Project-Team Ipso
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Research Program
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Bibliography

Major publications by the team in recent years
  • 1G. Andreoiu, E. Faou.
    Complete asymptotics for shallow shells, in: Asymptotic analysis, 2001, vol. 25, pp. 239-270.
  • 2F. 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.
  • 3F. 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.
  • 4P. 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
  • 5P. 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
  • 6N. 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
  • 7A. 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
  • 8E. Faou.
    Elasticity on a thin shell: Formal series solution, in: Asymptotic analysis, 2002, vol. 31, pp. 317-361.
  • 9E. 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
  • 10M. 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

Articles in International Peer-Reviewed Journals

  • 12A. Abdulle, Y. Bai, G. Vilmart.
    An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems, in: International Journal for Numerical Methods in Engineering, August 2014, vol. 99, no 7, pp. 469-486, 13 pages. [ DOI : 10.1002/nme.4682 ]
    https://hal.archives-ouvertes.fr/hal-00819565
  • 13A. Abdulle, Y. Bai, G. Vilmart.
    Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems, in: Discrete and Continuous Dynamical Systems - Series S, February 2015, vol. 8, no 1, pp. 91-118, forthcoming. [ DOI : 10.3934/dcdss.2015.8.91 ]
    https://hal.archives-ouvertes.fr/hal-00811490
  • 14A. Abdulle, G. Vilmart.
    Analysis of the finite element heterogeneous multiscale method for nonmonotone elliptic homogenization problems, in: Mathematics of Computation, 2014, vol. 83, no 286, pp. 513-536, forthcoming. [ DOI : 10.1090/S0025-5718-2013-02758-5 ]
    https://hal.archives-ouvertes.fr/hal-00746811
  • 15A. Abdulle, G. Vilmart, K. Zygalakis.
    High order numerical approximation of the invariant measure of ergodic SDEs, in: SIAM Journal on Numerical Analysis, 2014, vol. 52, no 4, pp. 1600-1622. [ DOI : 10.1137/130935616 ]
    https://hal.archives-ouvertes.fr/hal-00858088
  • 16B. Afeyan, F. Casas, N. Crouseilles, A. Dodhy, E. Faou, M. Mehrenberger, E. Sonnendrücker.
    Simulations of Kinetic Electrostatic Electron Nonlinear (KEEN) Waves with Variable Velocity Resolution Grids and High-Order Time-Splitting, in: European Physical Journal D, October 2014, vol. 68, no 10, article 295. [ DOI : 10.1140/epjd/e2014-50212-6 ]
    https://hal.archives-ouvertes.fr/hal-00977344
  • 17E. 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 ]
    https://hal.archives-ouvertes.fr/hal-00736916
  • 18V. Banica, E. Faou, E. Miot.
    Collisions of vortex filament pairs, in: Journal of Nonlinear Science, November 2014, vol. 24, no 6, 22 p.
    https://hal.inria.fr/hal-00948563
  • 19R. Belaouar, A. De Bouard, A. Debussche.
    Numerical analysis of the nonlinear Schrödinger equation with white noise dispersion, in: Stochastic Partial Differential Equations : Analysis and Computations, 2015. [ DOI : 10.1007/s40072-015-0044-z ]
    https://hal.archives-ouvertes.fr/hal-00948570
  • 20F. Castella, S. Madec.
    Coexistence phenomena and global bifurcation structure in a chemostat-like model with species-dependent diffusion rates, in: Journal of Mathematical Biology, 2014, vol. 68, no 1-2, pp. 377-415. [ DOI : 10.1007/s00285-012-0633-7 ]
    https://hal.archives-ouvertes.fr/hal-00777025
  • 21P. Chartier, N. Crouseilles, M. Lemou, F. Méhats.
    Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations, in: Numerische Mathematik, 2015, vol. 129, no 2, pp. 211-250. [ DOI : 10.1007/s00211-014-0638-9 ]
    https://hal.inria.fr/hal-00850092
  • 22P. Chartier, J. Makazaga, A. Murua, G. Vilmart.
    Multi-revolution composition methods for highly oscillatory differential equations, in: Numerische Mathematik, 2014, vol. 128, no 1, pp. 167-192. [ DOI : 10.1007/s00211-013-0602-0 ]
    https://hal.archives-ouvertes.fr/hal-00796581
  • 23N. Crouseilles, L. Einkemmer, E. Faou.
    Hamiltonian splitting for the Vlasov-Maxwell equations, in: Journal of Computational Physics, 2015, vol. 283, pp. 224-240. [ DOI : 10.1016/j.jcp.2014.11.029 ]
    https://hal.archives-ouvertes.fr/hal-00932122
  • 24N. Crouseilles, M. Giovanni.
    Asymptotic preserving schemes for the Wigner-Poisson-BGK equations in the diffusion limit, in: Computer Physics Communications, 2014, vol. 185, no 2, pp. 448-458. [ DOI : 10.1016/j.cpc.2013.06.002 ]
    https://hal.inria.fr/hal-00748134
  • 25N. Crouseilles, P. Glanc, S. A. Hirstoaga, E. Madaule, M. Mehrenberger, J. Pétri.
    A new fully two-dimensional conservative semi-Lagrangian method: applications on polar grids, from diocotron instability to ITG turbulence, in: European Physical Journal D, September 2014, vol. 68, no 9, article 252. [ DOI : 10.1140/epjd/e2014-50180-9 ]
    https://hal.archives-ouvertes.fr/hal-00977342
  • 26N. Crouseilles, P. Navaro, E. Sonnendrücker.
    Charge-conserving grid based methods for the Vlasov–Maxwell equations, in: Comptes Rendus Mécanique, 2014, vol. 342, pp. 636 - 646. [ DOI : 10.1016/j.crme.2014.06.012 ]
    https://hal.inria.fr/hal-01090678
  • 27A. Debussche, M. Romito.
    Existence of densities for the 3D Navier-Stokes equations driven by Gaussian noise, in: Probability Theory and Related Fields, 2014, vol. 158, no 3-4, pp. 575-596, 20 pages. [ DOI : 10.1007/s00440-013-0490-3 ]
    https://hal.archives-ouvertes.fr/hal-00676454
  • 28R. El Hajj, F. Méhats.
    Analysis of models for quantum transport of electrons in graphene layers, in: Mathematical Models and Methods in Applied Sciences, 2014, vol. 24, no 11, pp. 2287-2310. [ DOI : 10.1142/S0218202514500213 ]
    https://hal.archives-ouvertes.fr/hal-00850512
  • 29E. Faou, L. Gauckler, C. Lubich.
    Plane wave stability of the split-step Fourier method for the nonlinear Schrödinger equation, in: Forum of Mathematics, Sigma, 2014, vol. 2, no e5, 45 p, 34 pages. [ DOI : 10.1017/fms.2014.4 ]
    https://hal.archives-ouvertes.fr/hal-00833007
  • 30E. Faou, K. Schratz.
    Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime, in: Numerische Mathematik, 2014, vol. 126, no 3, pp. 441-469. [ DOI : 10.1007/s00211-013-0567-z ]
    https://hal.archives-ouvertes.fr/hal-00762161
  • 31A. Klak, F. Castella.
    Radiation condition at infinity for the high-frequency Helmholtz equation: optimality of a non-refocusing criterion, in: Hokkaido Mathematical Journal, 2014, vol. 43, no 3, pp. 275-325.
    https://hal.archives-ouvertes.fr/hal-00685845
  • 32G. Latu, V. Grandgirard, J. Abiteboul, N. Crouseilles, G. Dif-Pradalier, X. Garbet, P. Ghendrih, M. Mehrenberger, Y. Sarazin, E. Sonnendrücker.
    Improving conservation properties in a 5D gyrokinetic semi-Lagrangian code, in: European Journal of Physics D, 2014, vol. 68, no 11, 345 p.
    https://hal.inria.fr/hal-00966162
  • 33F. Méhats, Y. Privat, M. Sigalotti.
    On the Controllability of Quantum Transport in an Electronic Nanostructure, in: SIAM Journal on Applied Mathematics, 2014, vol. 74, no 6, pp. 1870–1894. [ DOI : 10.1137/130939328 ]
    https://hal.archives-ouvertes.fr/hal-01097162
  • 34F. Méhats, Y. Privat, M. Sigalotti.
    On the controllability of quantum transport in an electronic nanostructure, in: SIAM Journal on Applied Mathematics, December 2014, vol. 74, no 6, pp. 1870–1894. [ DOI : 10.1137/130939328 ]
    https://hal.archives-ouvertes.fr/hal-00868015
  • 35M. Roger, C. Caliot, N. Crouseilles, P. J. M. Coelho.
    A hybrid transport-diffusion model for radiative transfer in absorbing and scattering media, in: Journal of Computational Physics, 2014, vol. 275, pp. 346 - 362. [ DOI : 10.1016/j.jcp.2014.06.063 ]
    https://hal.inria.fr/hal-01090680
  • 36C. Steiner, M. Mehrenberger, N. Crouseilles, V. Grandgirard, G. Latu, F. Rozar.
    Gyroaverage operator for a polar mesh, in: European Physical Journal D, 2014, 221 p.
    https://hal.inria.fr/hal-01090681
  • 37G. Vilmart.
    Weak second order multi-revolution composition methods for highly oscillatory stochastic differential equations with additive or multiplicative noise, in: SIAM Journal on Scientific Computing, 2014, vol. 36, no 4, pp. 1770-1796, forthcoming. [ DOI : 10.1137/130935331 ]
    https://hal.archives-ouvertes.fr/hal-00856672

International Conferences with Proceedings

  • 38A. Crestetto, N. Crouseilles, M. Lemou.
    Asymptotic-Preserving scheme based on a Finite Volume/Particle-In-Cell coupling for Boltzmann- BGK-like equations in the diffusion scaling, in: Finite Volumes for Complex Applications VII, Berlin, Germany, June 2014, 827 p. [ DOI : 10.1007/978-3-319-05591-6_83 ]
    https://hal.archives-ouvertes.fr/hal-01015936

Internal Reports

  • 39N. Crouseilles, M. Kuhn, G. Latu.
    Comparison of numerical solvers for anisotropic diffusion equations arising in plasma physics, July 2014, no RR-8560.
    https://hal.inria.fr/hal-01020955

Other Publications

References in notes
  • 60E. Hairer.
    Geometric integration of ordinary differential equations on manifolds, in: BIT, 2001, vol. 41, pp. 996–1007.
  • 61E. 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.
  • 62E. Hairer, G. Wanner.
    Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics 14, 2, Springer-Verlag, Berlin, 1996.
  • 63C. Lubich.
    A variational splitting integrator for quantum molecular dynamics, in: Appl. Numer. Math., 2004, vol. 48, pp. 355–368.
  • 64C. Lubich.
    On variational approximations in quantum molecular dynamics, in: Mathematics of Computation, 2009.
  • 65J. M. Sanz-Serna, M. P. Calvo.
    Numerical Hamiltonian Problems, Chapman & Hall, London, 1994.

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