Identifiants chercheur

  • IdHAL : michel-mehrenberger
Nombre de documents




Michel MEHRENBERGER, born in 1977, married (3 children)

IRMA, Université de Strasbourg et CNRS
7, rue René Descartes
F-67084 Strasbourg
Office: P225


Professional experience

  • Assistant Professor 2006-present, University of Strasbourg (France)
  • INRIA researcher 2015-2016 (delegation), University of Strasbourg (France)
  • Postdoctorate 2013-2014, Max-Planck Institute für Plasmaphysik, Garching (Germany)
  • Half time CNRS researcher 2012-2013 (delegation), University of Strasbourg (France)
  • Postdoctorate 2005-2006, Gamma Project, INRIA Rocquencourt (France)
  • Invited researcher 2004/2005 (6 months), Università La Sapienza, Rome (Italy)
  • Teaching assistant (ATER) 2004/2005 (6 months), University of Strasbourg (France)


  • HDR thesis, 5.10.2012, University of Strasbourg (France)
      "Ingham inequalities and numerical resolution of the Vlasov equation"
  • PhD thesis, 15.12.2004, University of Strasbourg (France)
      "Observability inequalities and adaptive resolution of the Vlasov equation with hierarchical finite elements"
      Advisors: V. Komornik and E. Sonnendrücker
  • Master 2 (2001), University of Strasbourg (France), "good" rating
  • Agregation of Mathematics (2000), preparation in Strasbourg, rank: 174
  • Master 1 (1999), University of Mulhouse (France), "good" rating
  • CAPES of Mathematics (1999), rank: 6
  • Licence (1998), University of Mulhouse (France), "very good" rating

Research interests

  • Numerical resolution of the Vlasov equation
  • Semi-Lagrangian method
  • High-order methods for PDEs
  • Adaptive and multiscale schemes
  • Large scale applications
  • Plasma physics and gyrokinetics
  • Numerical simulations
  • Sotfware development
  • Observability inequalities and non harmonic Fourier series


  • Computer science:
    • Fortran 90, Fortran 2003, C; some C++
    • parallel computing: mpi, openmp; some cuda
    • python, scilab, maple
  • Mathematics:
    • numerical analysis
    • scientific computing
    • control of PDEs
  • Language:
    • French (native)
    • English, German; some Italian


I am interested in developing, analysing and testing numerical schemes.

The favourite PDE is the Vlasov equation which is a kinetic equation involving the distribution function which gives the statistical repartition of particles at fixed time, position and velocity. This equation is coupled with Maxwell equations for the self consistant fields acting in space and time.

The favourite numerical scheme is the semi-Lagrangian method that needs ODE solvers and interpolators.

The favourite application is in plasma physics, related to the ITER project. In particular micro-instabilities in tokamaks are modelled by the gyrokinetic equation which is a reduced model of the Vlasov equation, where the fast gyration of the particles is averaged, leading to a series of 4D equations (3D in space, 1D in velocity).

Such studies involve the development and testing of adapted numerical schemes that can work in a HPC context. A mathematical study of the underlying schemes also permits to justify the behavor of the numerical solutions.

I am also interested in the development of software, and my favourite library is Selalib (

I have also some input in control theory; there, my favourite method is to use Fourier series, more precisely Ingham type inequalities which are generalizations of the Parseval equality.



Article dans une revue29 documents

  • Fernando Casas, Nicolas Crouseilles, Erwan Faou, Michel Mehrenberger. High-order Hamiltonian splitting for Vlasov-Poisson equations. Numerische Mathematik, Springer Verlag, 2016. <hal-01206164>
  • Virginie Grandgirard, Jérémie Abiteboul, Julien Bigot, Thomas Cartier-Michaud, Nicolas Crouseilles, et al.. A 5D gyrokinetic full-f global semi-lagrangian code for flux-driven ion turbulence simulations. Computer Physics Communications, Elsevier, 2016, 207, pp.35-68. <10.1016/j.cpc.2016.05.007>. <cea-01153011v3>
  • Adnane Hamiaz, Michel Mehrenberger, Hocine Sellama, Eric Sonnendrücker. The semi-Lagrangian method on curvilinear grids. Communications in Applied and Industrial Mathematics, 2016. <hal-01213366>
  • Michel Mehrenberger, Laura S. Mendoza, Charles Prouveur, Eric Sonnendrücker. Solving the guiding-center model on a regular hexagonal mesh. ESAIM: Proceedings and Surveys, EDP Sciences, 2015, 53, pp.149-176. <10.1051/proc/201653010 >. <hal-01117196v3>
  • Christophe Steiner, Michel Mehrenberger, Nicolas Crouseilles, Virginie Grandgirard, Guillaume Latu, et al.. Gyroaverage operator for a polar mesh. European Physical Journal D, SpringerLink, 2015, 69 (1), pp.221. <10.1140/epjd/e2014-50211-7>. <hal-01090681>
  • Adnane Hamiaz, Michel Mehrenberger, Aurore Back, Pierre Navaro. Guiding center simulations on curvilinear grids. ESAIM: Proceedings, EDP Sciences, 2015, <10.1051/proc/201653007>. <hal-00908500v3>
  • Mohamed Jellouli, Michel Mehrenberger. Optimal decay rates for the stabilization of a string network. Comptes Rendus Mathématique, Elsevier Masson, 2014, <10.1016/j.crma.2014.03.023>. <hal-00977345>
  • Guillaume Latu, Virginie Grandgirard, Jérémie Abiteboul, Nicolas Crouseilles, Guilhem Dif-Pradalier, et al.. Improving conservation properties in a 5D gyrokinetic semi-Lagrangian code. European Journal of Physics D, 2014, 68 (11), pp.345. <10.1140/epjd/e2014-50209-1>. <hal-00966162>
  • Bedros Afeyan, Fernando Casas, Nicolas Crouseilles, Adila Dodhy, Erwan Faou, et al.. Simulations of Kinetic Electrostatic Electron Nonlinear (KEEN) Waves with Variable Velocity Resolution Grids and High-Order Time-Splitting. European Physical Journal D, SpringerLink, 2014, 68 (10), DOI: 10.1140/epjd/e2014-50212-6. <10.1140/epjd/e2014-50212-6>. <hal-00977344v2>
  • Nicolas Crouseilles, Pierre Glanc, Sever Adrian Hirstoaga, Eric Madaule, Michel Mehrenberger, et al.. A new fully two-dimensional conservative semi-Lagrangian method: applications on polar grids, from diocotron instability to ITG turbulence. European Physical Journal D, SpringerLink, 2014, 68 (9), DOI: 10.1140/epjd/e2014-50180-9. <10.1140/epjd/e2014-50180-9>. <hal-00977342v2>
  • Luca Marradi, Bedros Afeyan, Michel Mehrenberger, Nicolas Crouseilles, Christophe Steiner, et al.. Vlasov on GPU (VOG Project). ESAIM: Proceedings, EDP Sciences, 2013, 43, p. 37-58. <10.1051/proc/201343003>. <hal-00908498>
  • Nicolas Crouseilles, Pierre Glanc, Michel Mehrenberger, Christophe Steiner. Finite Volume Schemes for Vlasov. ESAIM Proceedings, EDP Sciences, 2012, CEMRACS'11: Multiscale Coupling of Complex Models in Scientific Computing, 38, pp.275-297. <10.1051/proc/201238015>. <hal-00653038>
  • Nicolas Crouseilles, Michel Mehrenberger, Francesco Vecil. Discontinuous Galerkin semi-Lagrangian method for Vlasov-Poisson. Proceeding ESAIM: CEMRACS 2010, 2011, pp.21. <10.1051/proc/2011022 >. <hal-00544677>
  • Kaïs Ammari, Michel Mehrenberger. Study of the nodal feedback stabilization of a string-beams network. Journal of Applied Mathematics and Computing, Springer, 2011, <10.1007/s12190-010-0412-9>. <hal-01298967>
  • Frédérique Charles, Bruno Després, Michel Mehrenberger. Enhanced convergence estimates for semi-lagrangian schemes Application to the Vlasov-Poisson equation. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2011, <10.1137/110851511>. <inria-00629081>
  • Nicolas Crouseilles, Michel Mehrenberger, Eric Sonnendrücker. Conservative semi-Lagrangian schemes for Vlasov equations. Journal of Computational Physics, Elsevier, 2010, pp.1927-1953. <10.1016/>. <hal-00363643>
  • Nicolas Crouseilles, Michel Mehrenberger, Hocine Sellama. Numerical solution of the gyroaverage operator for the finite gyroradius guiding-center model.. Communications in Computational Physics, Global Science Press, 2010, 8 (3), pp.484-510. <10.4208/cicp.010909.220110a>. <inria-00507301>
  • Alia Barhoumi, Vilmos Komornik, Michel Mehrenberger. A vectorial Ingham-Beurling type theorem. Annales Univ. Sci. Budapest., Sec. Math., 2010, <>. <hal-01298976>
  • Kaïs Ammari, Michel Mehrenberger. Stabilization of coupled systems. Acta Mathematica Hungarica, Springer Verlag, 2009, <10.1007/s10474-009-8011-7>. <hal-01298966>
  • Kaïs Ammari, Mohamed Jellouli, Michel Mehrenberger. Feedback stabilization of a coupled string-beam system. Networks and Heterogeneous Media (NHM), 2009, <10.3934/nhm.2009.4.19>. <hal-01298964>
  • Michel Mehrenberger. An Ingham type proof for the boundary observability of a N-d wave equation. Comptes Rendus Mathématique, Elsevier Masson, 2009, <10.1016/j.crma.2008.11.002>. <hal-00311730>
  • Paola Loreti, Michel Mehrenberger. An Ingham type proof for a two-grid observability theorem. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2008, <10.1051/cocv:2007062>. <hal-01298963>
  • Paola Loreti, Michel Mehrenberger. Observabilite uniforme de l'equation des ondes 1D . ESAIM: Proceedings, EDP Sciences, 2008, <10.1051/proc:082505>. <hal-01298974>
  • Nicolas Besse, Michel Mehrenberger. Convergence of classes of high-order semi-Lagrangian schemes for the Vlasov-Poisson system. Mathematics of Computation / Mathematics of Computation, American Mathematical Society, 2008, 77 (261), pp.93-123. <10.1090/S0025-5718-07-01912-6>. <hal-00594785>
  • Martin Campos Pinto, Michel Mehrenberger. Convergence of an adaptive semi-Lagrangian scheme for the Vlasov-Poisson system. Numerische Mathematik, Springer Verlag, 2007, 108 (3), pp.407-444. <10.1007/s00211-007-0120-z>. <hal-00320364>
  • Michel Mehrenberger, Eric Violard. A Hermite type adaptive semi-Lagrangian scheme. Applied Mathematics and Computer Science,, 2006, <10.2478/v10006-007-0027-y>. <inria-00110865>
  • Michel Mehrenberger, Eric Violard, Olivier Hoenen, Martin Campos Pinto, Eric Sonnendrücker. A Parallel Adaptive Vlasov Solver Based on Hierarchical Finite Element Interpolation. Nuclear Instruments and Methods in Physics Research, Elsevier, 2006, Proceedings of the 8th International Computational Accelerator Physics Conference - ICAP 2004, 558 (1), pp.188-191. <10.1016/j.nima.2005.11.225>. <inria-00111165>
  • Michel Mehrenberger. Critical length for a Beurling type theorem. Bollettino dell'Unione Matematica Italiana, 2005, 8, pp.251-258. <>. <hal-00139352>
  • Michel Mehrenberger. Observability of coupled systems. Acta Mathematica Hungarica, Springer Verlag, 2004, 4 (103), pp.321-348. <10.1023/B:AMHU.0000028832.47891.09>. <hal-00139351>

Communication dans un congrès6 documents

  • Michel Mehrenberger, Morgane Bergot, Virginie Grandgirard, Guillaume Latu, Hocine Sellama, et al.. Conservative Semi-Lagrangian solvers on mapped meshes. ICOPS International Conference on Plasma Science, Jul 2012, Edinburgh, United Kingdom. 2012, <10.1109/PLASMA.2012.6383972>. <hal-00759823>
  • Michel Mehrenberger, Nicolas Crouseilles, Virginie Grandgirard, Sever Adrian Hirstoaga, Eric Madaule, et al.. Berk-Breizman and diocotron instability testcases. AMVV Algorithm and Model Verification and Validation, Nov 2012, East-Lansing, United States. <hal-01298988>
  • Jean-Philippe Braeunig, Nicolas Crouseilles, Michel Mehrenberger, Eric Sonnendrücker. Guiding-center simulations on curvilinear meshes. Numerical Models for Controlled Fusion (NMCF09), 2009, Porquerolles, France. American Institute of Mathematical Sciences, Discrete and Continuous Dynamical Systems - Series S, 5 (2), pp.271-282, 2012, <10.3934/dcdss.2012.5.271>. <hal-01298727>
  • Michael Gutnic, Michel Mehrenberger, Eric Sonnendrücker, Olivier Hoenen, Guillaume Latu, et al.. Adaptive 2-D Vlasov Simulation of Particle Beams. ICAP 2006, Oct 2006, Chamonix, France. <>. <hal-01300207>
  • Michel Mehrenberger. High order semi Lagrangian schemes. Atelier du GdR CHANT sur les méthodes numériques pour les équations cinétiques, hyperboliques et de Hamilton-Jacobi, Nov 2005, Strasbourg, France. 2005, <>. <hal-01298992>
  • Olivier Hoenen, Michel Mehrenberger, Eric Violard. Parallelization of an Adaptive Vlasov Solver. EuroPMV/MPI, 2004, Budapest, Hungary. <10.1007/978-3-540-30218-6_59>. <hal-01298972>

Poster2 documents

  • Michel Mehrenberger, Nicolas Crouseilles, Eric Sonnendrücker, Bedros Afeyan. High-Order Numerical Methods for KEEN Wave Vlasov-Poisson Simulations. PPPS, Jun 2013, San Francisco, United States. <10.1109/PLASMA.2013.6634958>. <hal-01298979>
  • Nicolas Crouseilles, Michel Mehrenberger, Hocine Sellama. Résolution numérique de l'opérateur de gyromoyenne. CANUM, May 2010, Carcans-Maubuisson, France. <hal-01298977>

Chapitre d'ouvrage1 document

  • Martin Campos Pinto, Michel Mehrenberger. Adaptive numerical resolution of the Vlasov equation.. Numerical Methods for Hyperbolic and Kinetic Problems, 7, EMS, pp 43--58, 2005, IRMA Lectures in Mathematics and Theoretical Physics, <10.4171/012-1/3>. <hal-00137877>

Direction d'ouvrage, Proceedings1 document

Pré-publication, Document de travail6 documents

  • Guillaume Latu, Michel Mehrenberger, Yaman Güçlü, Maurizio Ottaviani, Eric Sonnendrücker. Field-aligned interpolation for semi-Lagrangian gyrokinetic simulations. 2016. <hal-01315889>
  • Christophe Steiner, Michel Mehrenberger, Nicolas Crouseilles, Philippe Helluy. Quasi-neutrality equation in a polar mesh. 2015. <hal-01248179>
  • Christophe Steiner, Michel Mehrenberger, Daniel Bouche. A semi-Lagrangian discontinuous Galerkin convergence. 2013. <hal-00852411>
  • Nicolas Crouseilles, Michel Mehrenberger, Francesco Vecil. A Discontinuous Galerkin semi-Lagrangian solver for the guiding-center problem. Marseille, France, 19 Juillet - 27 Août 2010. 2012. <hal-00717155>
  • Nicolas Crouseilles, Erwan Faou, Michel Mehrenberger. High order Runge-Kutta-Nyström splitting methods for the Vlasov-Poisson equation. 2011. <inria-00633934>
  • Jean-Philippe Braeunig, Nicolas Crouseilles, Virginie Grandgirard, Guillaume Latu, Michel Mehrenberger, et al.. Some numerical aspects of the conservative PSM scheme in a 4D drift-kinetic code.. 2011. <inria-00435203v2>

Rapport6 documents

  • G Latu, Michel Mehrenberger, M Ottaviani, Eric Sonnendrücker. Aligned interpolation and application to drift kinetic semi-Lagrangian simulations with oblique magnetic field in cylindrical geometry. [Research Report] IRMA. 2014. <hal-01098373>
  • Eric Madaule, Sever Adrian Hirstoaga, Michel Mehrenberger, Jérôme Pétri. Semi-Lagrangian simulations of the diocotron instability. [Research Report] 2013. <hal-00841504>
  • Guillaume Latu, Virginie Grandgirard, Jérémie Abiteboul, Morgane Bergot, Nicolas Crouseilles, et al.. Accuracy of unperturbed motion of particles in a gyrokinetic semi-Lagrangian code. [Research Report] RR-8054, INRIA. 2012, pp.17. <hal-00727118>
  • Jerome Guterl, Jean-Philippe Braeunig, Nicolas Crouseilles, Virginie Grandgirard, Guillaume Latu, et al.. Test of some numerical limiters for the conservative PSM scheme for 4D Drift-Kinetic simulations.. [Research Report] RR-7467, INRIA. 2010, pp.66. <inria-00540948>
  • Frédéric Alauzet, Michel Mehrenberger. P1-conservative solution interpolation on unstructured triangular meshes. [Research Report] RR-6804, INRIA. 2009, pp.48. <inria-00354509>
  • Martin Campos Pinto, Michel Mehrenberger. Convergence of an Adaptive Scheme for the one dimensional Vlasov-Poisson system. [Research Report] RR-5519, INRIA. 2005, pp.49. <inria-00070487>

Thèse1 document

  • Michel Mehrenberger. Inégalites d'observabilité et résolution adaptative de l'équation de Vlasov par éléments finis hiérarchiques. Informatique [cs]. Université Louis Pasteur - Strasbourg I, 2004. Français. <NNT : 2004STR13124>. <tel-00008254>

HDR1 document

  • Michel Mehrenberger. Inégalités d'Ingham et schémas semi-lagrangiens pour l'équation de Vlasov. Équations aux dérivées partielles [math.AP]. Université de Strasbourg, 2012. <tel-00735678>