Bibliography

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, n^o 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, n^o 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 ${\Phi }_d^{2n}$ 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, n^o 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, n^o 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, n^o 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, n^o 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 $H^2$-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, n^o 2, pp. 477-503. [ DOI : 10.1007/s10444-017-9557-5 ]
  https://hal.archives-ouvertes.fr/hal-01576947
• 18T. Wang, X. Zhao.
  Unconditional $L^{\infty }$-convergence of two compact conservative finite difference schemes for the nonlinear Schrödinger equation in multi-dimensions, in: Calcolo, September 2018, vol. 55, n^o 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, n^o 3, pp. 405-427, https://arxiv.org/abs/1611.01550 - 24 pages, 2 figures.
  https://hal.archives-ouvertes.fr/hal-01397333

Other Publications

• 20P. Alphonse, J. Bernier.
  Smoothing Properties of Fractional Ornstein-Uhlenbeck Semigroups and Null-Controllability, October 2018, https://arxiv.org/abs/1810.02629 - working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01888835
• 21N. Ayi, E. Faou.
  Analysis of an asymptotic preserving scheme for stochastic linear kinetic equations in the diffusion limit, 2018, https://arxiv.org/abs/1803.06130 - working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01734515
• 22J. Bernier.
  Bounds on the growth of high discrete Sobolev norms for the cubic discrete nonlinear Schrödinger equations on $h\mathbb{Z}$, November 2018, https://arxiv.org/abs/1805.02468 - working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01785953
• 23J. Bernier, E. Faou.
  Existence and stability of traveling waves for discrete nonlinear Schroedinger equations over long times, May 2018, https://arxiv.org/abs/1805.03578 - working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01788398
• 24J. Bernier, E. Faou, B. Grebert.
  Rational normal forms and stability of small solutions to nonlinear Schrödinger equations, December 2018, https://arxiv.org/abs/1812.11414 - working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01965082
• 25C. Buet, B. Despres, G. Morel.
  Trefftz Discontinuous Galerkin basis functions for a class of Friedrichs systems coming from linear transport, December 2018, working paper or preprint.
  https://hal.sorbonne-universite.fr/hal-01964528
• 26P. Chartier, N. Crouseilles, M. Lemou, F. Méhats, X. Zhao.
  Uniformly accurate methods for Vlasov equations with non-homogeneous strong magnetic field, February 2018, working paper or preprint.
  https://hal.inria.fr/hal-01703477
• 27P. Chartier, M. Lemou, F. Méhats, G. Vilmart.
  Highly-oscillatory problems with time-dependent vanishing frequency, July 2018, https://arxiv.org/abs/1807.07835 - working paper or preprint.
  https://hal.inria.fr/hal-01845614
• 28A. Crestetto, N. Crouseilles, G. Dimarco, M. Lemou.
  Time diminishing schemes (TDS) for kinetic equations in the diffusive scaling, July 2018, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01849671
• 29N. Crouseilles, S. Jin, M. Lemou, F. Méhats.
  A micro-macro method for a kinetic graphene model in one-space dimension, September 2018, working paper or preprint.
  https://hal.inria.fr/hal-01883237
• 30E. Faou.
  Linearized wave turbulence convergence results for three-wave systems, September 2018, https://arxiv.org/abs/1805.11269 - working paper or preprint.
  https://hal.inria.fr/hal-01801810
• 31M. Fontaine, M. Lemou, F. Méhats.
  Stable Ground States for the HMF Poisson Model, December 2018, https://arxiv.org/abs/1709.02234 - working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01582008
• 32N. J. Mauser, Y. Zhang, X. Zhao.
  On the rotating nonlinear Klein-Gordon equation: non-relativistic limit and numerical methods, December 2018, working paper or preprint.
  https://hal.archives-ouvertes.fr/hal-01956352

• 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.