Members
Overall Objectives
Research Program
Application Domains
New Results
Partnerships and Cooperations
Dissemination
Bibliography
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Bibliography

Major publications by the team in recent years
[1]
G. Andreoiu, E. Faou.
Complete asymptotics for shallow shells, in: Asymptotic analysis, 2001, vol. 25, pp. 239-270.
[2]
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.
[3]
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.
[4]
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.
http://dx.doi.org/10.1007/s00211-006-0003-8
[5]
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 ]
http://hal.inria.fr/hal-00750601
[6]
N. Crouseilles, M. Mehrenberger, E. Sonnendrücker.
Conservative semi-Lagrangian schemes for Vlasov equations, in: Journal of Computational Physics, 2010, pp. 1927-1953.
http://hal.archives-ouvertes.fr/hal-00363643
[7]
A. Debussche, Y. Tsutsumi.
1D quintic nonlinear Schrödinger equation with white noise dispersion, in: Journal de Mathématiques Pures et Appliquées, 2011.
http://dx.doi.org/10.1016/j.matpur.2011.02.002
[8]
E. Faou.
Elasticity on a thin shell: Formal series solution, in: Asymptotic analysis, 2002, vol. 31, pp. 317-361.
[9]
E. Faou.
Geometric numerical integration and Schrödinger equations, Zurich Lectures in Advanced Mathematics. Zürich: European Mathematical Society (EMS). viii, 138 p. , 2012.
http://dx.doi.org/10.4171/100
[10]
M. Lemou, F. Méhats, P. Raphaël.
Orbital stability of spherical galactic models, in: Invent. Math., 2012, vol. 187, no 1, pp. 145–194.
http://dx.doi.org/10.1007/s00222-011-0332-9
Publications of the year

Doctoral Dissertations and Habilitation Theses

[11]
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.
http://hal.inria.fr/tel-00916580
[12]
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).
http://hal.inria.fr/tel-00840733

Articles in International Peer-Reviewed Journals

[13]
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/j.jcp.2013.02.009 ]
http://hal.inria.fr/hal-00739757
[14]
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 ]
http://hal.inria.fr/hal-00746811
[15]
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 ]
http://hal.inria.fr/hal-00739756
[16]
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 ]
http://hal.inria.fr/hal-00739754
[17]
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 ]
http://hal.inria.fr/hal-00650081
[18]
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 ]
http://hal.inria.fr/hal-00736916
[19]
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 ]
http://hal.inria.fr/hal-00681730
[20]
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 ]
http://hal.inria.fr/hal-00752011
[21]
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 ]
http://hal.inria.fr/hal-00759579
[22]
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.
http://hal.inria.fr/hal-00831328
[23]
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 ]
http://hal.inria.fr/hal-00922682
[24]
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 ]
http://hal.inria.fr/hal-00678848
[25]
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. ]
http://hal.inria.fr/hal-00638617
[26]
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 ]
http://hal.inria.fr/hal-00748134
[27]
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.
http://hal.inria.fr/hal-00743077
[28]
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/j.jcp.2013.04.022 ]
http://hal.inria.fr/hal-00845872
[29]
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 ]
http://hal.inria.fr/hal-00794183
[30]
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 ]
http://hal.inria.fr/hal-00676454
[31]
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.
http://hal.inria.fr/hal-00622240
[32]
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 ]
http://hal.inria.fr/hal-00762161
[33]
M. Roger, N. Crouseilles.
A dynamic multi-scale model for transient radiative transfer calculations, in: Journal of Quantitative Spectroscopy and Radiative Transfer, 2013.
http://hal.inria.fr/hal-00728874

International Conferences with Proceedings

[34]
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.
http://hal.inria.fr/hal-00923631

Scientific Books (or Scientific Book chapters)

[35]
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 ]
http://hal.inria.fr/hal-00822011
[36]
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 ]
http://hal.inria.fr/hal-00821992

Internal Reports

[37]
P. Chartier, N. Crouseilles, M. Lemou, F. Méhats.
Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations, August 2013.
http://hal.inria.fr/hal-00850092
[38]
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.
http://hal.inria.fr/hal-00848869

Other Publications

[39]
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.
http://hal.inria.fr/hal-00819565
[40]
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.
http://hal.inria.fr/hal-00811490
[41]
A. Abdulle, G. Vilmart, K. Zygalakis.
High order numerical approximation of the invariant measure of ergodic SDEs, 2013, 23 pages p.
http://hal.inria.fr/hal-00858088
[42]
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.
http://hal.inria.fr/hal-00850518
[43]
C.-E. Bréhier, E. Faou.
Analysis of the Monte-Carlo error in a hybrid semi-Lagrangian scheme, 2013.
http://hal.inria.fr/hal-00800133
[44]
C.-E. Bréhier, M. Kopec.
Approximation of the invariant law of SPDEs: error analysis using a Poisson equation for a full-discretization scheme, 2013.
http://hal.inria.fr/hal-00910323
[45]
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.
http://hal.inria.fr/hal-00796581
[46]
P. Chartier, N. J. Mauser, F. Méhats, Y. Zhang.
Solving highly-oscillatory NLS with SAM: numerical efficiency and geometric properties, 2013.
http://hal.inria.fr/hal-00850513
[47]
N. Crouseilles, L. Einkemmer, E. Faou.
Hamiltonian splitting for the Vlasov-Maxwell equations, 2014.
http://hal.inria.fr/hal-00932122
[48]
A. Debussche, S. De Moor, M. Hofmanová.
A regularity result for quasilinear stochastic partial differential equations of parabolic type, 2013.
http://hal.inria.fr/hal-00935892
[49]
A. Debussche, M. Hofmanová, J. Vovelle.
Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case, 2013.
http://hal.inria.fr/hal-00863829
[50]
A. Debussche, J. Vovelle.
Invariant measure of scalar first-order conservation laws with stochastic forcing, October 2013.
http://hal.inria.fr/hal-00872657
[51]
R. El Hajj, F. Méhats.
Analysis of models for quantum transport of electrons in graphene layers, 2013.
http://hal.inria.fr/hal-00850512
[52]
E. Faou, L. Gauckler, C. Lubich.
Plane wave stability of the split-step Fourier method for the nonlinear Schrödinger equation, 2013, 34 p.
http://hal.inria.fr/hal-00833007
[53]
E. Faou, P. Germain, Z. Hani.
The weakly nonlinear large box limit of the 2D cubic nonlinear Schrödinger equation, 2013, 68 p, 1 figure.
http://hal.inria.fr/hal-00905851
[54]
E. Faou, T. Jézéquel.
Resonant time steps and instabilities in the numerical integration of Schrödinger equations, 2013.
http://hal.inria.fr/hal-00905856
[55]
S. Fiorelli Vilmart, G. Vilmart.
Les planètes tournent-elles rond ?, November 2013.
http://interstices.info/planetes, http://hal.inria.fr/hal-00912380
[56]
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.
http://hal.inria.fr/hal-00905689
[57]
M. Kopec.
Weak backward error analysis for overdamped Langevin processes, 2013, arXiv admin note: substantial text overlap with arXiv:1105.0489 by other authors.
http://hal.inria.fr/hal-00905684
[58]
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.
http://hal.inria.fr/hal-00908498
[59]
F. Méhats, Y. Privat, M. Sigalotti.
On the controllability of quantum transport in an electronic nanostructure, 2013.
http://hal.inria.fr/hal-00868015
[60]
G. Vilmart.
Rigid body dynamics, 2013, Encyclopedia of Applied and Computational Mathematics, Springer.
http://hal.inria.fr/hal-00912388
[61]
G. Vilmart.
Weak second order multi-revolution composition methods for highly oscillatory stochastic differential equations with additive or multiplicative noise, 2013, 23 p.
http://hal.inria.fr/hal-00856672
References in notes
[62]
E. Hairer.
Geometric integration of ordinary differential equations on manifolds, in: BIT, 2001, vol. 41, pp. 996–1007.
[63]
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.
[64]
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.
[65]
C. Lubich.
A variational splitting integrator for quantum molecular dynamics, in: Appl. Numer. Math., 2004, vol. 48, pp. 355–368.
[66]
C. Lubich.
On variational approximations in quantum molecular dynamics, in: Mathematics of Computation, 2009, to appear.
[67]
J. M. Sanz-Serna, M. P. Calvo.
Numerical Hamiltonian Problems, Chapman & Hall, London, 1994.