Publications by research topic

Development and analysis of Lagrangian and semi-Lagrangian numerical methods for transport

• F. Charles. Particle methods for transport equations: foundations and improved reconstruction methods. Lecture notes de l'école d’été "11th Summer School on Methods and Models of Kinetic Theory" (MMKT 22). Accepted for publication in Rivista di Matematica della Università di Parma, 2025. HAL
• From particle methods to forward-backward Lagrangian schemes, with Martin Campos Pinto. SMAI Journal of Computational Mathematics, 2018. HAL, Publication (open access), Bibtex.
• Convergence of a linearly transformed particle method for aggregation equations, with Martin Campos Pinto, José Antonio Carrillo de La Plata, Young-Pil Choi, Numerische mathematik, 2018. HAL, Publication, Bibtex.
• Uniform convergence of a linearly transformed particle method for the Vlasov-Poisson system, with Martin Campos Pinto, SIAM Journal on Numerical Analysis, 2016. HAL, Publication, Bibtex.
• Enhanced convergence estimates for semi-lagrangian schemes Application to the Vlasov-Poisson equation, with Bruno Després and Michel Mehrenberger. SIAM Journal of Numerical Analysis, 2013. HAL, Publication.

Kinetic models for rarefied gases and gas-particle flows, modeling, analysis, and numerical simulation

• Diffusion asymptotics of a kinetic model for gas-particle mixtures with energy exchanges, with Annamaria Massimini and Francesco Salvarani. Preprint, 2025. HAL.
• Local Conservation Laws and Entropy Inequality for Kinetic Models with Delocalized Collision Integrals, with Zhe Chen and François Golse. Accepted for publication in M3AS: Mathematical Models and Methods in Applied Sciences, Special Issue Essays and Reviews, 2025. ArXiv.
• From collisional kinetic models to sprays: internal energy exchanges, with Laurent Desvillettes, Communications in Mathematical Sciences, 23:173--193, 2025. HAL, Publication.
• Mathematical and numerical study of a kinetic model describing the evolution of planetary rings, with Annamaria Massimini and Francesco Salvarani, in Computers and Mathematics with Applications, 2023. Publication, HAL.
• Mathematical and numerical study of a dusty knudsen gas mixture : extension to non-spherical dust particles. Recent Advances in Kinetic Equations and Applications, Springer INdAM Series, 2021. HAL, Publication.
• Mathematical and Numerical study of a dusty knudsen gas mixture, with Francesco Salvarani, in Acta Applicandae Mathematicae, 2019. HAL, Publication, Bibtex
• Kinetic Modelling of the Transport of Dust Particles in a Rarefied Atmosphere, with Stéphane Dellacherie and Jacques Segré. Mathematical Models and Methods in Applied Sciences, 2012. Preprint, Publication
• Small Mass Ratio Limit of Boltzmann Equations in the Context of the Study of Evolution of Dust Particles in a Rarefied Atmosphere, with L. Desvillettes. Journal of Statistical Physics, 2009. Publication.
• Kinetic modelling and numerical simulations using particle methods for the transport of dust in a rarefied gas. American Institute of Physics. Proceeding of the 26 th symposium "Rarefied gas dynamics'' (RGD), 2008. HAL, Publication.

Analysis and numerical simulation of plasma models

• Discrete moments models for Vlasov equations with non constant strong magnetic limit, with Bruno Després, Ruiyang Dai, Sever Hirstoaga, Comptes Rendus Mécanique, 351:1–23, 2023. HAL, publication.
• The Vlasov-Ampère system and the Bernstein-Landau paradox, with Bruno Després, Alexandre Rege, Ricardo Weder, Journal of Statistical Physics, 2021. HAL, Publication
• Nonlinear stability of a Vlasov equation for magnetic plasmas, with Bruno Després, Benoît Perthame and Rémi Sentis. Kinetic and related Models, 2013. HAL, Publication
• Numerical Simulation By a Random Particle Method of Deuterium-Tritium Reactions in a Plasma, with C. Copol, S. Dellacherie, J.M Mounsamy. ESAIM PROCEEDINGS, 2012. HAL, Publication.
• Numerical approximation of Knudsen layer for the Euler-Poisson system, with N.Vauchelet, C. Besse, Th. Goudon, I. Lacroix-Violet,  J-P Dudon, L. Navoret. ESAIM PROCEEDINGS, 2011. HAL, Publication

Positive polynomial interpolation algorithms

• A projection algorithm on the set of polynomials with two bounds, with Martin Campos-Pinto, Bruno Després, Maxime Herda, Numerical Algorithms, 2020. HAL, Publication.
• Algorithms for Positive Polynomial Approximation, with Martin Campos Pinto and Bruno Després. SIAM Jounal of Numerical Analysis, 2019. HAL, Publication.

Miscellaneous

• An Efficient Kinetic Model for Assemblies of Amyloid Fibrils and Its Application to Polyglutamine Aggregation, with S. Prigent, A. Ballesta, P. Gabriel, L.M. Tine, H. Rezaei and M. Doumic. Plos One, 2012. HAL.
• Label structured cell proliferation models, with H.T. Banks, M. Doumic, K.L. Sutton, W.C. Thompson. Appl. Math. Lett., Vol. 23, No. 12, 1412--1415, 2010. HAL.