Publications of Erwan Faou


Book

Geometric numerical integration and Schrödinger equations.
European Math. Soc. 2012

cover


Papers

62.
Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to classical splitting schemes in the nonlinear Schrödinger limit pdf
with Simon Baumstark and Katharina Schratz
Math. Comp. (2017) https://doi.org/10.1090/mcom/3263
61.
Free vibrations of axisymmetric shells: Parabolic and elliptic cases pdf
with Marie Chaussade-Beaudouin, Monique Dauge and Zohar Yosibash
Asympt. Anal. 104 (2017)  1--47.
60.
Convergence of a normalized gradient algorithm for computing ground states pdf
with Tiphaine Jézéquel
IMA J. Numer. Anal. (2017) https://doi.org/10.1093/imanum/drx009
59.
High-order Hamiltonian splitting for Vlasov-Poisson equations pdf
with F. Casas, Nicolas Crouseilles and Michel Mehrenberger
Numer. Math. 135 (2017) 769--801.
58.
High frequency oscillations of first eigenmodes in axisymmetric shells as the thickness tends to zero pdf
with Marie Chaussade-Beaudouin, Monique Dauge and Zohar Yosibash
Operator Theory: Advances and Applications. 258 (2017) 89–110.
57.
Collision of almost parallel vortex filaments pdf
with Valeria Banica and Evelyne Miot
Comm. Pure Appl. Math. 70 (2017) 378--405
56.
On numerical Landau damping for splitting methods applied to the Vlasov-HMF model pdf
with Romain Horsin and Frédéric Rousset
Found. Comput. Math. (2016) https://doi.org/10.1007/s10208-016-9333-9
55.
An asymptotic preserving scheme for the relativistic Vlasov-Maxwell equations in the classical limit pdf
with Nicolas Crouseilles and Lukas Einkemmer
Comput. Phys. Comm. 209 (2016) 13-26.
54.
Landau damping in Sobolev spaces for the Vlasov-HMF model pdf
with Frédéric Rousset
Arch. Ration. Mech. Anal. 219 (2016) 887-902.
53.
The weakly nonlinear large box limit for the 2D cubic nonlinear Schrödinger equation pdf
with Pierre Germain and Zaher Hani
J. Amer. Math. Soc. 29 (2016) 915--982
http://dx.doi.org/10.1090/jams/845
52.
Fast weak-KAM integrators for separable Hamiltonian systems pdf
with Anne Bouillard and Maxime Zavidovique
Math. Comp. 85 (2016) 85-117
51.
Analysis of the Monte-Carlo error in a hybrid semi-lagrangian scheme pdf
with Charles-Edouard Bréhier
AMRX (2015) 167-203
50.
Hamiltonian splitting for the Vlasov-Maxwell equations pdf
with Nicolas Crouseilles and Lukas Einkemmer
J. Comput. Phys. 283 (2015) 224-240
49.
Resonant time steps and instabilities in the numerical integration of Schrödinger equations pdf
with Tiphaine Jézéquel
Differential and Integral Equations 28 (2015) 221-238
48.
Analysis of exponential splitting methods for inhomogeneous parabolic equations pdf
with Alexander Ostermann and Katharina Schratz
IMA J. Numer. Anal. 35 (2015) 161-178
47.
Simulations of Kinetic Electrostatic Electron Nonlinear (KEEN) Waves with Two-Grid, Variable Velocity Resolution and High-Order Time-Splitting pdf
with B. Afeyan, F. Casas, N. Crouseilles, A. Dodhy, M. Mehrenberger , E. Sonnendrücker,
EUR. Phys. J. D 68 (2014) 295
46.
Collisions of vortex filament pairs pdf
with Valeria Banica and Evelyne Miot
J. Nonlinear Sci. 24 (2014) 1262-1284
45.
Plane wave stability of the split-step Fourier method for the nonlinear Schrödinger equation pdf
with Ludwig Gauckler and Christian Lubich
Forum of Math. Sigma 2 (2014) e5 (45 pages)
44.
Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic regime pdf
with Katharina Schratz
Numer. Math. 126 (2014) 441-469
43.
Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus pdf
with Ludwig Gauckler and Christian Lubich 
Comm. PDE 38 (2013) 1123-1140
42.
A Nekhoroshev type theorem for the nonlinear Schrödinger equation on the torus pdf
with Benoît Grébert
Analysis & PDE 6 (2013) 1243-1262
41. Existence and stability of ground states for fully discrete approximations of the nonlinear Schrödinger equation pdf
with Dario Bambusi and Benoît Grébert
Numer. Math. 123 (2013) 461-492
40.
Quasi-periodic solutions of the 2D Euler equation pdf
with Nicolas Crouseilles
Asympt. Anal. 81 (2013) 31-34
39.
Weak backward error analysis for SDEs pdf
with Arnaud Debussche
SIAM J. Numer. Anal. 50 (2012) 1735-1752
38.
Energy cascades for NLS on the torus pdf
with Rémi Carles
Discrete Contin. Dyn. Syst. 32 (2012) 2063-2077
37.
On the influence of the geometry on skin effect in electromagnetism pdf
with Gabriel Caloz, Monique Dauge and Victor Péron
Comput. Methods Appl. Mech. Engrg. 200 (2011) 1053-1068
36.
Hamiltonian interpolation of splitting approximations for nonlinear PDEs pdf
with Benoît Grébert
Found. Comput. Math. 11 (2011) 381-415
35.
Reconciling alternate methods for the determination of charge distributions: A probabilistic approach to high-dimensional least-squares approximations pdf
with Nicolas Champagnat and Christophe Chipot
J. Math. Chem. 49 (2011) 296
34.
Comportement asymptotique à haute conductivité de l'épaisseur de peau en électromagnétisme pdf
with Monique Dauge and Victor Péron
C. R. Acad. Sci. Paris, Sér. I. 348 (2010) 385-390.
33.
Quasi invariant modified Sobolev norms for semi linear reversible PDEs pdf
with Benoît Grébert
Nonlinearity 23 (2010) 429-443
32.
A Regular Fast Multipole Method for geometric numerical integration of Hamiltonian systems pdf
with Philippe Chartier and Eric Darrigrand
BIT 50 (2010) 23-40
31.
Birkhoff normal form for splitting methods applied to semi linear Hamiltonian PDEs. Part I: Finite dimensional discretization pdf
with Benoît Grébert and Eric Paturel
Numer. Math. 114 (2010) 429-458
30.
Birkhoff normal form for splitting methods applied to semi linear Hamiltonian PDEs. Part II: Abstract splitting pdf
with Benoît Grébert and Eric Paturel
Numer. Math. 114 (2010) 459-490
29.
Koiter Estimate Revisited pdf
with Monique Dauge
Math. Models Methods Appl. Sci. (M3AS) 20 No 1 (2010)  1-42
28.
Modified energy for split-step methods applied to the linear Schrödinger equation pdf
with Arnaud Debussche
SIAM J. Numer. Anal. 47 (2009) 3705-3719
27.
Conservative stochastic differential equations: Mathematical and numerical analysis pdf
with Tony Lelièvre
Math. Comp. 78 (2009) 2047-2074
26.
An averaging technique for highly-oscillatory Hamiltonian problems pdf
with François Castella and Philippe Chartier
SIAM J. Numer. Anal. 47 No 4 (2009) 2808-2837
25.
Computing semi-classical quantum dynamics with Hagedorn wavepackets pdf
with Vasile Gradinaru and Christian Lubich
SIAM J. Sci. Comp. 31 No 4 (2009) 3027-3041
24.
Analysis of splitting methods for reaction-diffusion problems using stochastic calculus pdf
Math. Comp. 78 (2009) 1467-1483.
23.
Gauss-Hermite wavepacket dynamics: convergence of the spectral and pseudo-spectral approximation pdf
with Vasile Gradinaru
IMA J. Numer. Anal. 29 (2009) 1023-1045.
22.
A simple proof of the existence of adiabatic invariants for perturbed reversible problems pdf
with Philippe Chartier
J. Phys. A: Math. Theor. 41 No 47 (2008) 475204
21.
Geometric integrators for piecewise smooth Hamiltonian systems pdf
with Philippe Chartier
Math. Model. Numer. Anal. (M2AN) 42 No 2 (2008) 223-241
20.
Normal form and long time analysis of splitting schemes for the linear Schrödinger equation with small potential pdf
with Guillaume Dujardin
Numer. Math. 106 No 2 (2007) 223-262
19.
Long time behavior of splitting methods applied to the linear Schrödinger equation
with Guillaume Dujardin
C. R. Acad. Sci. Paris, Sér. I. 344 (2007) 89-92
18.
Nosé-Hoover dynamics in a shaker ps, pdf
J. Chem. Phys. 124 184104 (2006)
17.
An algebraic approach to invariant preserving integrators: The case of quadratic and Hamiltonian invariants pdf
with Philippe Chartier and Ander Murua
Numer. Math. 103 No 4 (2006) 575-590
16.
A Poisson integrator for Gaussian wavepacket dynamics ps
with Christian Lubich
Comput. Vis. Sci. 9 No 2 (2006) 45-55
15.
Long-time averaging for integrable Hamiltonian dynamics ps, pdf
with Eric Cancès, François Castella, Philippe Chartier, Claude Le Bris, Frédéric Legoll and Gabriel Turinici
Numer. Math. 100 No 2 (2005) 211-232
14.
Energy conservation with non-symplectic methods: Examples and counter-examples ps
with Ernst Hairer and Truong-Linh Pham
BIT 44 No 4 (2004) 699-709
13.
Modeling of multi-wavelength Raman fiber lasers using a new and fast algorithm pdf
with F. Leplingard, C. Martinelli, S. Borne, L. Lorcy, T. Lopez, D. Bayart, F. Castella and P. Chartier
IEEE Photonics Technology Letters 16 No 12 (2004) 2601-2603
12.
Multiscale Expansions for Linear Clamped Elliptic Shells ps, pdf
Comm. PDE 29 Vol 11 & 12 (2004) 1799-1845
11.
High-order averaging schemes with error bounds for thermodynamical properties calculations by molecular dynamics simulations INRIA Research Report
with Eric Cancès, François Castella, Philippe Chartier, Claude Le Bris, Frédéric Legoll and Gabriel Turinici
J. Chem. Phys. 121 No 21 (2004) 10346-10355
10.
Raman Laser Modeling: Mathematical and Numerical Analysis of a model ps, pdf
with François Castella, Philippe Chartier, Dominique Bayart, Florence Leplingard and Catherine Martinelli
Math. Model. Numer. Anal. (M2AN) 38 No 3 (2004) 457-475
9.
Plates and shells: Asymptotic expansions and hierarchical models abstract, pdf 
with Monique Dauge and Zohar Yosibash
Chapter 8, Vol I of the Encyclopedia for Computational Mechanics. Edited by Erwin Stein, René de Borst, Thomas J.R. Hughes (2004).
8.
Analysis of a Poisson system with boundary conditions ps
with François Castella and Philippe Chartier
C. R. Acad. Sci. Paris, Sér. I. 336 (2003) 703-708
7.
Elasticity on a thin shell: Formal series solution ps, pdf
Asympt. Anal. 31 (2002) 317-361
6.
Développements asymptotiques dans les coques elliptiques: Equations tridimensionnelles linéarisés ps, pdf
C. R. Acad. Sci. Paris, Sér. I. 333 (2001) 389-394
5.
Développements asymptotiques dans les coques elliptiques: Modèle de Koiter ps, pdf
C. R. Acad. Sci. Paris, Sér. I. 333 (2001) 139-143
4.
Complete asymptotics for shallow shells ps, pdf
with Georgiana Andreoiu
Asympt. Anal. 25 (2001) 239-270
3.
Développements asymptotiques complets pour des coques faiblement courbées encastrées ou libres ps, ps.gz
with Georgiana Andreoiu and Monique Dauge
C. R. Acad. Sci. Paris, Sér. I. 330 (2000) 523-528
2.
Elasticité linéarisée tridimensionnelle pour une coque mince: Résolution en série formelle en puissances de l'épaisseur ps, ps.gz
C. R. Acad. Sci. Paris, Sér. I. 330 (2000) 415-420
1.
Eigenmode Asymptotics in Thin Elastic Plates ps, ps.gz
with Monique Dauge, Ivica Djurdjevic and Andreas Rössle
J. Math. Pures Appl. 78 No 9 (1999) 925-964


Unpublished, preliminary versions

Resonances in long time integration of semi linear Hamiltonian PDEs pdf
with Benoît Grébert
Approximate travelling wave solutions to the 2D Euler equation on the torus pdf
with Nicolas Crouseilles
High order Runge-Kutta-Nyström splitting methods for the Vlasov-Poisson equation pdf
with Nicolas Crouseilles and Michel Mehrenberger
Sparse spectral approximations for computing polynomial functionals pdf
with Fabio Nobile and Christophe Vuillot


Thesis and HDR

PhD thesis (defended June 21, 2000)
Développements asymptotiques dans les coques minces linéairement élastiques
pdf file  --- ps file  --- ps.gz file 

Habilitation degree (defended October 16, 2007
)
Some geometrical aspects in shell theory and in numerical integration of hamiltonian systems.

pdf file of the document.

Teaching notes

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.