Erwan Faou

INRIA
Projet Ipso
ENS Cachan Bretagne
Avenue Robert Schumann
F-35170 Bruz

Phone: (33) 299 05 52 81
Fax: (33) 2 99 84 71 71
email: Erwan.Faou@inria.fr

Fotógrafo: B. Grébert, UNAM Cuernavaca, Mexico (March 2009....)
Other pictures: the AMS on the way to Iztaccihuatl

Figures: Numerical resonances in the approximation of NLS by splitting methods.
Left: The evolution of the actions associated with the solution of the Non Linear Schrödinger equation are represented in logarithmic scale: Illustration of Birkhoff normal form results!
Right: This is not the EEG monitoring of a trader in september 2008, but the same representation as before with a resonant time step very close (0.1%) to the one used in the left figure...

Explanations may be found in the slides of the talks I gave in Beijing (AMSS, Chinese Academy of Sciences, May 2009):
Normal form and geometric numerical integration of Hamiltonian PDE. Part I: Linear equations, and Part II: Non linear equations.

Publications
Thesis and HDR
2010 ETH Lecture on mathematics: Geometric numerical integration of semilinear Hamiltonian PDEs.
SciCADE'07
PhD Students
Teaching

What do bibliometric indicators measure?

(journal impact factor, h-number, citation index, etc...)

Text prepared by A-M. Kermarrec, E. Faou, J-P. Merlet (coordinator), P. Robert and L. Segoufin.

Validated by the INRIA Evaluation Committee, 12 September 2007.

Inria collaborative research action Prestissimo:

Conference: Molecular simulation: Algorithmic and mathematical aspects. December 2004

Workshop Prestissimo 2003.

Inria collaborative research Action HYBRID
Curriculum vitae: .pdf
Some slides

Publications:

P. Chartier and E. Faou, Equations différentielles ordinaires: analyse numérique géométrique
Book to be submitted to the collection Mathématiques appliquées pour le Master/SMAI.

Papers

Erwan Faou and Benoît Grébert Hamiltonian interpolation of splitting approximations for nonlinear PDEs Submitted	pdf
Monique Dauge, Erwan Faou and Victor Péron Comportement asymptotique à haute conductivité de l'épaisseur de peau en électromagnétisme To appear in C. R. Acad. Sci. Paris, Sér. I.	pdf
Erwan Faou and Benoît Grébert Resonances in long time integration of semi linear Hamiltonian PDEs Submitted	pdf
Nicolas Champagnat, Christophe Chipot and Erwan Faou A probabilistic approach to high-dimensional least-squares approximations. Submitted	pdf
Erwan Faou and Benoît Grébert Quasi invariant modified Sobolev norms for semi linear reversible PDEs Nonlinearity 23 (2010) 429-443	pdf
Philippe Chartier, Eric Darrigrand and Erwan Faou A Regular Fast Multipole Method for geometric numerical integration of Hamiltonian systems To appear in BIT	pdf
Erwan Faou, Benoît Grébert and Eric Paturel Birkhoff normal form for splitting methods applied to semi linear Hamiltonian PDEs. Part I: Finite dimensional discretization. Numer. Math. 114 (2010) 429-458	pdf
Erwan Faou, Benoît Grébert and Eric Paturel Birkhoff normal form for splitting methods applied to semi linear Hamiltonian PDEs. Part II: Abstract splitting. Numer. Math. 114 (2010) 459-490	pdf
Monique Dauge and Erwan Faou Koiter Estimate Revisited Math. Models Methods Appl. Sci. (M3AS) 20 No 1 (2010) 1-42	pdf
Arnaud Debussche and Erwan Faou Modified energy for split-step methods applied to the linear Schrödinger equation SIAM J. Numer. Anal. 47 (2009) 3705-3719	pdf
Erwan Faou and Tony Lelièvre Conservative stochastic differential equations: Mathematical and numerical analysis Math. Comp. 78 (2009) 2047-2074	pdf
François Castella, Philippe Chartier and Erwan Faou An averaging technique for highly-oscillatory Hamiltonian problems SIAM J. Numer. Anal. 47 No 4 (2009) 2808-2837	pdf
Erwan Faou, Vasile Gradinaru and Christian Lubich Computing semi-classical quantum dynamics with Hagedorn wavepackets SIAM J. Sci. Comp. 31 No 4 (2009) 3027-3041	pdf
Erwan Faou Analysis of splitting methods for reaction-diffusion problems using stochastic calculus Math. Comp. 78 (2009) 1467-1483.	pdf
Erwan Faou and Vasile Gradinaru Gauss-Hermite wavepacket dynamics: convergence of the spectral and pseudo-spectral approximation. IMA J. Numer. Anal. 29 (2009) 1023-1045.	pdf
Philippe Chartier and Erwan Faou A simple proof of the existence of adiabatic invariants for perturbed reversible problems J. Phys. A: Math. Theor. 41 No 47 (2008) 475204	pdf
Philippe Chartier and Erwan Faou Geometric integrators for piecewise smooth Hamiltonian systems. Math. Model. Numer. Anal. (M2AN) 42 No 2 (2008) 223-241	pdf
Guillaume Dujardin and Erwan Faou Normal form and long time analysis of splitting schemes for the linear Schrödinger equation with small potential. Numer. Math. 106 No 2 (2007) 223-262	pdf
Guillaume Dujardin and Erwan Faou Long time behavior of splitting methods applied to the linear Schrödinger equation. C. R. Acad. Sci. Paris, Sér. I. 344 (2007) 89-92
Erwan Faou Nosé-Hoover dynamics in a shaker. J. Chem. Phys. 124 184104 (2006)	ps, pdf
Philippe Chartier, Erwan Faou, Ander Murua An algebraic approach to invariant preserving integrators: The case of quadratic and Hamiltonian invariants. Numer. Math. 103 No 4 (2006) 575-590	pdf
Erwan Faou and Christian Lubich A Poisson integrator for Gaussian wavepacket dynamics. Comput. Vis. Sci. 9 No 2 (2006) 45-55	ps
Eric Cancès, François Castella, Philippe Chartier, Erwan Faou, Claude Le Bris, Frédéric Legoll and Gabriel Turinici Long-time averaging for integrable Hamiltonian dynamics. Numer. Math. 100 No 2 (2005) 211-232	ps, pdf
Erwan Faou, Ernst Hairer and Truong-Linh Pham Energy conservation with non-symplectic methods: Examples and counter-examples. BIT 44 No 4 (2004) 699-709	ps
F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, T. Lopez, D. Bayart, F. Castella, P. Chartier and E. Faou Modeling of multi-wavelength Raman fiber lasers using a new and fast algorithm. IEEE Photonics Technology Letters 16 No 12 (2004) 2601-2603	pdf
Erwan Faou Multiscale Expansions for Linear Clamped Elliptic Shells. Comm. P.D.E. 29 Vol 11 & 12 (2004) 1799-1845	ps, pdf
Eric Cancès, François Castella, Philippe Chartier, Erwan Faou, Claude Le Bris, Frédéric Legoll and Gabriel Turinici High-order averaging schemes with error bounds for thermodynamical properties calculations by molecular dynamics simulations. J. Chem. Phys. 121 No 21 (2004) 10346-10355	INRIA Research Report
François Castella, Philippe Chartier, Erwan Faou, Dominique Bayart, Florence Leplingard and Catherine Martinelli Raman Laser Modeling: Mathematical and Numerical Analysis of a model. Math. Model. Numer. Anal. (M2AN) 38 No 3 (2004) 457-475	ps, pdf
Monique Dauge, Erwan Faou and Zohar Yosibash Plates and shells: Asymptotic expansions and hierarchical models. Chapter 8, Vol I of the Encyclopedia for Computational Mechanics. Edited by Erwin Stein, René de Borst, Thomas J.R. Hughes (2004).	abstract, pdf
François Castella, Philippe Chartier and Erwan Faou Analysis of a Poisson system with boundary conditions. C. R. Acad. Sci. Paris, Sér. I. 336 (2003) 703-708	ps
Erwan Faou Elasticity on a thin shell: Formal series solution. Asympt. Anal. 31 (2002) 317-361	ps, pdf
Erwan Faou asymptotiques dans les coques elliptiques: Equations tridimensionnelles linéarisés. C. R. Acad. Sci. Paris, Sér. I. 333 (2001) 389-394	ps, pdf
Erwan Faou Développements asymptotiques dans les coques elliptiques: Modèle de Koiter. C. R. Acad. Sci. Paris, Sér. I. 333 (2001) 139-143	ps, pdf
Georgiana Andreoiu and Erwan Faou Complete asymptotics for shallow shells. Asympt. Anal. 25 (2001) 239-270	ps , pdf
Georgiana Andreoiu, Monique Dauge and Erwan Faou Développements asymptotiques complets pour des coques faiblement courbées encastrées ou libres. C. R. Acad. Sci. Paris, Sér. I. 330 (2000) 523-528	ps, ps.g
Erwan Faou Elasticité linéarisée tridimensionnelle pour une coque mince: Résolution en série formelle en puissances de l'épaisseur. C. R. Acad. Sci. Paris, Sér. I. 330 (2000) 415-420	ps, ps.gz
Monique Dauge, Ivica Djurdjevic, Erwan Faou and Andreas Rössle Eigenmode Asymptotics in Thin Elastic Plates. J. Math. Pures Appl. 78 No 9 (1999) 925-964	ps, ps.gz

Thesis and HDR

Thèse soutenue le 21 juin 2000
Développements asymptotiques dans les coques minces linéairement élastiques
pdf file --- ps file --- ps.gz file

Habilitation degree (obtained october 16, 2007)
Some geometrical aspects in shell theory and in numerical integration of hamiltonian systems.
pdf file of the document. The slides are also available, as well as the video (I cannot endure the preview very long....)

Teaching

You can download here (postscript file, 67 pages) the notes (in french) of a lecture on geometric integration and KAM theory given in june 2003, in collaboration with P.Chartier. These notes are inspired by the book "Geometric Numerical Integration, Structure-Preserving Algorithms for Ordinary Differential Equations" written by E. Hairer, C. Lubich and G. Wanner and published by Springer.

PhD. Students

Guillaume Dujardin (with F. Castella)
Marie Beaudouin (with M. Dauge)
Charles-Edouard Bréhier (with A. Debussche)

Some slides

Castellon Conference on Geometric Integration 2006 (site). "Normal form for splitting methods applied to the linear Schrödinger equation", joint work with Guillaume Dujardin. Here are the slides.

Talk on shell theory given in june 2006 in a meeting on asymptotic methods organized at the ENSTA by POEMs. Here are the slides (in french).

Slides of a talk on Gaussian Wave Packets approximation of the Schödinger equation given in SciCADE'05 in Nagoya (japan).

Choosing a resonant step size can lead to dramatic effects but beautiful pictures: This is behavior of the Fourier coefficients corresponding to the solution of the linear Schrödinger equation on a torus computed by a splitting method with a non-resonnant stepsize and an analytic potential.
non resonant case

Now here is the same picture but with a resonant stepsize....

resonant case

You can find here the corresponding movies of the solution of the linear Schrödinger equation using a splitting method with a good stepsize and a bad stepsize.