Bibliography

Publications of the year

Articles in International Peer-Reviewed Journals

• 1S. Balac, A. Fernandez, F. Mahé, F. Méhats, R. Texier-Picard.
  
  The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics, in: ESAIM: Mathematical Modelling and Numerical Analysis, June 2016, vol. 50, n^o 4, pp. 945-964. [ DOI : 10.1051/m2an/2015060 ]
  
  https://hal.archives-ouvertes.fr/hal-00850518
• 2V. Banica, E. Faou, E. Miot.
  
  Collision of almost parallel vortex filaments, in: Communications on Pure and Applied Mathematics, 2017, vol. 70, n^o 2, pp. 378-405. [ DOI : 10.1002/cpa.21637 ]
  
  https://hal.archives-ouvertes.fr/hal-01170929
• 3W. Bao, L. Le Treust, F. Méhats.
  
  Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime, in: Kinetic and Related Models , September 2017.
  
  https://hal.archives-ouvertes.fr/hal-01101793
• 4A. Bouillard, E. Faou, M. Zavidovique.
  
  Fast Weak-Kam Integrators for separable Hamiltonian systems, in: Mathematics of Computation, 2016, vol. 85, n^o 297, pp. 85-117.
  
  https://hal.archives-ouvertes.fr/hal-00743462
• 5F. Casas, N. Crouseilles, E. Faou, M. Mehrenberger.
  
  High-order Hamiltonian splitting for Vlasov-Poisson equations, in: Numerische Mathematik, 2016.
  
  https://hal.inria.fr/hal-01206164
• 6F. Castella, S. Madec, Y. Lagadeuc.
  
  Global behavior of N competing species with strong diffusion: diffusion leads to exclusion, in: Applicable Analysis, 2016, vol. 95, n^o 2, pp. 341-372. [ DOI : 10.1080/00036811.2015.1004320 ]
  
  https://hal.archives-ouvertes.fr/hal-01026195
• 7P. Chartier, N. J. Mauser, F. Méhats, Y. Zhang.
  
  Solving highly-oscillatory NLS with SAM: numerical efficiency and geometric properties, in: Discrete and Continuous Dynamical Systems - Series S, October 2016, vol. 9, n^o 5, pp. 1327-1349. [ DOI : 10.3934/dcdss.2016053 ]
  
  https://hal.archives-ouvertes.fr/hal-00850513
• 8P. Chartier, F. Méhats, M. Thalhammer, Y. Zhang.
  
  Improved error estimates for splitting methods applied to highly-oscillatory nonlinear Schrödinger equations, in: Mathematics of Computation, 2016, vol. 85, n^o 302, pp. 2863-2885. [ DOI : 10.1090/mcom/3088 ]
  
  https://hal.archives-ouvertes.fr/hal-01373280
• 9A. Chernov, A. Debussche, F. Nobile.
  
  Numerical methods for random and stochastic partial differential equations, in: Stochastics and Partial Differential Equations Analysis and Computations, March 2016, vol. 4, n^o 1, pp. 1-2. [ DOI : 10.1007/s40072-016-0073-2 ]
  
  https://hal.archives-ouvertes.fr/hal-01297401
• 10P. J. Coelho, N. Crouseilles, P. Pereira, M. Roger.
  
  Multi-scale methods for the solution of the radiative transfer equation, in: Journal of Quantitative Spectroscopy and Radiative Transfer, March 2016, vol. 172, pp. 36-49. [ DOI : 10.1016/j.jqsrt.2015.10.001 ]
  
  https://hal.archives-ouvertes.fr/hal-01274991
• 11N. Crouseilles, G. Dimarco, M. Lemou.
  
  Asymptotic preserving and time diminishing schemes for rarefied gas dynamic, in: Kinetic and Related Models , 2016.
  
  https://hal.inria.fr/hal-01392412
• 12N. Crouseilles, G. Dimarco, M.-H. Vignal.
  
  Multiscale schemes for the BGK-Vlasov-Poisson system in the quasi-neutral and fluid limits. Stability analysis and first order schemes, in: Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2016, vol. 14, n^o 1, pp. 65-95. [ DOI : 10.1137/140991558 ]
  
  https://hal.inria.fr/hal-01090676
• 13N. Crouseilles, L. Einkemmer, E. Faou.
  
  An asymptotic preserving scheme for the relativistic Vlasov–Maxwell equations in the classical limit, in: Computer Physics Communications, December 2016, vol. 209.
  
  https://hal.inria.fr/hal-01283779
• 14N. Crouseilles, H. Hivert, M. Lemou.
  
  Numerical schemes for kinetic equations in the anomalous diffusion limit. Part II: degenerate collision frequency. , in: SIAM Journal on Scientific Computing, 2016, vol. 38, n^o 4.
  
  https://hal.inria.fr/hal-01245312
• 15N. Crouseilles, H. Hivert, M. Lemou.
  
  Numerical schemes for kinetic equations in the diffusion and anomalous diffusion limits. Part I: the case of heavy-tailed equilibrium, in: SIAM J. Sci. Comput., 2016, vol. 38, n^o 2, pp. 737-764.
  
  https://hal.inria.fr/hal-01130002
• 16N. Crouseilles, M. Lemou, F. Méhats, X. Zhao.
  
  Uniformly accurate forward semi-Lagrangian methods for highly oscillatory Vlasov-Poisson equations, in: Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2017.
  
  https://hal.inria.fr/hal-01286947
• 17N. Crouseilles, M. Lemou, S. Raghurama Rao, A. Ruhi, M. Sekhar.
  
  Asymptotic Preserving scheme for a kinetic model describing incompressible fluids, in: Kinetic and Related Models , 2016, vol. 9, pp. 51-74.
  
  https://hal.inria.fr/hal-01090677
• 18N. Crouseilles, M. Lemou, G. Vilmart.
  
  Asymptotic Preserving numerical schemes for multiscale parabolic problems, in: Comptes Rendus Mathématique, 2016, vol. 354, n^o 3, pp. 271-276, 7 pages. [ DOI : 10.1016/j.crma.2015.11.010 ]
  
  https://hal.archives-ouvertes.fr/hal-01187092
• 19G. Da Prato, A. Debussche.
  
  An integral inequality for the invariant measure of a stochastic reaction–diffusion equation, in: Journal of Evolution Equations, 2016, pp. 1-18. [ DOI : 10.1007/s00028-016-0349-z ]
  
  https://hal.archives-ouvertes.fr/hal-01235038
• 20G. Da Prato, A. Debussche.
  
  Estimate for $P_{t}D$ for the stochastic Burgers equation, in: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2016, vol. 52, n^o 3, pp. 1248-1258. [ DOI : 10.1214/15-AIHP685 ]
  
  https://hal.archives-ouvertes.fr/hal-01110454
• 21A. Debussche, S. De Moor, J. Vovelle.
  
  Diffusion limit for the radiative transfer equation perturbed by a Markovian process, in: Asymptotic Analysis, 2016, vol. 98, n^o 1-2, pp. 31-58, 24 pages. arXiv admin note: text overlap with arXiv:1311.4743. [ DOI : 10.3233/ASY-161360 ]
  
  https://hal.archives-ouvertes.fr/hal-01044426
• 22A. Debussche, M. Hofmanová, J. Vovelle.
  
  Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case, in: The Annals of Probability, 2016, vol. 44, n^o 3, pp. 1916-1955. [ DOI : 10.1214/15-AOP1013 ]
  
  https://hal.archives-ouvertes.fr/hal-00863829
• 23E. Faou, P. Germain, Z. Hani.
  
  The weakly nonlinear large-box limit of the 2D cubic nonlinear Schrödinger equation, in: Journal of the American Mathematical Society, 2016, vol. 29, n^o 4, pp. 915-982, 68 pages, 1 figure. [ DOI : 10.1090/jams/845 ]
  
  https://hal.archives-ouvertes.fr/hal-00905851
• 24E. Faou, R. Horsin, F. Rousset.
  
  On numerical Landau damping for splitting methods applied to the Vlasov-HMF model, in: Foundations of Computational Mathematics, 2016, 38 p. [ DOI : 10.1007/s10208-016-9333-9 ]
  
  https://hal.archives-ouvertes.fr/hal-01219115
• 25E. Faou, F. Rousset.
  
  Landau damping in Sobolev spaces for the Vlasov-HMF model, in: Archive for Rational Mechanics and Analysis, 2016, vol. 219, n^o 2, pp. 887-902. [ DOI : 10.1007/s00205-015-0911-9 ]
  
  https://hal.archives-ouvertes.fr/hal-00956595
• 26S. Fournais, L. Le Treust, N. Raymond, J. Van Schaftingen.
  
  Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian, in: Journal of the Mathematical Society of Japan, 2017.
  
  https://hal.archives-ouvertes.fr/hal-01285311
• 27F. M. Hamelin, F. Castella, V. Doli, B. Marçais, V. Ravigné, M. A. Lewis.
  
  Mate Finding, Sexual Spore Production, and the Spread of Fungal Plant Parasites, in: Bulletin of Mathematical Biology, April 2016, vol. 78, n^o 4, pp. 695-712. [ DOI : 10.1007/s11538-016-0157-1 ]
  
  https://hal.archives-ouvertes.fr/hal-01313012
• 28M. Lemou.
  
  Extended Rearrangement inequalities and applications to some quantitative stability results, in: Communications in Mathematical Physics, 2016, vol. 348, n^o 2, pp. 695-727. [ DOI : 10.1007/s00220-016-2750-4 ]
  
  https://hal.archives-ouvertes.fr/hal-01207621
• 29F. Méhats, C. Sparber.
  
  Dimension reduction for rotating Bose-Einstein condensates with anisotropic confinement, in: Discrete and Continuous Dynamical Systems - Series A, 2016, vol. 36, n^o 9, pp. 5097-5118, 22 pages. [ DOI : 10.3934/dcds.2016021 ]
  
  https://hal.archives-ouvertes.fr/hal-01178431

Scientific Books (or Scientific Book chapters)

• 30M. Chaussade-Beaudouin, M. Dauge, E. Faou, Z. Yosibash.
  
  High frequency oscillations of first eigenmodes in axisymmetric shells as the thickness tends to zero, in: Operator Theory Advances and Application, Recent Trends in Operator Theory and Partial Differential Equations - The Roland Duduchava Anniversary Volume, Birkhäuser/Springer, 2017, vol. 258, pp. 89-110.
  
  https://hal.archives-ouvertes.fr/hal-01278861

Internal Reports

• 31E. Faou, E. Hairer, M. Hochbruck, C. Lubich.
  
  Geometric Numerical Integration, Mathematisches Forschungsinstitut Oberwolfach, 2016, n^o 18/2016, pp. 869 - 948, Oberwolfach Reports, vol. 13 n° 1 (2016). [ DOI : 10.4171/OWR/2016/18 ]
  
  https://hal.archives-ouvertes.fr/hal-01403326

Other Publications

• 32N. Arrizabalaga, L. Le Treust, N. Raymond.
  
  On the MIT bag model: self-adjointness and non-relativistic limit, July 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01343717
• 33I. Bailleul, A. Debussche, M. Hofmanova.
  
  Quasilinear generalized parabolic Anderson model, 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01389489
• 34S. Baumstark, E. Faou, K. Schratz.
  
  Uniformly accurate exponential-type integrators for klein-gordon equations with asymptotic convergence to classical splitting schemes in the nonlinear schroedinger limit, June 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01331949
• 35F. Castella, P. Chartier, J. Sauzeau.
  
  A formal series approach to the center manifold theorem, April 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01279715
• 36S. Cerrai, A. Debussche.
  
  Large deviations for the two-dimensional stochastic Navier-Stokes equation with vanishing noise correlation, 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01287049
• 37P. Chartier, N. Crouseilles, M. Lemou.
  
  An averaging technique for transport equations, September 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01374655
• 38P. Chartier, N. Crouseilles, M. Lemou.
  
  Averaging of highly-oscillatory transport equations, November 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01396685
• 39P. Chartier, L. Le Treust, F. Méhats.
  
  Uniformly accurate time-splitting methods for the semiclassical Schrödinger equationPart 2 : Numerical analysis of the linear case, January 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01257753
• 40P. Chartier, M. Lemou, F. Méhats.
  
  Highly-oscillatory evolution equations with multiple frequencies: averaging and numerics, October 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01281950
• 41M. Chaussade-Beaudouin, M. Dauge, E. Faou, Z. Yosibash.
  
  Free Vibrations of Axisymmetric Shells: Parabolic and Elliptic cases, January 2017, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01264125
• 42N. Crouseilles, S. Jin, M. Lemou.
  
  Nonlinear Geometric Optics method based multi-scale numerical schemes for highly-oscillatory transport equations, May 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01323721
• 43N. Crouseilles, M. Lemou, F. Méhats, X. Zhao.
  
  Uniformly accurate Particle-In-Cell method for the long time two-dimensional Vlasov-Poisson equation with strong magnetic field, December 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01418976
• 44A. Debussche, H. Weber.
  
  The Schrödinger equation with spatial white noise potential, 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01411205
• 45E. Faou, T. Jézéquel.
  
  Convergence of a normalized gradient algorithm for computing ground states, March 2016, working paper or preprint.
  
  https://hal.inria.fr/hal-01284679
• 46R. L. Frank, F. Méhats, C. Sparber.
  
  Averaging of nonlinear Schrödinger equations with strong magnetic confinement, 2016, 12 pages.
  
  https://hal.archives-ouvertes.fr/hal-01397325
• 47M. Lemou, F. Méhats, X. Zhao.
  
  Uniformly accurate numerical schemes for the nonlinear dirac equation in the nonrelativistic limit regime, May 2016, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01313976

References in notes

• 48E. Hairer.
  
  Geometric integration of ordinary differential equations on manifolds, in: BIT, 2001, vol. 41, pp. 996–1007.
• 49E. 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.
• 50E. Hairer, G. Wanner.
  
  Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics 14, 2, Springer-Verlag, Berlin, 1996.
• 51C. Lubich.
  
  A variational splitting integrator for quantum molecular dynamics, in: Appl. Numer. Math., 2004, vol. 48, pp. 355–368.
• 52C. Lubich.
  
  On variational approximations in quantum molecular dynamics, in: Mathematics of Computation, 2009.
• 53J. M. Sanz-Serna, M. P. Calvo.
  
  Numerical Hamiltonian Problems, Chapman & Hall, London, 1994.