Frédéric LEGOLL


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Je suis actuellement chercheur au sein du Laboratoire Navier et professeur à l'Ecole Nationale des Ponts et Chaussées.

Je suis membre de l'équipe MATHERIALS de l'INRIA (j'étais membre de l'équipe-projet MICMAC).

J'ai soutenu mon Habilitation à Diriger des Recherches le 17 octobre 2011 (résumé, mémoire; cf. aussi ici). Sujet: Contributions à l'étude mathématique et numérique de quelques modèles en simulation multi-échelle des matériaux.

Pendant l'année 2004-2005, j'étais en postdoc à l'Institute for Mathematics and its Applications (IMA) de l'Université du Minnesota (Minneapolis), dans le cadre de l'année thématique Mathematics of Materials and Macromolecules: Multiple Scales, Disorder, and Singularities.

J'ai soutenu ma thèse en mathématiques appliquées le 31 août 2004 (résumé, fichier ps.gz (862 Ko) ou pdf (2.5 Mo)).
Sujet: méthodes moléculaires et multi-échelles pour la simulation numérique des matériaux.
Direction: Claude Le Bris (CERMICS ENPC) et Yvon Maday (Laboratoire Jacques-Louis Lions, Université Paris 6).

Mon CV (au format pdf).




Open position:

We are looking for a Postdoctoral student to work on variance reduction approaches for random materials homogenization. See here for a complete description. This project, funded by the Labex MMCD, will be supervised by Sebastien Brisard, Claude Le Bris and Frederic Legoll. The work, in between PDEs, scientific computing and applied probability, can start as soon as possible. Please email me for more information.


Centres d'intérêts principaux:



Collaborations avec l'équipe Simulation moléculaire et multi-échelles du CERMICS.

Cf. aussi la page web de l'Action Concertée Incitative Simulation moléculaire.


Activité éditoriale:




Publications dans des revues à comité de lecture:

  1. S. Brisard et F. Legoll, Periodic homogenization using the Lippmann--Schwinger formalism, arxiv preprint 1411.0330 et HAL preprint 01080251.

  2. I.G. Tejada, L. Brochard, G. Stoltz, F. Legoll, T. Lelièvre et 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 IC-MSQUARE conference, à paraitre.

  3. F. Legoll et W. Minvielle, A control variate approach based on a defect-type theory for variance reduction in stochastic homogenization, arxiv preprint 1407.8029 et HAL preprint 01053459.

  4. F. Legoll, W. Minvielle, A. Obliger et M. Simon, A parameter identification problem in stochastic homogenization, ESAIM Proceedings, accepté pour publication, arxiv preprint 1402.0982 et HAL preprint 00942730.

  5. C. Le Bris, F. Legoll et A. Lozinski, An MsFEM type approach for perforated domains, SIAM Multiscale Modeling and Simulation, vol. 12 (3), 1046-1077 (2014).

  6. C. Le Bris, F. Legoll et 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 (7-8), 265-270 (2013).

  7. F. Legoll et W. Minvielle, Variance reduction using antithetic variables for a nonlinear convex stochastic homogenization problem, Discrete and Continuous Dynamical Systems - S, vol. 8 (1), 1-27 (2015).

  8. Y. Efendiev, C. Kronsbein et F. Legoll, Multi-Level Monte Carlo approaches for numerical homogenization, arxiv preprint 1301.2798 et HAL preprint 00776287.

  9. S. Lahbabi et F. Legoll, Effective dynamics for a kinetic Monte-Carlo model with slow and fast time scales, Journal of Statistical Physics, vol. 153 (6), 931-966 (2013).

  10. F. Legoll et 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), 347-386 (2014).

  11. C. Le Bris, F. Legoll et A. Lozinski, MsFEM à la Crouzeix-Raviart for highly oscillatory elliptic problems, Chinese Annals of Mathematics, Series B, vol. 34 (1), 113-138 (2013).

    Cet article a aussi été publié sous la référence suivante:

    C. Le Bris, F. Legoll et A. Lozinski, MsFEM à la Crouzeix-Raviart for highly oscillatory elliptic problems, in Partial Differential Equations: Theory, Control and Approximation, P. G. Ciarlet, T. Li, Y. Maday eds., Springer, 265-294 (2014).

  12. E. B. Tadmor, F. Legoll, W. K. Kim, L. M. Dupuy et R. E. Miller, Finite-Temperature Quasi-Continuum, Applied Mechanics Reviews, vol. 65 (1), 010803 (2013).

  13. F. Legoll, T. Lelièvre et G. Samaey, A micro-macro parareal algorithm: application to singularly perturbed ordinary differential equations, SIAM Journal on Scientific Computing, vol. 35 (4), A1951-A1986 (2013).

  14. M. Dobson, F. Legoll, T. Lelièvre et G. Stoltz, Derivation of Langevin Dynamics in a nonzero Background Flow Field, Mathematical Modelling and Numerical Analysis, vol. 47 (6), 1583-1626 (2013).

  15. C. Le Bris, F. Legoll et F. Thomines, Multiscale Finite Element approach for "weakly" random problems and related issues, Mathematical Modelling and Numerical Analysis, vol. 48 (3), 815-858 (2014).

  16. C. Le Bris, F. Legoll et 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).

  17. X. Blanc, F. Legoll et A. Anantharaman, Asymptotic behaviour of Green functions of divergence form operators with periodic coefficients, Applied Mathematics Research Express, vol. 2013 (1), 79-101 (2013).

  18. X. Blanc et 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).

  19. A. Iacobucci, F. Legoll, S. Olla et G. Stoltz, Negative thermal conductivity of chains of rotors with mechanical forcing, Phys. Rev. E, vol. 84 (6), 061108 (2011).

  20. X. Dai, C. Le Bris, F. Legoll et Y. Maday, Symmetric parareal algorithms for Hamiltonian systems, Mathematical Modelling and Numerical Analysis, vol. 47 (3), 717-742 (2013).

  21. F. Legoll et 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).

  22. F. Legoll et T. Lelièvre, Effective dynamics using conditional expectations, Nonlinearity, vol. 23 (9), 2131-2163 (2010).

  23. M. Dobson, C. Le Bris et 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) (version antérieure étendue: arxiv preprint 1008.1030 et HAL 00524814).

  24. A. Anantharaman, R. Costaouec, C. Le Bris, F. Legoll et 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).

  25. X. Blanc, R. Costaouec, C. Le Bris et F. Legoll, Variance reduction in stochastic homogenization using antithetic variables, Markov Processes and Related Fields, vol. 18 (1), 31-66 (2012) (lien).

  26. X. Blanc, R. Costaouec, C. Le Bris et 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).

  27. M. Dobson, C. Le Bris et 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).

  28. C. Le Bris et F. Legoll, Integrators for highly oscillatory Hamiltonian systems: an homogenization approach, Discrete and Continuous Dynamical Systems - B, vol. 13 (2), 347-373 (2010) (version antérieure étendue: preprint HAL 00165293).

  29. X. Blanc, C. Le Bris, F. Legoll et 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).

  30. R. Costaouec, C. Le Bris et F. Legoll, Variance reduction in stochastic homogenization: proof of concept, using antithetic variables, Boletin Soc. Esp. Mat. Apl., vol. 50, 9-27 (2010).

  31. A. Iacobucci, F. Legoll, S. Olla et G. Stoltz, Thermal conductivity of the Toda lattice with conservative noise, Journal of Statistical Physics, vol. 140 (2), 336-348 (2010).

  32. X. Blanc, C. Le Bris, F. Legoll et T. Lelièvre, Beyond multiscale and mutiphysics: multimaths for model coupling, Networks and Heterogeneous Media, vol. 5 (3), 423-460 (2010).

  33. B. Dickson, F. Legoll, T. Lelièvre, G. Stoltz et P. Fleurat-Lessard, Free energy calculations: An efficient adaptive biasing potential method, Journal of Physical Chemistry B, vol. 114 (17), 5823-5830 (2010).

  34. R. Costaouec, C. Le Bris et 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).

  35. 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 et P. Wittbold eds., de Gruyter Proceedings in Mathematics, 193-245 (2009).

  36. F. Legoll, M. Luskin et R. Moeckel, Non-ergodicity of Nosé-Hoover dynamics, Nonlinearity, vol. 22 (7), 1673-1694 (2009).

  37. M. Hammoud, D. Duhamel, K. Sab et F. Legoll, Coupled Discrete and Continuum Approach to the Behavior of Ballast, Ninth International Conference on Computational Structures Technology proceeding, Athènes (septembre 2008).

  38. E. Cancès, F. Legoll, M.-C. Marinica, K. Minoukadeh et 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).

  39. B. Leimkuhler, F. Legoll et E. Noorizadeh, A temperature control technique for nonequilibrium molecular simulation, Journal of Chemical Physics, vol. 128 (7), 074105 (2008).

  40. F. Legoll, T. Lelièvre et G. Stoltz, Some remarks on sampling methods in molecular dynamics, ESAIM Proceedings, vol. 22, 217-233 (2008).

  41. C. Le Bris et 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).

  42. F. Legoll, M. Luskin et R. Moeckel, Non-ergodicity of the Nosé-Hoover Thermostatted Harmonic Oscillator, Archive for Rational Mechanics and Analysis, vol. 184 (3), 449-463 (2007).

  43. E. Cancès, F. Legoll et G. Stoltz, Theoretical and numerical comparison of some sampling methods for molecular dynamics, Mathematical Modelling and Numerical Analysis, vol. 41 (2), 351-389 (2007).

  44. X. Blanc, C. Le Bris et 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).

  45. X. Blanc, C. Le Bris et F. Legoll, Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics, Mathematical Modelling and Numerical Analysis, vol. 39 (4), 797-826 (2005).

  46. Numerical homogenization of nonlinear viscoplastic two-dimensional polycrystals, Computational and Applied Mathematics, vol. 23 (2-3), 309-325 (2004).

  47. E. Cancès, F. Castella, Ph. Chartier, E. Faou, C. Le Bris, F. Legoll et 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).

  48. E. Cancès, F. Castella, Ph. Chartier, E. Faou, C. Le Bris, F. Legoll et G. Turinici, Long-time averaging for integrable Hamiltonian dynamics, Numerische Mathematik, vol. 100 (2), 211-232 (2005).

  49. F. Legoll et R. Monneau, Designing reversible measure invariant algorithms with applications to molecular dynamics, Journal of Chemical Physics, vol. 117 (23), 10452-10464 (2002).

Organisation de conférences / mini-symposium:


Séjours à l'étranger:


Enseignement:

Plus de renseignements sur la formation à l'ENPC.

Liens


Dernière mise à jour: novembre 2014.