Publications

Christophe Besse, Grégory Faye, Jean-Michel Roquejoffre, Mingmin Zhang (2023). The logarithmic Bramson correction for Fisher-KPP equations on the lattice $\mathbb{Z}$. Transactions of the American Mathematical Society.

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Christophe Besse, Romain Duboscq, Stéphane Le Coz (2023). Computation of excited states for the nonlinear Schrödinger equation: numerical and theoretical analysis. HAL.

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Christophe Besse, Tuan Dung Nguyen, François Rogier (2023). An implicit time integration approach for simulation of corona discharges. HAL.

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Christophe Besse, Sergey Gavrilyuk, Maria Kazakova, Pascal Noble (2022). Perfectly Matched Layers Methods for Mixed Hyperbolic--Dispersive Equations. Water Waves.

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Christophe Besse, Tuan Dung Nguyen, François Rogier (2022). High-order Scharfetter-Gummel-based schemes and applications to gas discharge modeling. J. Comput. Phys.

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Christophe Besse, Romain Duboscq, Stefan Le Coz (2022). Gradient Flow Approach to the Calculation of Ground States on Nonlinear Quantum Graphs. Annales Henri Lebesgue.

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Christophe Besse, Alexandre Capel, Grégory Faye, Guilhem Fouilhé (2022). Asymptotic behavior of nonlocal bistable reaction-diffusion equations. AIMS DCDS-B.

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Christophe Besse, Romain Duboscq, Stefan Le Coz (2021). Numerical Simulations on Nonlinear Quantum Graphs with the GraFiDi Library. SMAI Journal of Computational Mathematics.

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Christophe Besse, Grégory Faye (2021). Spreading properties for SIR models on homogeneous trees. Bull. Math. Biol..

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Christophe Besse, Grégory Faye (2021). Dynamics of epidemic spreading on connected graphs. J. Math. Biol.

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Christophe Besse, Stéphane Descombes, Guillaume Dujardin, Ingrid Lacroix-Violet (2020). Energy-preserving methods for nonlinear Schrödinger equations. IMA Journal of Numerical Analysis.

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Guillaume Bertoli, Christophe Besse, Gilles Vilmart (2020). Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with oblique boundary conditions. Math. of Comp.

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Christophe Besse, Jean-Francois Coulombel, Pascal Noble (2020). Discrete transparent boundary conditions for the two-dimensional leap-frog scheme. ESAIM: Mathematical Modelling and Numerical Analysis.

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Christophe Besse, Rémi Carles, Sylvain Ervedoza (2020). A conservation law with spatially localized sublinear damping. Ann. Inst. H. Poincaré Anal. Non Linéaire.

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Matthieu Maunoury, Christophe Besse, Vincent Mouysset, Sébastien Pernet, Pol-André Haas (2018). Well-suited and adaptive post-processing for the visualization of $hp$ simulation results. J. Comput. Phys..

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Christophe Besse, Benoît Mésognon-Gireau, Pascal Noble (2018). Artificial boundary conditions for the linearized Benjamin-Bona-Mahony equation. Numer. Math..

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Matthieu Maunoury, Christophe Besse, Vincent Mouysset, Sébastien Pernet (2018). Accurate, automatic and compressed visualization of radiated Helmholtz fields from boundary element solutions. Computational science—ICCS 2018. Part I.

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Juan Pablo Álvarez Zùñiga, Christophe Besse, Romain Duboscq, Juliette Billy, David Guéry-Odelin (2017). Restoring quasireversibility with a single topological charge. Phys. Rev. A.

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Christophe Besse, Feng Xing (2017). Schwarz waveform relaxation method for one-dimensional Schrödinger equation with general potential. Numer. Algorithms.

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C. Besse, G. Dujardin, I. Lacroix-Violet (2017). High order exponential integrators for nonlinear Schrödinger equations with application to rotating Bose-Einstein condensates. SIAM J. Numer. Anal..

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Christophe Besse, Feng Xing (2017). Domain decomposition algorithms for two dimensional linear Schrödinger equation. J. Sci. Comput..

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Christophe Besse, Pascal Noble, David Sanchez (2017). Discrete transparent boundary conditions for the mixed KDV-BBM equation. J. Comput. Phys..

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Xavier Antoine, Christophe Besse, Romain Duboscq, Vittorio Rispoli (2017). Acceleration of the imaginary time method for spectrally computing the stationary states of Gross-Pitaevskii equations. Comput. Phys. Commun..

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Xavier Antoine, Christophe Besse, Vittorio Rispoli (2016). High-order IMEX-spectral schemes for computing the dynamics of systems of nonlinear Schrödinger/Gross-Pitaevskii equations. J. Comput. Phys..

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Christophe Besse, Feng Xing (2016). Domain decomposition algorithms for the two dimensional nonlinear Schrödinger equation and simulation of Bose-Einstein condensates. SMAI J. Comput. Math..

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C. Besse, M. Ehrhardt, I. Lacroix-Violet (2016). Discrete artificial boundary conditions for the linearized Korteweg--de Vries equation. Numer. Methods Partial Differential Equations.

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(2015). Nonlinear optical and atomic systems. Springer, Cham; CEMPI, Villeneuve d’Ascq.

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Vidar Gudmundsson, Sigtryggur Hauksson, Arni Johnsen, Gilbert Reinisch, Andrei Manolescu, Christophe Besse, Guillaume Dujardin (2014). Excitation of radial collective modes in a quantum dot: Beyond linear response. Annalen der Physik.

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Christophe Besse, Julien Coatléven, Sonia Fliss, Ingrid Lacroix-Violet, Karim Ramdani (2013). Transparent boundary conditions for locally perturbed infinite hexagonal periodic media. Commun. Math. Sci..

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Christophe Besse, Fabrice Deluzet, Claudia Negulescu, Chang Yang (2013). Efficient numerical methods for strongly anisotropic elliptic equations. J. Sci. Comput..

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Xavier Antoine, Weizhu Bao, Christophe Besse (2013). Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations. Comput. Phys. Commun..

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Christophe Besse, Rémi Carles, Florian Méhats (2013). An asymptotic preserving scheme based on a new formulation for NLS in the semiclassical limit. Multiscale Model. Simul..

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Xavier Antoine, Christophe Besse, Pauline Klein (2013). Absorbing boundary conditions for the two-dimensional Schrödinger equation with an exterior potential. Part II: Discretization and numerical results. Numer. Math..

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Xavier Antoine, Christophe Besse, Pauline Klein (2012). Absorbing boundary conditions for the two-dimensional Schrödinger equation with an exterior potential. Part I: Construction and ıt a priori estimates. Math. Models Methods Appl. Sci..

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Xavier Antoine, Christophe Besse, Pauline Klein (2011). Numerical solution of time-dependent nonlinear Schrödinger equations using domain truncation techniques coupled with relaxation scheme. Laser Physics.

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Xavier Antoine, Christophe Besse, Pauline Klein (2011). Numerical solution of time-dependent nonlinear Schrödinger equations using domain truncation techniques coupled with relaxation scheme. Laser Physics.

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Christophe Besse, Fabrice Deluzet, Chang Yang (2011). Numerical Simulations of Ionospheric Dynamo Model in a Non‐uniform Magnetic Field . AIP Conference Proceedings.

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Fréderique Charles, Nicolas Vauchelet, Christophe Besse, Thierry Goudon, Ingrid Lacroix-Violet, Jean-Paul Dudon, Laurent Navoret (2011). Numerical approximation of Knudsen layer for the Euler-Poisson system. CEMRACS'10 research achievements: numerical modeling of fusion.

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Christophe Besse, Saja Borghol, Thierry Goudon, Ingrid Lacroix-Violet, Jean-Paul Dudon (2011). Hydrodynamic regimes, Knudsen layer, numerical schemes: definition of boundary fluxes. Adv. Appl. Math. Mech..

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Pauline Klein, Xavier Antoine, Christophe Besse, Matthias Ehrhardt (2011). Absorbing boundary conditions for solving $N$-dimensional stationary Schrödinger equations with unbounded potentials and nonlinearities. Commun. Comput. Phys..

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Xavier Antoine, Christophe Besse, Pauline Klein (2011). Absorbing boundary conditions for general nonlinear Schrödinger equations. SIAM J. Sci. Comput..

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Xavier Antoine, Pauline Klein, Christophe Besse (2010). Open boundary conditions and computational schemes for Schrödinger equations with general potentials and nonlinearities. Some problems on nonlinear hyperbolic equations and applications.

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Christophe Besse, Saja Borghol, Jean-Paul Dudon, Thierry Goudon, Ingrid Lacroix-Violet (2010). On hydrodynamic models for LEO spacecraft charging. Some problems on nonlinear hyperbolic equations and applications.

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Christophe Besse, Thierry Goudon (2010). Derivation of a non-local model for diffusion asymptotics---application to radiative transfer problems. Commun. Comput. Phys..

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Nicolas Vauchelet, Jean-Paul Dudon, Christophe Besse, Thierry Goudon (2010). Comparison of Vlasov solvers for spacecraft charging simulation. M2AN Math. Model. Numer. Anal..

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Xavier Antoine, Christophe Besse, Jérémie Szeftel (2009). Towards accurate artificial boundary conditions for nonlinear PDEs through examples. Cubo.

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(2009). CANUM 2008. EDP Sciences, Les Ulis.

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Xavier Antoine, Christophe Besse, Pauline Klein (2009). Absorbing boundary conditions for the one-dimensional Schrödinger equation with an exterior repulsive potential. J. Comput. Phys..

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Christophe Besse, Rémi Carles, Norbert J. Mauser, Hans Peter Stimming (2008). Monotonicity properties of the blow-up time for nonlinear Schrödinger equations: numerical evidence. Discrete Contin. Dyn. Syst. Ser. B.

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Xavier Antoine, Anton Arnold, Christophe Besse, Matthias Ehrhardt, Achim Schädle (2008). A review of transparent and artificial boundary conditions techniques for linear and nonlinear Schrödinger equations. Commun. Comput. Phys..

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Christophe Besse, Jean. Claudel, Pierre Degond, Fabrice Deluzet, Gérard Gallice, Christian Tessieras (2007). Numerical simulations of the ionospheric striation model in a non-uniform magnetic field. Computer Physics Communications.

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Christophe Besse, Pierre Degond, Hj. Hwang, Raphael Poncet (2007). Nonlinear instability of the two-dimensional striation model about smooth steady states. Comm. Partial Differential Equations.

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Xavier Antoine, Christophe Besse, Stéphane Descombes (2006). Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations. SIAM J. Numer. Anal..

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Christophe Besse, Norbert Mauser, Hans Peter Stimming (2005). Numerical studies for nonlinear Schrödinger equations: the Schrödinger-Poisson-X$α$ model and Davey-Stewartson systems. Numerical methods for hyperbolic and kinetic problems.

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Christophe Besse, ean. Claudel, Pierre Degond, Fabrice Deluzet, Gérard Gallice, Christian Tessieras (2005). Ionospheric plasmas: model derivation, stability analysis and numerical simulations. Numerical methods for hyperbolic and kinetic problems.

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Christophe Besse, Jean Claudel, Pierre Degond, Fabrice Deluzet, Gérard Gallice, Christian Tessieras (2005). Instability of the ionospheric plasma: modeling and analysis. SIAM J. Appl. Math..

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Christophe Besse, Norbert J. Mauser, Hans Peter Stimming (2004). Numerical study of the Davey-Stewartson system. M2AN Math. Model. Numer. Anal..

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Xavier Antoine, Christophe Besse, Vincent Mouysset (2004). Numerical schemes for the simulation of the two-dimensional Schrödinger equation using non-reflecting boundary conditions. Math. Comp..

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Christophe Besse (2004). A relaxation scheme for the nonlinear Schrödinger equation. SIAM J. Numer. Anal..

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Christophe Besse, Pierre Degond, Fabrice Deluzet, Jean Claudel, Gérard Gallice, Christian Tessieras (2004). A model hierarchy for ionospheric plasma modeling. Math. Models Methods Appl. Sci..

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Christophe Besse, Brigitte Bidégaray-Fesquet, Antoine Bourgeade, Pierre Degond, Olivier Saut (2004). A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals: an application to KDP. M2AN Math. Model. Numer. Anal..

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Xavier Antoine, Christophe Besse (2003). Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrödinger equation. J. Comput. Phys..

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Christophe Besse, Brigitte Bidégaray, Stéphane Descombes (2002). Order estimates in time of splitting methods for the nonlinear Schrödinger equation. SIAM J. Numer. Anal..

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Xavier Antoine, Christophe Besse (2001). Une étude microlocale quasi-analytique d'une condition transparente pour l'équation de Schrödinger linéaire. Actes des VI èmes Journées Zaragoza-Pau de Mathématiques Appliquées et de Statistiques (Jaca, 1999).

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Xavier Antoine, Christophe Besse (2001). Une étude microlocale quasi-analytique d'une condition transparente pour l'équation de Schrödinger linéaire. Actes des VI$^m̊ grave emes$ Journées Zaragoza-Pau de Mathématiques Appliquées et de Statistiques (Jaca, 1999).

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Christophe Besse, Brigitte Bidégaray (2001). Numerical study of self-focusing solutions to the Schrödinger-Debye system. M2AN Math. Model. Numer. Anal..

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Xavier Antoine, Christophe Besse (2001). Construction, structure and asymptotic approximations of a microdifferential transparent boundary condition for the linear Schrödinger equation. J. Math. Pures Appl. (9).

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Christophe Besse, David Lannes (2001). A numerical study of the long-wave short-wave resonance for 3D water waves. Eur. J. Mech. B Fluids.

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Xavier Antoine, Christophe Besse (2000). Étude microlocale d'une condition transparente pour l'équation de Schrödinger linéaire. C. R. Acad. Sci. Paris Sér. I Math..

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Christophe Besse (2000). Relaxation scheme for time dependent nonlinear Schrödinger equations. Mathematical and numerical aspects of wave propagation (Santiago de Compostela, 2000).

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Xavier Antoine, Christophe Besse (2000). Quasi-analytic determination of the Dirichlet-to-Neumann operator associated to a linear Schrödinger-type equation. Mathematical and numerical aspects of wave propagation (Santiago de Compostela, 2000).

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Christophe Besse (1998). Schéma de relaxation pour l'équation de Schrödinger non linéaire et les systèmes de Davey et Stewartson. C. R. Acad. Sci. Paris Sér. I Math..

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Christophe Besse, Charles-Henri Bruneau (1998). Numerical study of elliptic-hyperbolic Davey-Stewartson system: dromions simulation and blow-up. Math. Models Methods Appl. Sci..

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