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Bibliography

Publications of the year

Articles in International Peer-Reviewed Journals

  • 1Y. A. Barsamian, J. Bernier, S. A. Hirstoaga, M. Mehrenberger.

    Verification of 2D × 2D and two-species Vlasov-Poisson solvers, in: ESAIM: Proceedings and Surveys, 2018, vol. 63, pp. 78-108.

    https://hal.archives-ouvertes.fr/hal-01668744
  • 2S. Baumstark, E. Faou, K. Schratz.

    Uniformly accurate exponential-type integrators for Klein-Gordon equations with asymptotic convergence to classical splitting schemes in the nonlinear Schrödinger limit, in: Mathematics of Computation, 2018, vol. 87, no 311, pp. 1227-1254, https://arxiv.org/abs/1606.04652. [ DOI : 10.1090/mcom/3263 ]

    https://hal.archives-ouvertes.fr/hal-01331949
  • 3C.-E. Bréhier, A. Debussche.

    Kolmogorov Equations and Weak Order Analysis for SPDES with Nonlinear Diffusion Coefficient, in: Journal de Mathématiques Pures et Appliquées, 2018, vol. 116, pp. 193-254, https://arxiv.org/abs/1703.01095. [ DOI : 10.1016/j.matpur.2018.08.010 ]

    https://hal.archives-ouvertes.fr/hal-01481966
  • 4F. Castella, P. Chartier, J. Sauzeau.

    A formal series approach to the center manifold theorem, in: Foundations of Computational Mathematics, 2018, vol. 18, no 6, pp. 1397–1434. [ DOI : 10.1007/s10208-017-9371-y ]

    https://hal.inria.fr/hal-01279715
  • 5S. Cerrai, A. Debussche.

    Large deviations for the dynamic Φd2n model, in: Applied Mathematics and Optimization, 2018, pp. 1–22. [ DOI : 10.1007/s00245-017-9459-4 ]

    https://hal.archives-ouvertes.fr/hal-01518465
  • 6S. Cerrai, A. Debussche.

    Large deviations for the two-dimensional stochastic Navier-Stokes equation with vanishing noise correlation, in: Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2018, pp. 1-29.

    https://hal.archives-ouvertes.fr/hal-01942681
  • 7P. Chartier, N. Crouseilles, X. Zhao.

    Numerical methods for the two-dimensional Vlasov–Poisson equation in the finite Larmor radius approximation regime, in: Journal of Computational Physics, December 2018, vol. 375, pp. 619-640. [ DOI : 10.1016/j.jcp.2018.09.007 ]

    https://hal.archives-ouvertes.fr/hal-01920104
  • 8P. Chartier, L. Le Treust, F. Méhats.

    Uniformly accurate time-splitting methods for the semiclassical linear Schrödinger equation, in: ESAIM: Mathematical Modelling and Numerical Analysis, 2018, pp. 1-30, https://arxiv.org/abs/1601.04825.

    https://hal.archives-ouvertes.fr/hal-01257753
  • 9P. Chartier, M. Lemou, F. Méhats, G. Vilmart.

    A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations, in: Foundations of Computational Mathematics, 2018.

    https://hal.archives-ouvertes.fr/hal-01666472
  • 10A. Crestetto, N. Crouseilles, M. Lemou.

    A particle micro-macro decomposition based numerical scheme for collisional kinetic equations in the diffusion scaling, in: Communications in Mathematical Sciences, 2018, vol. 16, no 4, pp. 887-911. [ DOI : 10.4310/CMS.2018.v16.n4.a1 ]

    https://hal.archives-ouvertes.fr/hal-01439288
  • 11N. Crouseilles, L. Einkemmer, M. Prugger.

    An exponential integrator for the drift-kinetic model, in: Computer Physics Communications, 2018, vol. 224, pp. 144-153, https://arxiv.org/abs/1705.09923. [ DOI : 10.1016/j.cpc.2017.11.003 ]

    https://hal.archives-ouvertes.fr/hal-01538450
  • 12N. Crouseilles, S. A. Hirstoaga, X. Zhao.

    Multiscale Particle-in-Cell methods and comparisons for the long-time two-dimensional Vlasov-Poisson equation with strong magnetic field, in: Computer Physics Communications, 2018, vol. 222, pp. 136-151. [ DOI : 10.1016/j.cpc.2017.09.027 ]

    https://hal.archives-ouvertes.fr/hal-01496854
  • 13A. Debussche, H. Weber.

    The Schrödinger equation with spatial white noise potential, in: Electronic Journal of Probability, 2018, vol. 23, pp. 1-16.

    https://hal.archives-ouvertes.fr/hal-01942694
  • 14E. Faou, R. Horsin, F. Rousset.

    On numerical Landau damping for splitting methods applied to the Vlasov-HMF model, in: Foundations of Computational Mathematics, 2018, vol. 18, no 1, pp. 97-134, https://arxiv.org/abs/1510.06555. [ DOI : 10.1007/s10208-016-9333-9 ]

    https://hal.archives-ouvertes.fr/hal-01219115
  • 15E. Faou, T. Jézéquel.

    Convergence of a normalized gradient algorithm for computing ground states, in: IMA Journal of Numerical Analysis, 2018, vol. 38, no 1, pp. 360-376, https://arxiv.org/abs/1603.02658. [ DOI : 10.1093/imanum/drx009 ]

    https://hal.inria.fr/hal-01284679
  • 16A. Soffer, X. Zhao.

    Modulation equations approach for solving vortex and radiation in nonlinear Schrodinger equation, in: IMA Journal of Applied Mathematics, 2018, vol. 83, no 3, pp. 496–513, https://arxiv.org/abs/1605.00888 - 14 pages, 7 figures. [ DOI : 10.1093/imamat/hxy016 ]

    https://hal.archives-ouvertes.fr/hal-01328959
  • 17T. Wang, X. Zhao, J. Jiang.

    Unconditional and optimal H2-error estimates of two linear and conservative finite difference schemes for the Klein-Gordon-Schrödinger equation in high dimensions, in: Advances in Computational Mathematics, 2018, vol. 44, no 2, pp. 477-503. [ DOI : 10.1007/s10444-017-9557-5 ]

    https://hal.archives-ouvertes.fr/hal-01576947
  • 18T. Wang, X. Zhao.

    Unconditional L∞-convergence of two compact conservative finite difference schemes for the nonlinear Schrödinger equation in multi-dimensions, in: Calcolo, September 2018, vol. 55, no 3.

    https://hal.archives-ouvertes.fr/hal-01940369
  • 19Y. Wang, X. Zhao.

    Symmetric high order Gautschi-type exponential wave integrators pseudospectral method for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime, in: International Journal of Numerical Analysis and Modeling, 2018, vol. 15, no 3, pp. 405-427, https://arxiv.org/abs/1611.01550 - 24 pages, 2 figures.

    https://hal.archives-ouvertes.fr/hal-01397333

Other Publications

References in notes
  • 33C. Birdsall, A. Langdon.

    Plasmas physics via computer simulations, Taylor and Francis, New York, 2005.
  • 34A. Brizard, T. Hahm.

    Foundations of nonlinear gyrokinetic theory, in: Reviews of Modern Physics, 2007, vol. 79.
  • 35J. Carr.

    Applications of Centre Manifold Theory, in: Applied Mathematical Sciences Series, 1981, vol. 35.
  • 36P. Chartier, N. Crouseilles, M. Lemou, F. Méhats.

    Uniformly accurate numerical schemes for highly-oscillatory Klein-Gordon and nonlinear Schrödinger equations, in: Numer. Math., 2015, vol. 129, pp. 513–536.
  • 37P. Chartier, A. Murua, J. Sanz-Serna.

    Higher-order averaging, formal series and numerical integration III: error bounds, in: Foundation of Comput. Math., 2015, vol. 15, pp. 591–612.
  • 38A. Debussche, J. Vovelle.

    Diffusion limit for a stochastic kinetic problem, in: Commun. Pure Appl. Anal., 2012, vol. 11, pp. 2305–2326.
  • 39E. Faou, F. Rousset.

    Landau damping in Sobolev spaces for the Vlasov-HMF model, in: Arch. Ration. Mech. Anal., 2016, vol. 219, pp. 887–902.
  • 40E. 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.
  • 41S. Jin, H. Lu.

    An Asymptotic-Preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings, in: J. Comp. Phys., 2017, vol. 334, pp. 182–206.
  • 42M. Lemou, F. Méhats, P. Raphaël.

    Orbital stability of spherical galactic models, in: Invent. Math., 2012, vol. 187, pp. 145–194.
  • 43C. Mouhot, C. Villani.

    On Landau damping, in: Acta Math., 2011, vol. 207, pp. 29–201.
  • 44S. Nazarenko.

    Wave turbulence, Springer-Verlag, 2011.
  • 45L. Perko.

    Higher order averaging and related methods for perturbed periodic and quasi-periodic systems, in: SIAM J. Appl. Math., 1969, vol. 17, pp. 698–724.


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