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, n^o 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, n^o 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, n^o 1, pp. 145–194.
  
  http://dx.doi.org/10.1007/s00222-011-0332-9

Publications of the year

Articles in International Peer-Reviewed Journals

• 11A. 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, n^o 1, pp. 91-118, to appear in DCDS-S, 26 pages. [ DOI : 10.3934/dcdss.2015.8.91 ]
  
  https://hal.archives-ouvertes.fr/hal-00811490
• 12A. Abdulle, G. Vilmart, K. Zygalakis.
  
  Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics, in: SIAM Journal on Numerical Analysis, 2015, vol. 53, n^o 1, pp. 1-16, to appear in SIAM J. Numer. Anal., 23 pages. [ DOI : 10.1137/140962644 ]
  
  https://hal.archives-ouvertes.fr/hal-00965354
• 13S. 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, 2015, forthcoming. [ DOI : 10.1051/m2an/2015060 ]
  
  https://hal.archives-ouvertes.fr/hal-00850518
• 14W. Bao, L. Le Treust, F. Méhats.
  
  Dimension reduction for anisotropic Bose-Einstein condensates in the strong interaction regime, in: Nonlinearity, 2015, vol. 28, n^o 3, pp. 755-772. [ DOI : 10.1088/0951-7715/28/3/755 ]
  
  https://hal.archives-ouvertes.fr/hal-00959084
• 15L. Barletti, F. Méhats, C. Negulescu, S. Possanner.
  
  Numerical study of a quantum-diffusive spin model for two-dimensional electron gases, in: Communications in Mathematical Sciences, 2015, vol. 13, n^o 6, pp. 1347-1378. [ DOI : 10.4310/CMS2015.v13.n6.a1 ]
  
  https://hal.archives-ouvertes.fr/hal-01166320
• 16R. 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, vol. 3, n^o 1, pp. 103-132. [ DOI : 10.1007/s40072-015-0044-z ]
  
  https://hal.archives-ouvertes.fr/hal-00948570
• 17C.-E. Bréhier, E. Faou.
  
  Analysis of the Monte-Carlo error in a hybrid semi-Lagrangian scheme, in: Applied Mathematics Research eXpress, 2015, n^o 2, pp. 167-203. [ DOI : 10.1093/amrx/abv001 ]
  
  https://hal.archives-ouvertes.fr/hal-00800133
• 18F. Castella, P. Chartier, F. Méhats, A. Murua.
  
  Stroboscopic Averaging for the Nonlinear Schrödinger Equation, in: Foundations of Computational Mathematics, April 2015, vol. 15, n^o 2, pp. 519-559. [ DOI : 10.1007/s10208-014-9235-7 ]
  
  https://hal.archives-ouvertes.fr/hal-00732850
• 19F. Castella, S. Madec, Y. Lagadeuc.
  
  Global behavior of N competing species with strong diffusion: diffusion leads to exclusion, in: Applicable Analysis, January 2015. [ DOI : 10.1080/00036811.2015.1004320 ]
  
  https://hal.archives-ouvertes.fr/hal-01026195
• 20P. 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, n^o 2, pp. 211-250. [ DOI : 10.1007/s00211-014-0638-9 ]
  
  https://hal.inria.fr/hal-00850092
• 21P. Chartier, A. Murua, J. M. Sanz-Serna.
  
  Higher-order averaging, formal series and numerical integration III: error bounds, in: Foundations of Computational Mathematics, 2015, vol. 15, n^o 2, pp. 591-612. [ DOI : 10.1007/s10208-013-9175-7 ]
  
  https://hal.inria.fr/hal-00922682
• 22P.-H. Chavanis, M. Lemou, F. Méhats.
  
  Models of dark matter halos based on statistical mechanics: I. The classical King model, in: Physical Review D, 2015, vol. 91, n^o 6, 30 p. [ DOI : 10.1103/PhysRevD.91.063531 ]
  
  https://hal.archives-ouvertes.fr/hal-01094150
• 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, H. Hivert, M. Lemou.
  
  Multiscale numerical schemes for kinetic equations in the anomalous diffusion limit, in: Comptes Rendus Mathématique, 2015, vol. 353, n^o 8, pp. 755-760. [ DOI : 10.1016/j.crma.2015.05.003 ]
  
  https://hal.archives-ouvertes.fr/hal-01151518
• 25N. Crouseilles, M. Kuhn, G. Latu.
  
  Comparison of numerical solvers for anisotropic diffusion equations arising in plasma physics, in: Journal of Scientific Computing, 2015, vol. 65, n^o 3, pp. 1091-1128.
  
  https://hal.inria.fr/hal-01020955
• 26N. 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 (KRM), 2016, vol. 9, pp. 51-74.
  
  https://hal.inria.fr/hal-01090677
• 27A. Debussche, S. De Moor, M. Hofmanová.
  
  A Regularity Result for Quasilinear Stochastic Partial Differential Equations of Parabolic Type, in: SIAM Journal on Mathematical Analysis, 2015, vol. 47, n^o 2, pp. 1590-1614. [ DOI : 10.1137/130950549 ]
  
  https://hal.archives-ouvertes.fr/hal-00935892
• 28A. Debussche, S. De Moor, J. Vovelle.
  
  Diffusion limit for the radiative transfer equation perturbed by a Wiener process, in: Kinetic and related models, 2015, vol. 8, n^o 3, pp. 467-492, 27 pages. [ DOI : 10.3934/krm.2015.8.467 ]
  
  https://hal.archives-ouvertes.fr/hal-01044419
• 29A. Debussche, J. Vovelle.
  
  Invariant measure of scalar first-order conservation laws with stochastic forcing, in: Probability Theory and Related Fields, 2015, vol. 163, n^o 3-4, pp. 575-611. [ DOI : 10.1007/s00440-014-0599-z ]
  
  https://hal.archives-ouvertes.fr/hal-00872657
• 30E. Faou, T. Jézéquel.
  
  Resonant time steps and instabilities in the numerical integration of Schrödinger equations, in: Differential and integral equations, 2015, vol. 28, n^o 3-4, pp. 221-238.
  
  https://hal.archives-ouvertes.fr/hal-00905856
• 31E. Faou, A. Ostermann, K. Schratz.
  
  Analysis of exponential splitting methods for inhomogeneous parabolic equations, in: IMA Journal of Numerical Analysis, 2015, vol. 35, n^o 1, pp. 161-178. [ DOI : 10.1093/imanum/dru002 ]
  
  https://hal.archives-ouvertes.fr/hal-00769628
• 32G. Leboucher.
  
  Stroboscopic averaging of highly oscillatory nonlinear wave equations, in: Mathematical Methods in the Applied Sciences, 2015, vol. 38, n^o 9, pp. 1746-1766. [ DOI : 10.1002/mma.3183 ]
  
  https://hal.archives-ouvertes.fr/hal-01160869
• 33C. Steiner, M. Mehrenberger, N. Crouseilles, V. Grandgirard, G. Latu, F. Rozar.
  
  Gyroaverage operator for a polar mesh, in: European Physical Journal D, 2015, vol. 69, n^o 1, 221 p. [ DOI : 10.1140/epjd/e2014-50211-7 ]
  
  https://hal.inria.fr/hal-01090681

International Conferences with Proceedings

• 34E. Anceaume, F. Castella, A. Mostefaoui, B. Sericola.
  
  A Message-Passing and Adaptive Implementation of the Randomized Test-and-Set Object, in: International Symposium on Network Computing and Applications (NCA), Boston, United States, September 2015, 9 p.
  
  https://hal.archives-ouvertes.fr/hal-01190379
• 35M. Kuhn, G. Latu, N. Crouseilles, S. Genaud.
  
  Parallelization of an Advection-Diffusion Problem Arising in Edge Plasma Physics Using Hybrid MPI/OpenMP Programming, in: 21st International Conference on Parallel and Distributed Computing (Euro-Par), Vienne, Austria, J. L. Traff, S. Hunold, F. Versaci (editors), Lecture Notes in Computer Science, Springer, August 2015, vol. 9233, pp. 545-557, ISBN : 9783662480953. [ DOI : 10.1007/978-3-662-48096-0_42 ]
  
  https://hal.archives-ouvertes.fr/hal-01243542

Other Publications

• 36A. Abdulle, M. Huber, G. Vilmart.
  
  Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems, June 2015, to appear in SIAM Multiscale Model. Simul. (2015), 30 pages.
  
  https://hal.archives-ouvertes.fr/hal-01017106
• 37E. Anceaume, F. Castella, A. Mostefaoui, B. Sericola.
  
  A Message-Passing and Adaptive Implementation of the Randomized Test-and-Set Object, August 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01075650
• 38V. Banica, E. Faou, E. Miot.
  
  Collision of almost parallel vortex filaments, July 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01170929
• 39W. Bao, L. Le Treust, F. Méhats.
  
  Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime, January 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01101793
• 40F. Casas, N. Crouseilles, E. Faou, M. Mehrenberger.
  
  High-order Hamiltonian splitting for Vlasov-Poisson equations, September 2015, working paper or preprint.
  
  https://hal.inria.fr/hal-01206164
• 41F. Castella, P. Chartier, J. Sauzeau.
  
  Analysis of a time-dependent problem of mixed migration and population dynamics, 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01255118
• 42P. Chartier, L. Le Treust, F. Méhats.
  
  Uniformly accurate time-splitting schemes for NLS in the semiclassical limit, April 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01140880
• 43N. Crouseilles, H. Hivert, M. Lemou.
  
  Numerical schemes for kinetic equations in the anomalous diffusion limit. Part II: degenerate collision frequency. , December 2015, working paper or preprint.
  
  https://hal.inria.fr/hal-01245312
• 44N. 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, March 2015, working paper or preprint.
  
  https://hal.inria.fr/hal-01130002
• 45N. Crouseilles, M. Lemou, G. Vilmart.
  
  Asymptotic Preserving numerical schemes for multiscale parabolic problems, August 2015, 7 pages.
  
  https://hal.archives-ouvertes.fr/hal-01187092
• 46G. Da Prato, A. Debussche.
  
  An integral inequality for the invariant measure of a stochastic reaction–diffusion equation, 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01235038
• 47G. Da Prato, A. Debussche.
  
  Estimate for $P_{t}D$ for the stochastic Burgers equation, January 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01110454
• 48G. Da Prato, A. Debussche.
  
  Existence of the Fomin derivative of the invariant measure of a stochastic reaction–diffusion equation, 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01126707
• 49E. Faou, R. Horsin, F. Rousset.
  
  On numerical Landau damping for splitting methods applied to the Vlasov-HMF model, October 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01219115
• 50C. F. Kammerer, F. Méhats.
  
  A kinetic model for the transport of electrons in a graphen layer, June 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01160791
• 51M. Lemou.
  
  Extended Rearrangement inequalities and applications to some quantitative stability results, October 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01207621
• 52M. Lemou, A. M. Luz, F. Méhats.
  
  Nonlinear stability criteria for the HMF Model, October 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01207626
• 53F. Méhats, O. Pinaud.
  
  The quantum Liouville-BGK equation and the moment problem, 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01255137
• 54F. Méhats, C. Sparber.
  
  Dimension reduction for rotating Bose-Einstein condensates with anisotropic confinement, July 2015, 22 pages.
  
  https://hal.archives-ouvertes.fr/hal-01178431
• 55C. Steiner, M. Mehrenberger, N. Crouseilles, P. Helluy.
  
  Quasi-neutrality equation in a polar mesh, December 2015, working paper or preprint.
  
  https://hal.archives-ouvertes.fr/hal-01248179

References in notes

• 56E. Hairer.
  
  Geometric integration of ordinary differential equations on manifolds, in: BIT, 2001, vol. 41, pp. 996–1007.
• 57E. 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.
• 58E. Hairer, G. Wanner.
  
  Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics 14, 2, Springer-Verlag, Berlin, 1996.
• 59C. Lubich.
  
  A variational splitting integrator for quantum molecular dynamics, in: Appl. Numer. Math., 2004, vol. 48, pp. 355–368.
• 60C. Lubich.
  
  On variational approximations in quantum molecular dynamics, in: Mathematics of Computation, 2009.
• 61J. M. Sanz-Serna, M. P. Calvo.
  
  Numerical Hamiltonian Problems, Chapman & Hall, London, 1994.