical methods and their applications in molecular simulation (ICNAAM 2009 conference, Crete, September 18-22, 2009), organized with E. Cancès.

Mini-symposium "Multimodel and Multiscale Approaches in Solid Mechanics: Algorithms and Applications Advances" (10th US National Congress on Computational Mechanics, Columbus, July 16-19, 2009), organized with H. Ben Dhia.

Workshop Numerical methods in molecular simulation (HIM, Bonn, April 7-11, 2008), organised with Tony Lelièvre, Mathias Rousset and Gabriel Stoltz.

Workshop on Models and numerical methods for granular materials (ENPC, November 19-21, 2007), organized with François Castella (this workshop is part of the GdR CHANT activities).

Mini-symposium Molecular dynamics (SciCADE 2007 conference, Saint-Malo, July 9-13, 2007), organised with Eric Darve.

Conference on Molecular simulation: algorithmic and mathematical aspects (IHP, Paris, 1-3 december 2004).

Workshop PRESTISSIMO (IHP, Paris, 11-12 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. 2008: Multiscale problems: theoretical and numerical aspects (M2 Mathématiques et Applications, Université Pierre et Marie Curie Paris 6).
- The course webpage (in french).

since sept. 2006: Mathematics of multiscale models (39h in the second term), with Mathieu Lewin.
- The course webpage (in french).

in 2007-2008: Introduction to statistical physics and quantum physics (39h in the second term), with Ismaila Dabo, Jean-Noel Roux and Stephane Rodts.
- The course webpage (in french).

since sept. 2002: Analysis course (36h in the first term), managed by Eric Cancès.
- Course syllabus, course webpage (in french).

More details on the cursus at the ENPC.