Overall Objectives
Research Program
Application Domains
New Results
Partnerships and Cooperations
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Major publications by the team in recent years
G. Andreoiu, E. Faou.
Complete asymptotics for shallow shells, in: Asymptotic analysis, 2001, vol. 25, pp. 239-270.
F. Castella.
From the von Neumann equation to the Quantum Boltzmann equation in a deterministic framework, in: J. Stat. Phys., 2001, vol. 104–1/2, pp. 387–447.
F. Castella.
Propagation of space moments in the Vlasov-Poisson Equation and further results, in: Ann. I.H.P., Anal. NonLin., 1999, vol. 16–4, pp. 503–533.
P. Chartier, E. Faou, A. Murua.
An algebraic approach to invariant preserving integators: the case of quadratic and Hamiltonian invariants, in: Numer. Math., 2006, vol. 103, no 4, pp. 575-590.
P. Chartier, A. Murua, J. M. Sanz-Serna.
Higher-order averaging, formal series and numerical integration II: the quasi-periodic case, in: Foundations of Computational Mathematics, April 2012, vol. 12, no 4, pp. 471-508. [ DOI : 10.1007/s10208-012-9118-8 ]
N. Crouseilles, M. Mehrenberger, E. Sonnendrücker.
Conservative semi-Lagrangian schemes for Vlasov equations, in: Journal of Computational Physics, 2010, pp. 1927-1953.
A. Debussche, Y. Tsutsumi.
1D quintic nonlinear Schrödinger equation with white noise dispersion, in: Journal de Mathématiques Pures et Appliquées, 2011.
E. Faou.
Elasticity on a thin shell: Formal series solution, in: Asymptotic analysis, 2002, vol. 31, pp. 317-361.
E. Faou.
Geometric numerical integration and Schrödinger equations, Zurich Lectures in Advanced Mathematics. Zürich: European Mathematical Society (EMS). viii, 138 p. , 2012.
M. Lemou, F. Méhats, P. Raphaël.
Orbital stability of spherical galactic models, in: Invent. Math., 2012, vol. 187, no 1, pp. 145–194.
Publications of the year

Doctoral Dissertations and Habilitation Theses

M. Hofmanová.
Degenerate parabolic stochastic partial differential equations, École normale supérieure de Cachan - ENS Cachan and Charles University. Faculty of mathematics and physics. Department of metal physics (Prague), July 2013.
G. Vilmart.
Méthodes numériques géométriques et multi-échelles pour les équations différentielles (in English), École normale supérieure de Cachan - ENS Cachan, July 2013, Habilitation (HDR) soutenue le 2 juillet 2013 à l'Ecole Normale Supérieure de Cachan, antenne de Bretagne (ENS Rennes).

Articles in International Peer-Reviewed Journals

A. Abdulle, G. Vilmart.
PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise, in: Journal of Computational Physics, June 2013, vol. 242, pp. 869-888. [ DOI : 10.1016/ ]
A. Abdulle, G. Vilmart.
Analysis of the finite element heterogeneous multiscale method for nonmonotone elliptic homogenization problems, in: Math. Comp., 2014, vol. 83, pp. 513-536, to appear in Math. Comp.. [ DOI : 10.1090/S0025-5718-2013-02758-5 ]
A. Abdulle, G. Vilmart, K. Zygalakis.
Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations, in: BIT Numerical Mathematics, 2013, vol. 53, no 4, pp. 827-840. [ DOI : 10.1007/s10543-013-0430-8 ]
A. Abdulle, G. Vilmart, K. Zygalakis.
Weak second order explicit stabilized methods for stiff stochastic differential equations, in: SIAM J. Sci. Comput., April 2013, vol. 35, no 4, pp. 1792-1814. [ DOI : 10.1137/12088954X ]
E. Anceaume, F. Castella, R. Ludinard, B. Sericola.
Markov Chains Competing for Transitions: Application to Large-Scale Distributed Systems, in: Methodology and Computing in Applied Probability, June 2013, vol. 15, no 2, pp. 305–332. [ DOI : 10.1007/s11009-011-9239-6 ]
E. Anceaume, F. Castella, B. Sericola.
Analysis of a large number of Markov chains competing for transitions, in: International Journal of Systems Science, March 2014, vol. 45, no 3, pp. 232–240. [ DOI : 10.1080/00207721.2012.704090 ]
D. Bambusi, E. Faou, B. Grébert.
Existence and stability of solitons for fully discrete approximations of the nonlinear Schrödinger equation, in: Numerische Mathematik, 2013, vol. 123, pp. 461-492. [ DOI : 10.1007/s00211-012-0491-7 ]
C. Besse, R. Carles, F. Méhats.
An asymptotic preserving scheme based on a new formulation for NLS in the semiclassical limit, in: Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2013, vol. 11, no 4, pp. 1228-1260, 31 (colored) figures. [ DOI : 10.1137/120899017 ]
S. Blanes, F. Casas, P. Chartier, A. Murua.
Optimized high-order splitting methods for some classes of parabolic equations, in: Mathematics of Computation, July 2013. [ DOI : 10.1090/S0025-5718-2012-02657-3 ]
J. Charrier, A. Debussche.
Weak truncation error estimates for elliptic PDES with lorgnormal coefficients, in: Stochastic partial differential equations: analysis and computations, 2013, vol. 1, no 1, pp. 63-93.
P. Chartier, A. Murua, J. M. Sanz-Serna.
Higher-order averaging, formal series and numerical integration III: error bounds, in: Foundations of Computational Mathematics, October 2013. [ DOI : 10.1007/s10208-013-9175-7 ]
N. Crouseilles, E. Faou.
Quasi-periodic solutions of the 2D Euler equation, in: Asymptotic Analysis, 2013, vol. 81, no 1, pp. 31-34. [ DOI : 10.3233/ASY-2012-1117 ]
N. Crouseilles, E. Frenod, S. Hirstoaga, A. Mouton.
Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field, in: Mathematical Models and Methods in Applied Sciences, 2013, vol. 23, no 08, pp. 1527–1559. [ DOI : 10.1142/S0218202513500152. ]
N. Crouseilles, M. Giovanni.
Asymptotic preserving schemes for the Wigner-Poisson-BGK equations in the diffusion limit, in: Computer Physics Communications, June 2013, vol. 185, pp. 448-458. [ DOI : 10.1016/j.cpc.2013.06.002 ]
N. Crouseilles, M. Lemou, F. Méhats.
Asymptotic preserving schemes for highly oscillatory kinetic equation, in: Journal of Computational Physics, September 2013, vol. 248, pp. 287-308.
N. Crouseilles, M. Lemou, F. Méhats.
Asymptotic Preserving schemes for highly oscillatory Vlasov-Poisson equations, in: Journal of Computational Physics, 2013, vol. 248, pp. 287-308. [ DOI : 10.1016/ ]
A. Debussche, N. Fournier.
Existence of densities for stable-like driven SDE's with Holder continuous coefficients, in: Journal of Functional Analysis, 2013, vol. 264, no 8, pp. 1757-1778. [ DOI : 10.1016/j.jfa.2013.01.009 ]
A. Debussche, M. Romito.
Existence of densities for the 3D Navier-Stokes equations driven by Gaussian noise, in: Probability Theory and Related Fields, 2013, 22 p. [ DOI : 10.1007/s00440-013-0490-3 ]
E. Faou, L. Gauckler, C. Lubich.
Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus, in: Communications in Partial Differential Equations, 2013, vol. 38, pp. 1123-1140.
E. Faou, K. Schratz.
Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime, in: Numerische Mathematik, 2013, pp. 10.1007/s00211-013-0567-z. [ DOI : 10.1007/s00211-013-0567-z ]
M. Roger, N. Crouseilles.
A dynamic multi-scale model for transient radiative transfer calculations, in: Journal of Quantitative Spectroscopy and Radiative Transfer, 2013.

International Conferences with Proceedings

F. Méhats, Y. Privat, M. Sigalotti.
Shape dependent controllability of a quantum transistor, in: IEEE Conference on Decision and Control, Florence, Italy, 2013, pp. 1253-1258.

Scientific Books (or Scientific Book chapters)

P. Constantin, A. Debussche, G. P. Galdi, M. Ruzicka, G. Seregin.
H. Beirao da Veiga, F. Flandoli (editors), Topics in mathematical fluid mechanics, Lecture notes in mathematics, 2073, Springer, 2013, pp. vii-313, The series of lectures delivered at the CIME school on "Topics in mathematical fluid mechanics", in Cetraro, Italy, september 2010. [ DOI : 10.1007/978-3-642-36297-2 ]
A. Debussche.
Ergodicity results for the stochastic Navier-Stokes equations: an introduction, in: Topics in mathematical fluid mechanics, H. Beirao da Veiga, F. Flandoli (editors), Lecture notes in mathematics, 2073, Springer, 2013, pp. 23-108, Cetraro, Italy 2010. [ DOI : 10.1007/978-3-642-36297-2_2 ]

Internal Reports

P. Chartier, N. Crouseilles, M. Lemou, F. Méhats.
Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations, August 2013.
M. Kuhn, G. Latu, S. Genaud, N. Crouseilles.
Optimization and parallelization of Emedge3D on shared memory architecture, Inria, July 2013, no RR-8336, 18 p.

Other Publications

A. Abdulle, Y. Bai, G. Vilmart.
An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems, 2013, 13.
A. Abdulle, Y. Bai, G. Vilmart.
Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems, 2013, 26 p, to appear in DCDS-S.
A. Abdulle, G. Vilmart, K. Zygalakis.
High order numerical approximation of the invariant measure of ergodic SDEs, 2013, 23 pages p.
S. Balac, A. Fernandez, F. Mahé, F. Méhats, R. Texier-Picard.
The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics, August 2013.
C.-E. Bréhier, E. Faou.
Analysis of the Monte-Carlo error in a hybrid semi-Lagrangian scheme, 2013.
C.-E. Bréhier, M. Kopec.
Approximation of the invariant law of SPDEs: error analysis using a Poisson equation for a full-discretization scheme, 2013.
P. Chartier, J. Makazaga, A. Murua, G. Vilmart.
Multi-revolution composition methods for highly oscillatory differential equations, 2013, 23 p, to appear in Numerische Mathematik.
P. Chartier, N. J. Mauser, F. Méhats, Y. Zhang.
Solving highly-oscillatory NLS with SAM: numerical efficiency and geometric properties, 2013.
N. Crouseilles, L. Einkemmer, E. Faou.
Hamiltonian splitting for the Vlasov-Maxwell equations, 2014.
A. Debussche, S. De Moor, M. Hofmanová.
A regularity result for quasilinear stochastic partial differential equations of parabolic type, 2013.
A. Debussche, M. Hofmanová, J. Vovelle.
Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case, 2013.
A. Debussche, J. Vovelle.
Invariant measure of scalar first-order conservation laws with stochastic forcing, October 2013.
R. El Hajj, F. Méhats.
Analysis of models for quantum transport of electrons in graphene layers, 2013.
E. Faou, L. Gauckler, C. Lubich.
Plane wave stability of the split-step Fourier method for the nonlinear Schrödinger equation, 2013, 34 p.
E. Faou, P. Germain, Z. Hani.
The weakly nonlinear large box limit of the 2D cubic nonlinear Schrödinger equation, 2013, 68 p, 1 figure.
E. Faou, T. Jézéquel.
Resonant time steps and instabilities in the numerical integration of Schrödinger equations, 2013.
S. Fiorelli Vilmart, G. Vilmart.
Les planètes tournent-elles rond ?, November 2013.,
M. Kopec.
Weak backward error analysis for Langevin process, 2013, arXiv admin note: substantial text overlap with arXiv:1105.0489 by other authors; and substantial text overlap with arXiv:1310.2404.
M. Kopec.
Weak backward error analysis for overdamped Langevin processes, 2013, arXiv admin note: substantial text overlap with arXiv:1105.0489 by other authors.
L. Marradi, B. Afeyan, M. Mehrenberger, N. Crouseilles, C. Steiner, E. Sonnendrücker.
Vlasov on GPU (VOG Project), 2013, 20 p, 7 figures. ESAIM Proceedings 2013.
F. Méhats, Y. Privat, M. Sigalotti.
On the controllability of quantum transport in an electronic nanostructure, 2013.
G. Vilmart.
Rigid body dynamics, 2013, Encyclopedia of Applied and Computational Mathematics, Springer.
G. Vilmart.
Weak second order multi-revolution composition methods for highly oscillatory stochastic differential equations with additive or multiplicative noise, 2013, 23 p.
References in notes
E. Hairer.
Geometric integration of ordinary differential equations on manifolds, in: BIT, 2001, vol. 41, pp. 996–1007.
E. Hairer, C. Lubich, G. Wanner.
Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations, Second edition, Springer Series in Computational Mathematics 31, Springer, Berlin, 2006.
E. Hairer, G. Wanner.
Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics 14, 2, Springer-Verlag, Berlin, 1996.
C. Lubich.
A variational splitting integrator for quantum molecular dynamics, in: Appl. Numer. Math., 2004, vol. 48, pp. 355–368.
C. Lubich.
On variational approximations in quantum molecular dynamics, in: Mathematics of Computation, 2009, to appear.
J. M. Sanz-Serna, M. P. Calvo.
Numerical Hamiltonian Problems, Chapman & Hall, London, 1994.