Publications
- On the approximation of the von Neumann equation in the semi-classical limit. Part II : numerical analysis,
preprint (2024), with F. Golse.
- On the approximation of the von Neumann equation in the semi-classical limit. Part I : numerical algorithm,
preprint (2024), with F. Golse.
- Trend
to equilibrium and diffusion limit for the
inertial Kuramoto-Sakaguchi equation,
preprint (2023), with M. Kang.
- A
structure and asymptotic preserving scheme for
the Vlasov-Poisson-Fokker-Planck model,
J. Comput. Physics
(2024), with A. Blaustein.
- On a
discrete framework of hypocoercivity for
kinetic equations, Mathematics of
Computation, 93 (2024),
with A. Blaustein.
- On the convergence of discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system, SIAM J. Numer. Analysis (2023), no. 5,
with M. Bessemoulin-Chatard.
- Asymptotically
preserving particle methods for strongly
magnetized plasmas in a torus, J. Comput. Physics, vol. 480 (2023) #112015,
with L. M. Rodrigues.
- Concentration
phenomena in Fitzhugh-Nagumo's equations: a
mesoscopic approach, SIAM J. Math. Anal. 55 (2023), no. 1, 367–404,
with A. Blaustein.
- Fokker-Planck
multi-species equations in the adiabatic
asymptotics,
J. Comput. Phys. 471 (2022), Paper No. 111642,
28 pp,
with C. Negulescu.
- On the
stability of conservative discontinuous
Galerkin/Hermite spectral methods for the
Vlasov-Poisson system,
J. Comput. Phys. 451 (2022), with M. Bessemoulin-Chatard.
- Conservative
discontinuous Galerkin/Hermite Spectral Method for
the Vlasov-Poisson System,
Commun. Appl. Math. Comput. 4 (2022), with
T. Xiong.
- Convergence Analysis of Asymptotic Preserving Schemes for Strongly Magnetized plasmas, Numer. Math. 149 (2021), with L. M. Rodrigues and H. Zakerzadeh.
-
Asymptotic preserving schemes for the FitzHugh-Nagumo transport
equation with strong local interactions, BIT Numerical Algorithm, (2021), with J. Crevat.
- Asymptotics of the three dimensional Vlasov equation in the large magnetic field limit,
Journal Ecole Polytechnique, Tome 7, (2020), pp. 1009-1067, with L. M. Rodrigues.
- Convergence of a Finite Volume
Scheme for a System of Interacting Species with
Cross-Diffusion, Numerische Mathematik, 145 (2020),
pp. 473-511, with J. A. Carrillo
and M. Schmidtchen.
- Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system,
SIAM J. Math. Analysis, 51 (2019), pp. 346–373, with J. Crevat and G. Faye.
- A Hybrid Discontinuous Galerkin
Scheme for Multi-scale Kinetic Equations,
J. Comput. Physics, 372 (2018), pp. 841–863, with T. Xiong.
- On the Vlasov-Maxwell system
with a strong magnetic field SIAM J. Applied Mathematics, vol 78, (2018), pp. 1030-1055, with T. Xiong and E. Sonnendrücker.
- A p-adaptive local discontinuous
Galerkin level set method for Willmore flow, J.
Sci. Computing, 76 (2018), no. 2, pp. 1148–1167, with R. Guo.
- Discontinuous Galerkin methods
for a kinetic model of self-organized dynamics,
Math. Meth. Model. Applied Sciences, 28, no. 6 (2018), pp. 1171–1197, with C. W. Shu.
- Asymptotically preserving
Particle-In-Cell methods for inhomogeneous stongly magnetized
plasmas, SIAM J. Numer. Analysis, 55 (2017), no. 5, pp. 2416–2443, with L. M. Rodrigues.
- On a three dimensional vision
based collision avoidance model, J. Stat
Physics, vol. 168, (2017) pp. 680-716, with C. Parzani.
- A finite volume method for
driven-boundary convection-diffusion equations with relative entropy
structure, Numerische Mathematik, 137 (2017), no. 3,
pp. 535–577, with M. Herda.
- On the
asymptotic limit of the three dimensional Vlasov-Poisson system for
large magnetic field : formal derivation.
J. Stat. Physics, vol. 165 (2016), pp. 765--784, with P. Degond.
- Efficient high order
semi-implicit time discretization and local discontinuous Galerkin
methods for highly nonlinear PDEs, J. Sci. Computing, 68
(2016), no. 3, pp. 1029–1054, with R. Guo and Y. Xu.
- Asymptotically stable particle-in-cell methods for the
Vlasov-Poisson system with a strong external magnetic
field, SIAM J. Numer. Analysis, vol. 54 (2016),
pp. 1120-1146, with L. M. Rodrigues.
- High order time discretization
for backward semi-Lagrangian methods, Journal of
Computational and Applied Mathematics, vol 303, (2016) pp. 171–188, with C. Prouveur.
- On steady-state preserving spectral methods for homogeneous Boltzmann equations,
Comptes Rendus Mathematiques, vol. 353, issue: 4 (2015),
pp. 309-314, with L. Pareschi and T. Rey.
- A hierarchy of hybrid numerical methods for multi-scale kinetic equations, SIAM J. Sci. Computing, 37 issue 3, pp. A1218-A1247 (2015), with T. Rey.
- High order semi-Implicit schemes
for time dependent partial differential equations,
J. Sci. Comput. 68 (2016), no. 3, pp. 975–1001, with S. Boscarino and G. Russo.
- On discrete functional
inequalities for some finite volume schemes, IMA
J. Num. Analysis, 35 no. 3 (2015), pp. 1125–-1149, with M. Bessemoulin-Chatard and C. Chainais-Hillairet Click here for the link on HAL.
- Conservative and
non-conservative methods based on Hermite weighted
essentially-non-oscillatory reconstruction for Vlasov
equations, J. Comput. Physics, vol. 279 (2014) pp. 18-36, with C. Yang.
- Numerical Simulations of Kinetic
Models for chemotaxis, SIAM J. Scientific Computing,
vol. 36, no. 3 (2014), with C. Yang.
- Analysis of an Asymptotic
Preserving Scheme for Relaxation Systems, ESAIM -
Math. Mod. Num. Anal. vol. 47 (2013), pp. 609--633, with A
Rambaud.
Click here
for the link on HAL
- Inverse Lax-Wendroff methods for boundary conditions of Boltzmann type models, J. Comput. Physics, vol 245, pp. 43-61 (2013)with C. Yang Click here for the link on HAL
- A Rescaling Velocity Method for Dissipative Kinetic Equations - Applications to Granular Media., J. Comput. Physics, vol 248, pp. 177-199 (2013) with Th. Rey Click here for the link on HAL
- A finite volume scheme for nonlinear degenerate parabolic equations, SIAM J. Scientific Computing, vol. 34, no. 5 (2012), pp. 559--583, with M. Bessemoulin-Chatard Click here for the link on HAL
- On deterministic approximation of the Boltzmann equation in a bounded domain, Multiscale Modeling and Simulation vol 10 issue 3 (2012), pp. 792--817. Click here for the link on HAL
- Numerical study of a nonlinear heat equation for plasma physics, International Journal of Computer Mathematics vol. 89 issue 8 (2012), pp. 1060--1082, with C. Negulescu and C. Yang. Click here for the link on HAL
- A Numerical Scheme for the Quantum Boltzmann Equation Efficient in the Fluid Regime, ESAIM - Math. Mod. Num. Anal. vol. 46 (2012), pp. 443--463, with J. Hu and S. Jin. Click here for the link on HAL
- Analysis of a High Order Finite Volume Scheme for the Vlasov-Poisson System, DCDS-S, vol. 5 (2012), pp. 283--305, with R. Duclous and B. Dubroca
- An Asymptotic Preserving Scheme
for the ES-BGK model pof the Boltzmann
equation, J. Sci. Computing, vol. 46, Number 2 (2011),
pp. 204-224, with S. Jin.
- Analysis of spectral methods for the homogeneous Boltzmann equation, Trans. AMS vol. 363 (2011), pp. 1947-1980, with C. Mouhot
- A class of asymptotic preserving
schemes for kinetic equations and related problems with stiff
sources, J. Comp. Phys. vol. 229 no 20, (2010), pp. 7625-7648, with S. Jin.
- High order resolution of the
Maxwell-Fokker-Planck-Landau model intended for ICF
applications, J. Comput. Phys, vol. 228, no 14 (2009), pp. 5072-5100, with R. Duclous, B. Dubroca and V. Tikhonchuk.
- Semi-lagrangian schemes applied to moving boundary problems for the BGK model of rarefied gas dynamics. Kin. and Related Models, vol. 2 no. 1, (2009), pp. 231--250, with G. Russo.
- An Asymptotically Stable Scheme for Diffusive Coagulation-Fragmentation Models, Comm. Math. Sciences vol 6 no. 2 (2008), pp. 257--280.
- Convergence of a Finite Volume Scheme for the Coagulation-Fragmentation Equations, Maths. Comp. vol. 77, (2008), pp. 851--882, with J.-P. Bourgade.
- Asymptotic Behavior of a Finite Volume Scheme for the Transient Drift-Diffusion Model, IMA J. Num. Anal. vol. 27 no. 4, (2007), pp. 689--716. with C. Chainais-Hillairet
- A Finite Volume Scheme for the
Patlak-Keller-Segel Chemotaxis Model, Numerische
Mathematik, vol. 104, (2006), pp. 457--488.
- Solving the Boltzmann Equation in N log(N) with Deterministic Methods, SIAM J. Scientific Computing, vol. 28 no. 3, (2006), pp. 1029--1053, with C. Mouhot and L. Pareschi.
- Modeling and Numerical Simulation of Space Charge Dominated Beams in the Paraxial Approximation, Mathematical Models and Methods in the Applied Sciences, vol. 16 no. 5, (2006) pp. 763--791, with E. Sonnendrucker
- Approximation of Hyperbolic Models for Chemosensitive Movement, SIAM J. Scientific Computing, vol. 27 no. 3, (2005), pp. 850--872, with C.-W. Shu.
- Derivation of Hyperbolic Models for Chemosensitive Movement, J. Math. Biology, vol. 50 (2005) no. 2, pp. 189--207, with Ph. Laurencot and B. Perthame.
- Accurate Numerical Methods for the Collisional Motion of (Heated) Granular Flows, J. Comput. Physics, 202 no. 1, (2005), 216--235, with L. Pareschi and G. Toscani
- Analysis of the Reduced Vlasov-Maxwell Model with Boundary Conditions, Quarterly Applied Math., vol. 63 no 4, (2005) pp. 691-714, with Y. Guo and C.-W. Shu
- A conservative and entropic method for the Vlasov-Fokker-Planck-Landau equation, Numerical Methods for Hyperbolic and Kinetic Problems, IRMA Lectures in Mathematics and Theoretical Physics with N. Crouseilles
- Numerical Approximation of Collisional Plasma by High Order Methods, J. Comput. Physics, vol. 201 no. 2, (2004), pp. 546--572, with N. Crouseilles
- Vlasov Simulations of Beams by a Moving Grid, Comput. Phys. Communications, vol. 164 no. 1-3, (2004), pp. 390--395, with E. Sonnendrucker, E. Oudet, A. Friedman and J.-L. Vay
- Mass Conserving Solutions and Non Conserving Approximation to the Smoluchowski Coagulation Equation, Archiv der Mathematik, vol. 83 no. 6, (2004), pp. 558--567 with Ph. Laurencot.
- A rescaling velocity method for
kinetic equations: I. homogeneous case, Proceedings
Modelling and Numerics of Kinetic Dissipative Systems, Lipari,
Italy, 2004, Nova-Science with G. Russo
- Numerical Simulation of the Smoluchowski Coagulation Equation, SIAM J. of Scientific Computing, vol. 25 no. 6, (2004), pp. 2004-2028 with Ph. Laurencot.
- High order Numerical Methods for the Space Non Homogeneous Boltzmann Equation, J. Comput. Physics, vol. 186 no. 2, (2003), pp. 457--480, with G. Russo
- Numerical Approximation of the Lifschitz-Slyozov-Wagner Equation, SIAM J. Numer. Analysis, 41 no. 2, (2003), pp. 563--588, with Ph. Laurencot
- Global Existence for the Vlasov-Darwin System in R3 for Small Initial Data, Math. Methods Appl. Sciences, vol. 26 no. 4 (2003), pp. 297--319, with S. Benachour, Ph. Laurencot and E. Sonnendrucker
- Comparison of Eulerian Vlasov Solvers, Comput. Phys. Communications, vol. 150 no. 3 (2003), pp. 247--266, with E. Sonnendrucker
- A Numerical Method for the Accurate Solution of the Fokker-Planck-Landau Equation in the Non Homogeneous Case, J. Comput. Physics vol. 179 no. 1, (2002), pp. 1--26, with L. Pareschi
- Direct Axisymmetric Vlasov
Simulations of Space Charged Dominated Beams, Lecture Notes
in Computer Sciences, ICCS 2002, part 3, (2002) 305--314, with E. Sonnendrucker and J.-L. Lemaire
- Parallelization of a Vlasov Solver by Communication Overlapping, Proceedings PDPTA 2002 (2002), with E. Violard
- An adaptive numerical method for the Vlasov equation based on a multiresolution analysis, Brezzi, Franco (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2001, the 4th European conference, Ischia, July 2001. Berlin: Springer pp. 437--446 (2003) with N. Besse, M. Gutnic, I. Paun and E. Sonnendrucker
- Numerical Methods for the Vlasov Equation, Brezzi, Franco (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2001, the 4th European conference, Ischia, July 2001. Berlin: Springer pp. 459--468 (2003), with E. Sonnendrucker
- Convergence of a Finite Volume Scheme for the One Dimensional Vlasov-Poisson System, SIAM J. Numer. Analysis, vol. 39 no. 4, (2001), pp. 1146--1169
- Conservative Numerical Schemes for the Vlasov Equation, J. Comput. Physics 172 no. 1, (2001), pp. 166--187, with E. Sonnendrucker and P. Bertrand
- Numerical Solution of the Non Homogeneous
Fokker-Planck-Landau Equation, Mathematics in Industry,
VOL. 1: Anile, A.M.; Capasso, V.; Greco, A., (Eds.) Progress in
Industrial Mathematics at ECMI 2000 (Springer), 325--331 (2000),
with L. Pareschi
- Convergence d'un schéma de type volumes finis pour le système de Vlasov-Poisson, Comptes Rendus Mathématiques 330, série I Mathématique pp. 979--984 (2000)
- Comparison of Numerical Schemes for Fokker-Planck-Landau Equation, ESAIM Proceedings, vol. 10, Soc. Math. Appl. Industry, Paris, (1999); pp. 161--181, with C. Buet and S. Cordier