Articles publiés ou acceptés

  • Design of asymptotic preserving finite volume schemes for hyperbolic heat equation on unstructured meshes, C. Buet, B. Després, E. Franck, Numerische Mathematik, Octobre 2012, Volume 122, Issue 2, pp 227-278. ( Version publiée ).
  • An asymptotic preserving scheme with the maximum principle for the M1 model on distorted meshes, C. Buet, B. Després, E. Franck, Comptes Rendus Mathematique, Volume 350, Issues 11-12, Juin 2012, Pages 633-638. ( Version publiée ).
  • Asymptotic preserving schemes for Friedrichs systems with stiff relaxation on unstructured meshes: applications to the angular discretization models in linear transport, C. Buet, B. Després, E. Franck, Journal Scientific Computing, Volume 62 Issue 2, February 2015, Pages 371-398. ( Preprint ), ( Version publiée ).
  • Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK code, E. Franck, M. Hölzl, A. Lessig, E. Sonnendrücker. ( Preprint ), ( Version publiée ), ESAIM: M2AN Volume 49, Numéro 5, Septembre-Octobre 2015.
  • Mechanism of Edge Localized Mode mitigation by Resonant Magnetic Perturbations, M. Bécoulet, F. Orain, X. Garbet, G. T. A Huijsmans, S. Pamela, P. Cahyna, M. Hölzl, E. Franck, E. Sonnendrücker, G. Dif-Pradalier, C. Passeron, G. Latu, J. Morales, E. Nardon, A. Fil, B. Nkonga, A. Ratnani, Phys. Rev. Lett. 113, 155001, september 2014. ( Version publiée ).
  • Proof of uniform convergence for a cell-centered AP discretization of the hyperbolic heat equation on general meshes, C. Buet, B. Després, E. Franck, T. Leroy. (publienglish.html Preprint ), ( Version publiée ) Mathematics of computation, 12 Septembre 2016.
  • Finite volume scheme with local high order discretization of hydrostatic equilibrium for Euler equations with external forces, E. Franck, L. Mendoza. ( Preprint ), ( Version publiée ) Journal of Scientific Computing, Octobre 2016, Volume 69, pp 314-354.
  • Stability of a Kirchhoff-Roe scheme for multi-dimensional linearized Euler systems, E. Franck, L. Gosse. ( Version publiée ), Annali Dell' Universita' Di Ferrara, Décembre 2017.
  • An analysis of over-relaxation in kinetic approximation, F.Drui, E. Franck, P. Helluy, L. Navoret. ( Preprint ), ( Version publiée ). Comptes Rendus Mécanique Volume 347, Issue 3, March 2019, Pages 259-269
  • Implicit time schemes for compressible fluid models based on relaxation methods, D. Coulette, E. Franck, P. Helluy, A. Ratnani, E. Sonnendruecker. ( Preprint ), ( Version publiée ). Computers and Fluids, Volume 188, 30 June 2019, Pages 70-85.
  • High-order implicit palindromic discontinuous Galerkin method for kinetic-relaxation approximation, D. Coulette, E. Franck, P. Helluy, M. Mehrenberger, L. Navoret. ( Preprint ), ( Version publiée ) Computers and Fluids, Volume 190, 15 August 2019, Pages 485-502.
  • Vectorial kinetic relaxation model with central velocity. Application to implicit relaxations schemes , D. Coulette, C. Courtès, E. Franck, L. Navoret. ( Preprint ), ( Version publiée ) Commun. Comput. Phys., 27 (2020), pp. 976-1013.
  • The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas, M. Hoelzl et al ( Preprint ), ( Version publiée ). Nuclear Fusion, Volume 61, Number 6
  • A low cost semi-implicit low-Mach relaxation scheme for the full Euler equations , F. Bouchut, E. Franck, L. Navoret. ( Preprint ), ( Version publiée ) Journal of Scientific Computing volume 83, 24 (2020).
  • A neural network closure for the Euler-Poisson system based on kinetic simulations , L. Bois, E. Franck, L. Navoret, V. Vigon ( Preprint ), ( Version publiée ). "Kinetic and related models", Février 2022, 15(1): 49-89.
  • Accelerate Newton convergence for nonlinear elliptic PDE using PINO deep learning approach , E. Franck, R. Hild, V. Vigon, V. Michel-Dansac, J. Aghili ( preprint ). Accepté dans Communications in Nonlinear Science and Numerical Simulation.
  • Parallel kinetic scheme in complex toroidal geometry , M. Boileau, B. Bramas, E. Franck, R.Hélie, P. Helluy, L. Navoret. ( Preprint ), ( Version publiée ). "The SMAI Journal of computational mathematics, Volume 8 (2022), pp. 249-271.
  • A kinetic method for solving the MHD equations. Application to the computation of tilt instability on uniform fine meshes , H. Baty, F. Drui, E. Franck, P. Helluy, C. Klingenberg, L. Tannhaueser. ( Preprint ). ( Version publiée ). Applied Mathematics and Computation, Volume 440 , 1 March 2023, 127667
  • Reduced modelling and optimal control of epidemiological individual-based models with contact heterogeneity , C. Courtès, E. Franck, K. Lutz, L. Navoret, Y. Privat. ( Preprint ). ( Version publiée ). Optimal control in therapeutics and epidemiology, Optimal Control Applications and Methods, 10.1002/oca.3114, 45, 2, (457-458), (2024).
  • Approximately well-balanced Discontinuous Galerkin methods using bases enriched with Physics-Informed Neural Networks , V. M. Dansac, E. Franck, L. Navoret. ( Preprint ). ( Version publiée ). Journal of Computational Physics Volume 512 , 1 September 2024, 113144
  • Optimal scenario for road evacuation in an urban environment , M. Bestard, E. Franck L. Navoret, Y. Privat. ( preprint ). ( Version publiée ). Z. Angew. Math. Phys. 75, 146 (2024)
  • Optimal control deep learning approach for viscosity design in DG schemes , L. Bois, E. Franck, L. Navoret, V. Vigon. ( Preprint ). ( Version publiée ).Journal of Scientific Computing, 04 November 2024 Volume 101, article number 70, (2024)
  • Accelerate Newton convergence for nonlinear elliptic PDE using PINO deep learning approach , E. Franck, R. Hild, V. Vigon, V. Michel-Dansac, J. Aghili ( Preprint ), ( Version finale ). Communications in Nonlinear Science and Numerical Simulation Volume 140, Part 2, January 2025, 108434
  • Reduced order modeling using auto-encoder and Hamiltonian neural networks , E. Franck, L. Navoret, V. Vigon, G. Steimer. ( preprint ). Accepté dans CICP
  • Volume-preserving physics-informed geometric shape optimization of the Dirichlet ene , A. Belieres, E. Franck, V. Michel Dansac, Y. Privat. ( preprint ). Accepté dans Neural Networks

    • Proceedings publiés ou acceptés

  • An asymptotic preserving scheme for P1 model using classical diffusion schemes on unstructured polygonal meshes, E. Franck, P. Hoch, P. Navaro and G. Samba, ESAIM: PROCEEDINGS, Octobre 2011, Vol. 32, p. 56-75. ( Version publiée ).
  • Asymptotic Preserving Finite Volumes Discretization For Non-Linear Moment Model On Unstructured Meshes, C. Buet, B. Després, E. Franck, Finite Volumes for Complex Applications VI Problems and Perspectives, Springer Proceedings in Mathematics Volume 4, 2011, pp 467-474. ( Version publiée ).
  • A priori analysis of asymptotic preserving schemes with the modified equation, B. Després (main author), C. Buet et E. Franck. Hyperbolic problems: theory, numerics and applications, AIMS on Applied Mathematics,vol 8, pp 501. ( Première version en ligne ).
  • Modified Finite Volume Nodal Scheme for Euler Equations with Gravity and Friction, E. Franck, Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects Springer Proceedings in Mathematics & Statistics Volume 77, 2014, pp 285-292. ( Version publiée ).
  • Anisotropic diffusion in toroidal geometry , A. Ratnani, B. Nkonga, E. Franck, A. Eksaeva, M. Kazakova. ( Preprint ), ( Version publiée ) ESAIM Proc, Volume 53, Mars 2016, pp 77-98.
  • Study of physic-based preconditioning with high order Galerkin method discretization for hyperbolic wave problems, C. Courtes, E. Franck ,P. Helluy and H. Oberlin. ( Version publiée ). ESAIM: PROCEEDINGS AND SURVEYS, December 2016, Vol. 55, p. 61-82.
  • Palindromic discontinuous Galerkin method, D. Coulette, E. Franck, P. Helluy, M. Mehrenberger, L. Navoret. ( Version publiée). FVCA 2017: Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems, pp 171-178.
  • Task-based parallelization of an implicit kinetic scheme, J. Badwaik, M. Boileau, D. Coulette, E. Franck, P. Helluy, L. Mendoza, H. Oberlin. ( Preprint ), ( Version publiée ).
  • Linear stability of a vectorial kinetic relaxation scheme with a central velocity , C. Courtès, E. Franck. ( Preprint ). Hyperbolic Problems : Theory, Numerics and Applications, AIMS on Applied Mathematics, Vol. 10, 2020, p. 400-407.
  • Semi-implicit two-speed Well-Balanced relaxation scheme for Ripa model , E. Franck, L. Navoret. ( Preprint ). FVCA 2020: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples pp 735–743..
  • Kinetic over-relaxation method for the convection equation with Fourier solver , R. Hélie, P. Helluy, E. Franck, L. Navoret. ( Preprint ). FVCA 2020: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects.
  • A composite finite volume scheme for Euler equations with source term on unstructured meshes , M. Boujoudar, E. Franck, P. Hoch, C. Lasuen, Y. Le Hénaff and P. Paragot. ( Preprint ) Accepté dans ESAIM: PROCEEDINGS AND SURVEYS
  • Hyperbolic reduced model for Vlasov-Poisson equation with Fokker-Planck collision , E. Franck, I. Lannabi, Y. Nasseri, L. Navoret, G. Parasiliti, and G. Steimer. ( Preprint ) Accepté dans ESAIM: PROCEEDINGS AND SURVEYS

    • Preprint ou articles et proceedings soumis

  • Two layers Sindy approach for function and ODE discovery , C. Fiorini, C. Flint, L. Fostier, E. Franck, R. Hashemi, V. Michel-Dansac, W. Tenachi, ( preprint ). Soumis dans ESAIM: PROCEEDINGS AND SURVEYS

    • Articles en cours de redaction

  • Enhanced finite element methods using neural networks , F.Lecourtier,H. Barucq, E. Franck, F. Foucher, N. Victorion, V. Lleras, M. Duprez,V. Michel Dansac. En cours de rédaction
  • Nonlinear reduced order modeling for PIC Vlasov scheme using POD Auto-Encoder networks , E. Franck, L. Navoret, V. Vigon, G. Steimer. En cours de redaction
  • Neural symplectic forms based on discrete Lagrangians for long-time simulation , C. Courtès, E. Franck, M. Kraus, L. Navoret, L. Trémant. En cours de rédaction

    • Autre

  • Participation au rapport d'un workshop d'Oberwolfach : Time implicit schemes for the JOREK MHD code: Newton procedure, continuation and preconditioning, E. Franck, E. Sonnendrücker, M. Hölzl.