Laboratoire NAVIER - UMR 8205

I am currently a researcher at NAVIER laboratory and Professor at Ecole Nationale des Ponts et Chaussées.

I am a member of the MATHERIALS project-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).

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, multiscale-in-time problems, parareal algorithms, highly oscillatory Hamiltonians, sampling).
• Numerical analysis of micro-macro models for solids, coupling an atomistic model with a continuum mechanics model (variational problems, coarse-graining, finite temperature).

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

Editorial activity :

• SIAM Multiscale Modeling and Simulation
• ESAIM Proceedings

Journal articles :

1. E. Cancès, V. Ehrlacher, F. Legoll, B. Stamm and S. Xiang, An embedded corrector problem for homogenization. Part II : Algorithms and discretization, arxiv preprint 1810.09885 and HAL preprint 01903486.
2. F. Legoll, T. Lelièvre and U. Sharma, Effective dynamics for non-reversible stochastic differential equations : a quantitative study, arxiv preprint 1809.10498 and HAL preprint 01883330.
3. E. Cancès, V. Ehrlacher, F. Legoll, B. Stamm and S. Xiang, An embedded corrector problem for homogenization. Part I : Theory , arxiv preprint 1807.05131 and HAL preprint 01840993.
4. T. Hudson, F. Legoll and T. Lelièvre, Stochastic homogenization of a scalar viscoelastic model exhibiting stress-strain hysteresis, arxiv preprint 1802.05549 and HAL preprint 01710772.
5. C. Le Bris, F. Legoll and F. Madiot, Multiscale Finite Element methods for advection-dominated problems in perforated domains, arxiv preprint 1710.09331 and HAL preprint 01624049.
6. L. Chamoin and F. Legoll, A posteriori error estimation and adaptive strategy for the control of MsFEM computations, Computer Methods in Applied Mechanics and Engineering, vol. 336, 1-38 (2018).
7. M. Josien, Y.-P. Pellegrini, F. Legoll and C. Le Bris, Fourier-based numerical approximation of the Weertman equation for moving dislocations, International Journal for Numerical Methods in Engineering, vol. 113 (12), 1827-1850 (2018).
8. C. Le Bris, F. Legoll and S. Lemaire, On the best constant matrix approximating an oscillatory matrix-valued coefficient in divergence-form operators, Control, Optimisation and Calculus of Variations, accepted for publication, arxiv preprint 1612.05807 and HAL preprint 01420187.
9. C. Le Bris, F. Legoll and F. Madiot, Stable approximation of the advection-diffusion equation using the invariant measure, arxiv preprint 1609.04777 and HAL preprint 01367417.
10. F. Legoll, T. Lelièvre and S. Olla, Pathwise estimates for an effective dynamics, Stochastic Processes and their Applications, vol. 127 (9), 2841-2863 (2017).
11. C. Le Bris and F. Legoll, Examples of computational approaches for elliptic, possibly multiscale PDEs with random inputs, Journal of Computational Physics, vol. 328, 455-473 (2017).
12. C. Le Bris, F. Legoll and F. Madiot, Stabilisation de problèmes non coercifs via une méthode numérique utilisant la mesure invariante (Stabilization of non-coercive problems using the invariant measure), C. R. Acad. Sci. Paris, Serie I, vol. 354 (8), 799-803 (2016).
13. T. Jourdan, G. Stoltz, F. Legoll and L. Monasse, An accurate scheme to solve cluster dynamics equations using a Fokker-Planck approach, Computer Physics Communications, vol. 207, 170-178 (2016).
14. C. Le Bris, F. Legoll and F. Madiot, A numerical comparison of some Multiscale Finite Element approaches for advection-dominated problems in heterogeneous media, Mathematical Modelling and Numerical Analysis, vol. 51 (3), 851-888 (2017) (earlier extended version : arxiv preprint 1511.08453 and HAL preprint 01235642).
15. 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).
16. 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), 25-54 (2016).
17. I.G. Tejada, L. Brochard, T. Lelièvre, G. Stoltz, F. Legoll and E. Cancès, Combining a reactive potential with a harmonic approximation for atomistic simulations of material failure, Computer Methods in Applied Mechanics and Engineering, vol. 305, 422-440 (2016).
18. K. Sab, F. Legoll and S. Forest, Stress Gradient elasticity theory : existence and uniqueness of solution, J. of Elasticity, vol. 123 (2), 179-201 (2016).
19. 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), 801-806 (2015).
20. S. Brisard and F. Legoll, Periodic homogenization using the Lippmann-Schwinger formalism, arxiv preprint 1411.0330 and HAL preprint 01080251.
21. 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, Journal of Physics : Conference Series, vol. 574, 012041 (2015).
22. F. Legoll and W. Minvielle, A control variate approach based on a defect-type theory for variance reduction in stochastic homogenization, SIAM Multiscale Modeling and Simulation, vol. 13 (2), 519-550 (2015).
23. F. Legoll, W. Minvielle, A. Obliger and M. Simon, A parameter identification problem in stochastic homogenization, ESAIM Proceedings, vol. 48, 190-214 (2015).
24. 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).
25. 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).
26. 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).
27. Y. Efendiev, C. Kronsbein and F. Legoll, Multi-Level Monte Carlo approaches for numerical homogenization, SIAM Multiscale Modeling and Simulation, vol. 13 (4), 1107-1135 (2015).
28. 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).
29. 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).
30. 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).

31. E. B. Tadmor, F. Legoll, W. K. Kim, L. M. Dupuy and R. E. Miller, Finite-Temperature Quasicontinuum, Applied Mechanics Reviews, vol. 65 (1), 010803 (2013).
32. 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).
33. 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).
34. 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).
35. 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).
36. 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).
37. 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).
38. 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).
39. 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).
40. 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).
41. F. Legoll and T. Lelièvre, Effective dynamics using conditional expectations, Nonlinearity, vol. 23 (9), 2131-2163 (2010).
42. 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).
43. 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, 2011.
44. 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).
45. 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).
46. 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).
47. 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).
48. 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).
49. 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).
50. 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).
51. 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).
52. 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).
53. 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).
54. 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).
55. F. Legoll, M. Luskin and R. Moeckel, Non-ergodicity of Nosé-Hoover dynamics, Nonlinearity, vol. 22 (7), 1673-1694 (2009).
56. 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).
57. 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).
58. B. Leimkuhler, F. Legoll and E. Noorizadeh, A temperature control technique for nonequilibrium molecular simulation, Journal of Chemical Physics, vol. 128 (7), 074105 (2008).
59. F. Legoll, T. Lelièvre and G. Stoltz, Some remarks on sampling methods in molecular dynamics, ESAIM Proceedings, vol. 22, 217-233 (2008).
60. 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).
61. 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).
62. 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).
63. 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).
64. 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).
65. F. Legoll, Numerical homogenization of nonlinear viscoplastic two-dimensional polycrystals, Computational and Applied Mathematics, vol. 23 (2-3), 309-325 (2004).
66. 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).
67. 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).
68. 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 :

• Conference SciCADE 2017, 11-15 september 2017, Bath : with A. Abdulle (EPFL), we co-organized the mini-symposium "Multiscale modelling : numerical methods and applications".
• Member of the scientific committee SciCADE 2017.
• 14th U.S. National Congress on Computational Mechanics (14th USNCCM), July 17-20, 2017, Montreal : with L. Chamoin (LMT Cachan) and K. Van der Zee (Nottingham), we co-organized a mini-symposium on "Adaptivity for multiscale problems".
• 8th International Conference on Multiscale Materials Modeling, 10-14 october 2016, Dijon : with W. Curtin (EPFL), C. Garcia-Cervera (UCSB), J. Kermode (Warwick), X. Li (Penn State), A. Lozinski (Besancon), M. Luskin (Minneapolis) and C. Ortner (Warwick), we co-organized the mini-symposium "Mathematical theory and computational techniques for multiscale materials modeling".
• Member of the scientific committee SciCADE 2015.
• Workshop Stochastic and multiscale inverse problems (ENPC, 2-3 october 2014), organized with Virginie Ehrlacher, Tony Lelièvre and Karam Sab.
• SciCADE 2013 conference, September 16-20, 2013, Valladolid : with Yvon Maday (Paris 6), we have co-organized a mini-symposium on "Recent advances on parareal algorithms".
• 12th U.S. National Congress on Computational Mechanics (12th USNCCM), July 22-25, 2013, Raleigh : with Régis Cottereau (Centrale Paris), Lori Graham-Brady (Johns Hopkins) and Martin Ostoja-Starzewski (U. of Illinois), we co-organized a mini-symposium on "Multi-scale methods for heterogeneous materials".
• 12th U.S. National Congress on Computational Mechanics (12th USNCCM), July 22-25, 2013, Raleigh : 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 "The atomistic basis of non-equilibrium thermal processes in materials".
• 22nd International Workshop on Computational Mechanics of Materials (IWCMM XXII), September 24-26, 2012, Baltimore : 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, IHP (see also here for the program).
• Dynamics Days Europe 2010, September 6-10, 2010, Bristol : with B. Leimkuhler, we co-organized a mini-symposium on "Molecular Dynamics".
• Multiscale Molecular Modelling conference, June 30 - July 3, 2010, Edinburgh : 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, Paris : 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, fall 2017 : 4 weeks (core participant within the "Complex high-dimensional energy landscapes" program, Sept.-Dec. 2017).
• 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 (ENPC first year, 15h).
  • The course webpage (lecture notes in english, practical informations in french).
• since sept. 2015 : Mathematical Tools for Engineers (ENPC first year, 9h), managed by Eric Cances.
• 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. 2018 : in charge of the course Time-dependent problems (ENPC second year, 39h).
  • The course webpage (in french).

Last update : december 2018.