Tony LELIEVRE
Version
française
I am currently researcher at the CERMICS laboratory, in the Ecole
Nationale des Ponts et Chaussées.
I am in charge of the Molecular
and
Multiscale
Modelling group of CERMICS,
department of Applied Mathematics of the Ecole des Ponts ParisTech.
I am a member of the MICMAC project-team, at INRIA.
Here is my cv (pdf).
I defended my habilitation thesis on 3rd June 2009 (abstract, manuscript). Title: Mathematical and numerical analysis of some models for materials, from the microscopic scale to the macroscopic scale.
During year 2004-2005, I had a post-doc position at the Centre
de Recherches Mathématiques at the University of
Montreal,
in the context of a special year about the
Mathematics of Stochastic and Multiscale Modeling.
I defended my PhD thesis on 21st June 2004 (abstract, manuscript). Title: Multiscale models for viscoelastic fluids. PhD supervisors: Benjamin
Jourdain and Claude
Le Bris.
Open position : Convergence of adaptive MCMC methods, see this for more details.
Past events:
Research interests
- Micro-macro models for viscoelastic fluids (dumbbell model,
CONNFFESSIT method, variance reduction methods, entropy estimates).
- Free surface flow and magnetohydrodynamics. Application to
the simulation of aluminium electrolysis cells (Arbitrary Lagrangian
Eulerian method, moving contact line problem).
- Molecular simulation (molecular dynamics, constrained dynamics,
adaptive methods, Quantum Monte Carlo methods).
Journal articles
- (with B. Jourdain and C. Le Bris) Numerical analysis of
micro-macro
simulations of polymeric fluid flows: a simple case, Mathematical
Models
and Methods in Applied Sciences, 12(9),
1205-1243, (2002).
- (with J-F. Gerbeau and C. Le Bris) Simulations of MHD flows
with
moving
interfaces, Journal of Computational Physics, 184, 163-191, (2003).
- (with J-F. Gerbeau and C. Le Bris) Modelling and simulation
of the
industrial
production of aluminium: the nonlinear approach, Computers and
Fluids, 33, 801-814, (2004).
- Optimal error estimate for the CONNFFESSIT approach in a
simple
case,
Computers and Fluids, 33,
815-820, (2004).
- (with B. Jourdain and C. Le Bris) Existence of solution for a
micro-macro
model of polymeric fluid : the FENE model, Journal of Functional
Analysis, 209, 162-193, (2004).
- (with B. Jourdain and C. Le Bris) On a variance reduction
technique
for micro-macro simulations of polymeric fluids, Journal of
Non-Newtonian
Fluid Mechanics, 122, 91-106,
(2004).
- (with F. Dubois) Efficient pricing of Asian options by the
PDE
approach,
Journal of Computational Finance, 8(2),
55-64, (2005). See also the
program in C, implemented in Premia,
and some first attempts on the subject (ps
in French).
- (with J.P. Croisille, A. Ern et J. Proft) Analysis and
simulation
of
a coupled hyperbolic/parabolic model problem, Journal of Numerical
Mathematics, 13(2), 81-156,
(2005). See
also the reference
solutions
files.
- (with B. Jourdain and C. Le Bris) An elementary argument
regarding
the
long-time behaviour of the solution to a stochastic differential
equation, Annals of Craiova University, Mathematics and Computer
Science
series, 32, 39-47, (2005).
- (with B. Jourdain, C. Le Bris and F. Otto) Long-time asymptotics of a multiscale
model for polymeric fluid flows, Archive for Rational Mechanics
and
Analysis, 181(1),
97-148, (2006).
- (with E. Cancès and B. Jourdain) Quantum Monte Carlo
simulations
of fermions. A mathematical analysis of the fixed-node approximation,
Mathematical
Models
and Methods in Applied Sciences, 16(9),
1403-1440, (2006).
- (with M. Rousset and G. Stoltz) Computation
of free energy differences through nonequilibrium stochastic dynamics:
the reaction coordinate case, Journal of Computational Physics, 222(2), 624-643, (2007).
- (with M. Caffarel, E. Cancès, A. Scemama and G. Stoltz) An efficient sampling algorithm for
Variational Monte Carlo, Journal of Chemical Physics, 125,
114105 (2006).
- (with G. Ciccotti and E. Vanden-Eijnden) Projection of diffusions on submanifolds:
Application to mean force computation, Communications on Pure
and
Applied Mathematics, 61(3), 371-408, (2008).
- (with M. El Makrini and B. Jourdain) Diffusion Monte Carlo method: numerical
analysis in a simple case, Mathematical Modelling and Numerical
Analysis, 41(2), 189-213,
(2007).
- (with M. Rousset and G. Stoltz) Computation
of free energy profiles with parallel adaptive dynamics, Journal
of Chemical Physics 126,
134111 (2007).
- (with A. Ern) Adaptive models
for polymeric fluid flow simulation, C. R. Acad. Sci. Paris, Ser. I, 344(7), 473-476 (2007).
- (with D. Hu) New entropy
estimates for the Oldroyd-B model, and related models,
Communications in Mathematical Sciences 5(4), 909-916 (2007).
- (with C. Le Bris and E. Vanden-Eijnden) Analysis of some discretization schemes
for constrained Stochastic Differential Equations,
C.
R. Acad.
Sci. Paris, Ser. I, 346(7-8),
471-476 (2008).
- (with M. Rousset and G. Stoltz) Long-time
convergence of an Adaptive
Biasing Force method, Nonlinearity, 21, 1155-1181 (2008).
- (with E. Faou) Conservative stochastic differential
equations: Mathematical and numerical analysis, Mathematics of Computation, 78, 2047-2074 (2009).
- (with J-F. Gerbeau) Generalized
Navier Boundary Condition and Geometric Conservation Law for surface
tension, Computer Methods in Applied Mechanics and Engineering, 198(5-8), 644-656, (2009).
- A general two-scale criteria for logarithmic Sobolev inequalities, Journal of Functional Analysis, 256(7), 2211-2221 (2009).
- (with S. Boyaval and C. Mangoubi) Free-energy-dissipative schemes for the
Oldroyd-B model, Mathematical Modelling and Numerical
Analysis, 43, 523-561, (2009).
- (with C. Le Bris and Y. Maday) Results and questions on a nonlinear approximation approach for solving high-dimensional partial differential equations, Constructive Approximation, 30(3), 621-651, (2009).
- (with S. Boyaval) A variance reduction method for parametrized stochastic differential equations using the reduced basis paradigm, to appear in Communications
in Mathematical Sciences.
- (with B. Jourdain and R. Roux) Existence, uniqueness and convergence of a particle approximation for the Adaptive Biasing Force process, to appear in Mathematical Modelling and
Numerical Analysis.
- (with C. Chipot and K. Minoukadeh) Potential of mean force calculations: a multiple-walker adaptive biasing force approach, to appear in Journal of Chemical Theory and Computation.
- (with S. Boyaval, C. Le Bris, Y. Maday, N.C. Nguyen and A.T. Patera) Reduced basis techniques for stochastic problems, to appear in Archives of Computational Methods in Engineering.
Research reports / Proceeding papers
- (with J-F. Gerbeau, C. Le Bris and N. Ligonesche) Metal
pad roll instabilities, proceeding of the 2002 TMS Annual
Meeting
and Exhibition, Light Metals, p. 483-487, 2002.
- (with B. Jourdain) Mathematical analysis of a stochastic
differential
equation arising in the micro-macro modelling of polymeric fluids, CERMICS
2002-225 report, Probabilistic Methods in Fluids Proceedings of the
Swansea 2002 Workshop, Eds: I M Davies, N Jacob, A Truman, O Hassan, K
Morgan & N P Weatherill, p. 205-223.
- (with J-F. Gerbeau and C. Le Bris) Numerical simulations of
two-fluids
MHD flows, Fundamental and Applied MHD. Proceedings of the Fifth
international
PAMIR Conference, p. I.101-I.105, 2002.
- (with J-F. Gerbeau and C. Le Bris) Modeling and simulation of
MHD
phenomena
in aluminium reduction cells, Proceedings of the fourth
International
Conference on Electromagnetic Processing of Materials, EPM 2003,
C3-10.4,
p. 57-62, 2003.
- (with B. Jourdain) Convergence of a stochastic particle
approximation
of the stress tensor for the FENE-P model, CERMICS
2004-263 report .
- (with B. Jourdain and C. Le Bris) Coupling PDEs and SDEs: the
illustrative
example of the multiscale simulation of viscoelastic flows,
in
Multiscale Methods in Science and Engineering, B. Engquist, P.
Lötstedt,
O. Runborg, eds., Lecture Notes in Computational Science and
Engineering 44,
Springer,
151-170, (2005).
- (with T. Tomasino, M. Le Hervet and O. Martin) Stability analysis of simplified
electrolysis cells with Mistral, proceeding of the 2006 TMS
Annual
Meeting
and Exhibition, Light Metals, p. 335-340, 2006.
- (with J.-F. Gerbeau, C. Le Bris, A. Orriols and T. Tomasino) Linear versus nonlinear approaches for the
stability analysis of aluminium production cells, Proceedings of
the 2006 ECCOMAS conference.
- (with J.-F. Gerbeau) Variational
formulation of the Generalized Navier Boundary Condition, http://hal.inria.fr/inria-00081751,
in Recent Progress in Scientific computing, SCPDE05 conference proceeding,
Eds: W Liu, M Ng and Z-C Shi, Science Press, Beijing, 2007.
- (with Y. Achdou and O. Bokanowski) Partial differential equations in finance,
CERMICS
2007-363 report .
- (with F. Legoll and G. Stoltz) Some
remarks on sampling methods in molecular dynamics, ESAIM Proceedings, 22, 217-233, (2008).
- (with C. Le Bris) Multiscale
modelling of complex fluids: A mathematical initiation, in Multiscale Modeling and Simulation in Science Series, B.
Engquist, P. Lötstedt, O. Runborg, eds., Lecture Notes in Computational
Science and Engineering 66, Springer, p. 49-138, (2009).
To get the Matlab programs, contact me.
- (with F. Legoll) Effective dynamics using conditional expectations, http://arxiv.org/abs/0906.4865 .
- (with B. Dickson, F. Legoll, G. Stoltz and P.
Fleurat-Lessard) Free energy calculations: An efficient adaptive biasing
potential method, http://arxiv.org/abs/0911.2090 .
- (with N. Chopin et G. Stoltz) Free energy methods for efficient exploration of mixture posterior densities, http://arxiv.org/abs/1003.0428 .
Books
- (with J-F. Gerbeau and C. Le Bris) Mathematical methods for
the Magnetohydrodynamics of liquid metals, Numerical Mathematics
and Scientific
Computation, Oxford University Press, 2006.
- (with M. Rousset and G. Stoltz) Free energy computations: A mathematical perspective, Imperical College Press, 2010.
Scientific awards
Teaching activities
Some scientific links...
- A report on the continued fractions algorithm (ps
in French), training period supervised by Pierre
Arnoux.
- Some mathemtical links:
- Some links about computers and programming :
... and some non scientific ones.
- About the guitar :
- Miscellaneous :
Last update: March 3rd, 2010.
