Frédéric LEGOLL


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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 research-team, at INRIA (I was a member of the MICMAC project-team).

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).




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.


Research themes:



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

See also the Action Concertée Incitative Simulation moléculaire webpage.


Editorial activity:




Journal articles:

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

  2. 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 IC-MSQUARE conference, to appear.

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

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

  5. C. Le Bris, F. Legoll and 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 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 (7-8), 265-270 (2013).

  7. 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), 1-27 (2015).

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

  9. S. Lahbabi and 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 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), 347-386 (2014).

  11. 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).

    This article has been also published as:

    C. Le Bris, F. Legoll and 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 and R. E. Miller, Finite-Temperature Quasi-Continuum, Applied Mechanics Reviews, vol. 65 (1), 010803 (2013).

  13. F. Legoll, T. Lelièvre and 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 and 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 and 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 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).

  17. 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).

  18. 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).

  19. 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).

  20. 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).

  21. 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).

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

  23. 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).

  24. 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).

  25. 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).

  26. 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).

  27. 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).

  28. 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).

  29. 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).

  30. 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).

  31. 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).

  32. 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).

  33. 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).

  34. 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).

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

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

  37. 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).

  38. 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).

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

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

  41. 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).

  42. 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).

  43. 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).

  44. 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).

  45. 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).

  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 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).

  48. 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).

  49. 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:


Short term visits:


Teaching activities:

More details on the cursus at the ENPC.

Links


Last update: november 2014.