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Numerical Simulations on Nonlinear Quantum Graphs with the GraFiDi Library

Christophe Besse , Romain Duboscq , Stefan Le Coz
SMAI Journal of Computational Mathematics, 2022, 8, pp.1-47
Journal articles hal-03164639v1

Hydrodynamic regimes, Knudsen layer, numerical schemes: Definition of boundary fluxes

Christophe Besse , Saja Borghol , Thierry Goudon , Ingrid Lacroix-Violet , Jean-Paul Dudon
Advances in Applied Mechanics, 2011, 3 (5), pp.519--561
Journal articles hal-00905330v1

Numerical approximation of Knudsen layer for Euler-Poisson system

Frédérique Charles , Nicolas Vauchelet , Christophe Besse , Thierry Goudon , Ingrid Violet , et al.
ESAIM: Proceedings, 2011, CEMRACS'10 research achievements: Numerical modeling of fusion, 32, pp.177--194. ⟨10.1051/proc/2011020⟩
Journal articles hal-00905329v1
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Discrete transparent boundary conditions for the two-dimensional leap-frog scheme

Christophe Besse , Jean-François Coulombel , Pascal Noble
ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55, pp.S535-S571
Journal articles hal-02280886v1
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Restoring quasireversibility with a single topological charge

Juan Pablo Álvarez Zúñiga , Christophe Besse , Romain Duboscq , Juliette Billy , David Guéry-Odelin
Physical Review A : Atomic, molecular, and optical physics [1990-2015], 2017, 96 (5), pp.053618. ⟨10.1103/PhysRevA.96.053618⟩
Journal articles hal-01634474v1

Unconditionally Stable Discretization Schemes of Non-Reflecting Boundary Conditions for the One-Dimensional Schrödinger Equation

Xavier Antoine , Christophe Besse
Journal of Computational Physics, 2003, 188 (1), pp.157-175. ⟨10.1016/S0021-9991(03)00159-1⟩
Journal articles istex hal-00347877v1

A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations

Xavier Antoine , Anton Arnold , Christophe Besse , Matthias Ehrhardt , Achim Schädle
Communications in Computational Physics, 2008, 4 (4), pp.729-796
Journal articles hal-00347884v1
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High order exponential integrators for nonlinear Schrödinger equations with application to rotating Bose-Einstein condensates

Christophe Besse , Guillaume Dujardin , Ingrid Lacroix-Violet
SIAM Journal on Numerical Analysis, 2017, 55 (3), pp.1387-1411. ⟨10.1137/15M1029047⟩
Journal articles hal-01170888v2
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Domain decomposition algorithms for two dimensional linear Schrödinger equation

Christophe Besse , Feng Xing
Journal of Scientific Computing, 2017, 72 (2), pp.735-760. ⟨10.1007/s10915-017-0375-1⟩
Journal articles hal-01165101v2
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Monotonicity properties of blow-up time for nonlinear Schrödinger equation: numerical tests

Christophe Besse , Rémi Carles , Norbert Mauser , Hans-Peter Stimming
Discrete and Continuous Dynamical Systems - Series B, 2008, 9 (1), pp.11-36. ⟨10.3934/dcdsb.2008.9.11⟩
Journal articles hal-00020062v2
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Discrete transparent boundary conditions for the mixed KDV-BBM equation

Christophe Besse , Pascal Noble , David Sanchez
Journal of Computational Physics, 2017, 345, pp.484-509. ⟨10.1016/⟩
Journal articles hal-01373388v1
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An implicit time integration approach for simulation of corona discharges

Christophe Besse , Tuan Dung Nguyen , François Rogier
Preprints, Working Papers, ... hal-04102798v1
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Discrete transparent boundary conditions for the two-dimensional leap-frog scheme: approximation and fast implementation

Christophe Besse , Jean-François Coulombel , Pascal Noble
ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55, pp.S535-S571. ⟨10.1051/m2an/2020052⟩
Journal articles hal-03154036v1
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Spreading properties for SIR models on homogeneous trees

Christophe Besse , Grégory Faye
Bulletin of Mathematical Biology, 2021
Journal articles hal-03251359v1
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Dynamics of epidemic spreading on connected graphs

Christophe Besse , Grégory Faye
Journal of Mathematical Biology, 2021, 82 (6), pp.52. ⟨10.1007/s00285-021-01602-5⟩
Journal articles hal-03019230v1
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Order estimates in time of splitting methods for the nonlinear Schrödinger equation

Christophe Besse , Brigitte Bidégaray , Stéphane Descombes
SIAM Journal on Numerical Analysis, 2002, 40 (1), pp.26-40. ⟨10.1137/S0036142900381497⟩
Journal articles hal-00319991v1
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Numerical study of self-focusing solutions to the Schrödinger-Debye system

Christophe Besse , Brigitte Bidégaray
ESAIM: Mathematical Modelling and Numerical Analysis, 2001, 35 (1), pp.35-55. ⟨10.1051/m2an:2001106⟩
Journal articles hal-00319989v1
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A conservation law with spatially localized sublinear damping

Christophe Besse , Rémi Carles , Sylvain Ervedoza
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2020, 37 (1), pp.13-50. ⟨10.1016/j.anihpc.2019.03.002⟩
Journal articles hal-01741189v2
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Schéma de relaxation pour l'équation de Schrödinger non linéaire et les systèmes de Davey et Stewartson

Christophe Besse
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1998, 326 (12), pp.1427-1432. ⟨10.1016/s0764-4442(98)80405-9⟩
Journal articles hal-01741535v1
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Computation of excited states for the nonlinear Schrödinger equation: numerical and theoretical analysis

Christophe Besse , Romain Duboscq , Stefan Le Coz
Preprints, Working Papers, ... hal-04151806v1
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Absorbing Boundary Conditions for the Two-Dimensional Schrödinger Equation with an Exterior Potential. Part I: Construction and a priori Estimates

Xavier Antoine , Christophe Besse , Pauline Klein
Mathematical Models and Methods in Applied Sciences, 2012, 22 (10), pp.1250025. ⟨10.1142/S021820251250025X⟩
Journal articles hal-00755639v1
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Towards Accurate Artificial Boundary Conditions for Nonlinear PDEs Through Examples

Xavier Antoine , Christophe Besse , Jeremie Szeftel
Cubo, a Mathematical Journal, 2009, 11 (4), pp.1008-1033
Journal articles hal-00755572v1
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Transparent boundary conditions for locally perturbed infinite hexagonal periodic media.

Christophe Besse , Julien Coatleven , Sonia Fliss , Ingrid Lacroix-Violet , Karim Ramdani
Communications in Mathematical Sciences, 2013, 11 (4), pp.907-938
Journal articles hal-00698916v1
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Absorbing boundary conditions for the two-dimensional Schrödinger equation with an exterior potential. Part II: Discretization and numerical results

Xavier Antoine , Christophe Besse , Pauline Klein
Numerische Mathematik, 2013, 125 (2), pp.191-223
Journal articles hal-00931115v1
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Domain decomposition algorithms for the two dimensional nonlinear Schrödinger equation and simulation of Bose-Einstein condensates

Christophe Besse , Feng Xing
SMAI Journal of Computational Mathematics, 2016, 2, pp.277-300. ⟨10.5802/smai-jcm.17⟩
Journal articles hal-01285359v1

Excitation of radial collective modes in a quantum dot: Beyond linear response

Vidar Gudmundsson , Sigtryggur Hauksson , Arni Johnsen , Gilbert Reinisch , Andrei Manolescu , et al.
Annalen der Physik, 2014, 526 (5-6), pp.14. ⟨10.1002/andp.201400048⟩
Journal articles hal-00907845v1

Artificial Boundary Conditions for Schrödinger-type Equations and their Numerical Approximation

Xavier Antoine , Christophe Besse
Y.Y. Lu, W.W. Sun and Tao Tang. Advances in Scientific Computing and Applications, Science Press, pp.8-21, 2004
Book sections hal-00141072v1
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Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and Nonlinearities

Pauline Klein , Xavier Antoine , Christophe Besse , Matthias Ehrhardt
Communications in Computational Physics, 2011, 10 (5), pp.1280-1304
Journal articles hal-00755605v1
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High-order Scharfetter-Gummel-based schemes and applications to gas discharge modeling

Tuan Dung Nguyen , Christophe Besse , François Rogier
Journal of Computational Physics, 2022, 461
Journal articles hal-03352814v1
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Accurate, Automatic and Compressed Visualization of Radiated Helmholtz Fields from Boundary Element Solutions

Matthieu Maunoury , Christophe Besse , Vincent Mouysset , Sébastien Pernet
Lecture Notes in Computer Science, 10860, Springer International Publishing AG, 2018, Computational Science – ICCS 2018, 978-3-319-93698-7. ⟨10.1007/978-3-319-93698-7_54⟩
Book sections hal-01743384v1