Garching, 27 May 2019

Eric Sonnendrücker
Max-Planck-Institut für Plasmaphysik
Zentrum Mathematik, TU München

List of publications

International journals:

  1. A. Mishchenko, R. Hatzky, E. Sonnendrücker, R. Kleiber, A. Könies. An iterative approach to an arbitrarily short-wavelength solver in global gyrokinetic simulations. Journal of Plasma Physics, 85(1), (2019).
  2. D. Coulette, E. Franck, P. Helluy, A. Ratnani, E. Sonnendrücker (2019). Implicit time schemes for compressible fluid models based on relaxation methods. Computers & Fluids (2019).


  3. Francis Filbet, Tao Xiong, Eric Sonnendrücker. On the Vlasov–Maxwell System with a Strong Magnetic Field. SIAM Journal on Applied Mathematics, 78(2), 1030-1055 (2018). SIAM Journal on Applied Mathematics 78.2 (2018): 1030-1055,
  4. Guillaume Latu, Michel Mehrenberger, Yaman Güçlü, Maurizio Ottaviani, Eric Sonnendrücker. Field-aligned interpolation for semi-Lagrangian gyrokinetic simulations. Journal of Scientific Computing, 74(3), 1601-1650 (2018).


  5. Natalia Tronko, Alberto Bottino, Tobias Görler, Eric Sonnendrücker, Daniel Told, Laurent Villard. Verification of Gyrokinetic codes: theoretical background and applications. Physics of Plasmas, 24(5), 056115 (2017).,
  6. Alexey Mishchenko, Alberto Bottino, Roman Hatzky, Eric Sonnendrücker, Ralf Kleiber, Axel Könies. Mitigation of the cancellation problem in the gyrokinetic particle-in-cell simulations of global electromagnetic modes. Physics of Plasmas, 24(8), 081206 (2017).
  7. Michael Kraus, Katharina Kormann, Philip J. Morrison, and Eric Sonnendrücker. GEMPIC: Geometric electromagnetic particle-in-cell methods. Journal of Plasma Physics, 83(4), (2017).
  8. Martin Campos Pinto, and Eric Sonnendrücker. Compatible Maxwell solvers with particles I: conforming and non-conforming 2D schemes with a strong Ampere law. SMAI Journal of Computational Mathematics, Vol. 3, 53-89 (2017).
  9. Martin Campos Pinto, and Eric Sonnendrücker. Compatible Maxwell solvers with particles II: conforming and non-conforming 2D schemes with a strong Faraday law. SMAI Journal of Computational Mathematics, Vol. 3, 91-116 (2017).


  10. Natalia Tronko, Alberto Bottino, and Eric Sonnendrücker. ”Second order gyrokinetic theory for particle-in-cell codes.” Physics of Plasmas 23.8 (2016): 082505.,
  11. Martin Campos Pinto, and Eric Sonnendrücker. ”Gauss-compatible Galerkin schemes for time-dependent Maxwell equations.” Mathematics of Computation 85.302 (2016): 2651-2685.,
  12. Claus-Dieter Munz, and Eric Sonnendrücker. ”Maxwell and Magnetohydrodynamic Equations.” Handbook of Numerical Analysis (2016).
  13. Ralf Kleiber, Roman Hatzky, Axel Könies, Alexey Mishchenko, Eric Sonnendrücker, (2016). An explicit large time step particle-in-cell scheme for nonlinear gyrokinetic simulations in the electromagnetic regime. Physics of Plasmas, 23(3), 032501.
  14. Adnane Hamiaz, Michel Mehrenberger, Hocine Sellama, Eric Sonnendrücker (2016): The semi-lagrangian method on curvilinear grids. Communications in Applied and Industrial Mathematics, 7(3), 99-137.
  15. Martin Campos Pinto, Marie Mounier, and Eric Sonnendrücker. ”Handling the divergence constraints in Maxwell and Vlasov–Maxwell simulations.” Applied Mathematics and Computation 272 (2016): 403-419.,
  16. Michel Mehrenberger, Laura Mendoza, Charles Prouveur, Eric Sonnendrücker (2016). Solving the guiding-center model on a regular hexagonal mesh. ESAIM: Proceedings and Surveys, 53, 149-176.
  17. Katharina Kormann, and Eric Sonnendrücker. ”Sparse Grids for the Vlasov–Poisson Equation.” Sparse Grids and Applications-Stuttgart 2014. Springer International Publishing, 2016. 163-190.


  18. Alberto Bottino, Eric Sonnendrücker (2015). Monte Carlo particle-in-cell methods for the simulation of the Vlasov-Maxwell gyrokinetic equations. Journal of Plasma Physics, 81(5): 435810501.
  19. Eric Sonnendrücker, Abigail Wacher, Roman Hatzky, Ralf Kleiber (2015); A split control variate scheme for PIC simulations with collisions, J. Comput. Phys., 295, pp. 402–419.,
  20. Emmanuel Franck, Matthias Hölzl, Alexander Lessig, Eric Sonnendrücker (2015): Energy Conservation and numerical stability for the reduced MHD models of the non-linear JOREK code. ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN), 49(5), pp. 1331–1365.
  21. Emmanuel Frenod, Sever A. Hirstoaga and Eric Sonnendrücker (2015): An exponential integrator for a highly oscillatory vlasov equation, Disc. cont. dyn. syst. series S 8 (1), pp. 169–183,,
  22. Emmanuel Frenod, Sever A. Hirstoaga, Matthieu Lutz and Eric Sonnendrücker (2015): Long Time Behaviour of an Exponential Integrator for a Vlasov-Poisson System with Strong Magnetic Field, Communications in Computational Physics 18 (2), pp. 263–296,,


  23. Martin Campos Pinto, Eric Sonnendrücker, Alex Friedman, David P. Grote, Steve M. Lund (2014): Noiseless Vlasov-Poisson simulations with linearly transformed particles. J. Comput. Phys. 275, pp. 236–256.,
  24. Eric Madaule, Marco Restelli, and Eric Sonnendrücker (2014): Energy conserving discontinuous Galerkin spectral element method for the Vlasov-Poisson system. J. Comput. Phys. 279, pp. 261–188.
  25. Aurore Back, and Eric Sonnendrücker (2014): Finite Element Hodge for spline discrete differential forms. Application to the Vlasov-Poisson system. Appl. Numer. Math. 79, pp. 124-136.
  26. Nicolas Crouseilles, Pierre Navaro, and Eric Sonnendrücker (2014): Charge-conserving grid based methods for the Vlasov–Maxwell equations. Comptes Rendus Mécanique 342 (10-11), pp. 636–646.
  27. Martin Campos Pinto, Sébastien Jund, Stéphanie Salmon, Eric Sonnendrücker (2014): Charge conserving FEM-PIC schemes on general grids, Comptes Rendus Mécanique 342 (10-11), pp. 570–582.


  28. Nicolas Crouseilles, Ahmed Ratnani, Eric Sonnendrücker (2012): An Isogeometric Analysis Approach for the study of the gyrokinetic quasi-neutrality equation, J. Sci. Comput. 231 (2), pp. 373-393.,
  29. Sébastien Jund, Stéphanie Salmon, Eric Sonnendrücker (2012): High-order low dissipation conforming finite-element discretization of the Maxwell equations, Commun. in Comput. Phys. 11 (3), pp. 863-892.


  30. Ahmed Ratnani, Eric Sonnendrücker (2011): Arbitrary High-Order Spline Finite Element Solver for the Time Domain Maxwell equations, J. Sci. Comput. 51 (1), pp. 87–106.,
  31. Thomas Respaud, Eric Sonnendrücker (2011): Analysis of a new class of Forward Semi-Lagrangian schemes for the 1D Vlasov-Poisson Equations, Numer. Math. 118 (2), pp. 329-366.,


  32. Nicolas Crouseilles, Michel Mehrenberger, Eric Sonnendrücker (2010): Conservative semi-Lagrangian schemes for the Vlasov equation, J. Comput. Phys. 229, pp 1927-1953.,


  33. Radouin Belaouar, Nicolas Crouseilles, Pierre Degond, Eric Sonnendrücker (2009): An asymptotically stable semi-Lagrangian scheme in the quasi-neutral limit, J. Sci. Comput. 41, pp. 341–365.,
  34. Nicolas Crouseilles, Thomas Respaud, Eric Sonnendrücker (2009): A forward semi-Lagrangian method for the numerical solution of the Vlasov equation, Comput. Phys. Comm., 180, pp. 1730-1745.,
  35. Emmanuel Frénod, Francesco Salvarani, Eric Sonnendrücker (2009): Long time simulation of a beam in a periodic focusing channel via a two-scale PIC-method. Math. Models Methods Appl. Sci. 19 , no. 2, 175–197.,
  36. Nicolas Crouseilles, Guillaume Latu, Eric Sonnendrücker (2009): A parallel Vlasov solver based on local cubic spline interpolation on patches. J. Comput. Phys. 228, no. 5, 1429–1446.
  37. Mohamed Hayek, Philippe Ackerer, Eric Sonnendr¨c   ker (2009): A new refinement indicator for adaptive parameterization: application to the estimation of the diffusion coefficient in an elliptic problem. J. Comput. Appl. Math. 224, no. 1, 307–319.


  38. Nicolas Besse, Guillaume Latu, Alain Ghizzo, Eric Sonnendrücker and Pierre Bertrand (2008): A wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov-Maxwell system. J. Comput. Phys. 227, no. 16, 7889–7916.


  39. E. Frénod, A. Mouton, E. Sonnendrücker (2007): Two-scale numerical simulation of the weakly compressible 1D isentropic Euler equations. Numer. Math. 108, no. 2, 263–293.,
  40. R. Barthelmé, P. Ciarlet Jr., E. Sonnendrücker (2007): Generalized formulations of Maxwell’s equations for numerical Vlasov-Maxwell simulations. Math. Models Methods Appl. Sci. 17, no. 5, 657–680.
  41. M. Bostan, E. Sonnendrücker (2007): Periodic solutions for nonlinear elliptic equations. Application to charged particle beam focusing systems. M2AN Math. Model. Numer. Anal. 40, no. 6, 1023–1052.
  42. N. Besse, N.J. Mauser, E. Sonnendrücker (2007): Numerical approximation of self-consistent Vlasov models for low-frequency electromagnetic phenomena. Int. J. Appl. Math. Comput. Sci. 17, no. 3, 361–374.
  43. N. Crouseilles, G. Latu, E. Sonnendrücker (2007): Hermite spline interpolation on patches for parallelly solving the Vlasov-Poisson equation. Int. J. Appl. Math. Comput. Sci. 17, no. 3, 335–349.
  44. V. Grandgirard, Y. Sarazin, P. Angelino, B. Alberto, N. Crouseilles, G. Darmet, G. Dif-Pradalier, X. Garbet, P. Ghendrih, S. Jolliet, G. Latu, L. Villard, E. Sonnendrücker (2007): Global full-f gyrokinetic simulations of plasma turbulence, Plasma physics and controlled fusion, Vol. 49, pp. B173-B182.


  45. F. Filbet and E. Sonnendrücker (2006): Modeling and Numerical Simulation of Space Charge Dominated Beams in the Paraxial Approximation. Math. Models Methods Appl. Sci. 16, no. 5, 763–791.,
  46. V. Grandgirard, M. Brunetti, P. Bertrand, N. Besse, X. Garbet, P. Ghendrih, G. Manfredi, Y. Sarazin, O. Sauter, E. Sonnendrücker, J. Vaclavik, L. Villard (2006): A drift-kinetic semi-Lagrangian 4D code for ion turbulence simulation J. Comput. Phys. 217 (2), 395–423.


  47. N. Besse, J. Segré and E. Sonnendrücker (2005): Semi-Lagrangian schemes for the two-dimensional Vlasov-Poisson system on unstructured meshes. Trans. Th. Stat. Phys. 34 (3-5), p. 311-332.


  48. E. Sonnendrücker, F. Filbet, A. Friedman, E. Oudet and J.-L. Vay (2004): Vlasov simulations of beams with a moving grid, Computer Physics Communications 164 (1-3), p. 390-395 .,
  49. M. Gutnic, M. Haefele, I. Paun and E. Sonnendrücker (2004): Vlasov simulations on an adaptive phase-space grid. Computer Physics Communications 164 (1-3), p. 214-219.


  50. N. Besse, E. Sonnendrücker (2003): Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space. J. Comput. Phys. 191 (2), 341–376.
  51. F. Huot, A. Ghizzo, P. Bertrand, E. Sonnendrücker, O. Coulaud (2003): Instability of the time splitting scheme for the one-dimensional and relativistic Vlasov-Maxwell system. J. Comput. Phys. 185 (2), 512–531.
  52. S. Benachour, F. Filbet, Ph. Laurençot, E. Sonnendrücker (2003): Global existence for the Vlasov-Darwin system in R3 for small initial data. Math. Methods Appl. Sci. 26, 4, 297–319.
  53. F. Filbet, E. Sonnendrücker (2003): Comparison of Eulerian Vlasov Solvers. Comp. Phys. Comm. 150, no. 3 pp. 247-266


  54. F. Filbet, E. Sonnendrücker, P. Bertrand (2001): Conservative Numerical Schemes for the Vlasov Equation, J. Comput. Phys. 172, no. 1, 1–22.
  55. E. Frénod, P.-A. Raviart, E. Sonnendrücker (2001): Two-scale expansion of a singularly perturbed convection equation, J. Math. Pures Appl. 80, no. 8, 815–843.
  56. E. Frénod, E. Sonnendrücker (2001): The Finite Larmor Radius Approximation, SIAM J. Math. Anal. 32, no. 6, 1227–1247.


  57. E. Frénod et E. Sonnendrücker (2000): Long Time Behavior of The Two-Dimensional Vlasov Equation with a Strong External Magnetic Field, Math. Models Methods Appl. Sci. 10, no. 4, 539–553.
  58. C.-D. Munz, P. Omnes, R. Schneider, E. Sonnendrücker, U. Voss (2000): Divergence correction techniques for Maxwell solvers based on a hyperbolic model, J. Comput. Phys. 161, no. 2, 484–511.


  59. C.-D. Munz, R. Schneider, E. Sonnendrücker, U. Voss (1999): Maxwell’s equations when the charge conservation is not satisfied, C. R. Acad. Sci. Paris Sér. I Math. 328, no. 5, 431–436.
  60. E. Sonnendrücker, J. Roche, P. Bertrand, A. Ghizzo (1999): The Semi-Lagrangian Method for the Numerical Resolution of Vlasov Equations, J. Comput. Phys 149, 201–220.
  61. F. Assous, P. Ciarlet Jr., P.-A. Raviart et E. Sonnendrücker (1999): Characterization of the Singular Part of the Solution of Maxwell’s Equations in a Polyhedral Domain, Math. Meth. Appl. Sci. 22, 485–499.<485::AID-MMA46>3.0.CO;2-E
  62. C.-D. Munz, R. Schneider, E. Sonnendrücker, E. Stein, U. Voss, T. Westermann (1999): A Finite-Volume Particle-In-Cell Method for the Numerical Treatment of Maxwell-Lorentz Equations on Boundary Fitted Meshes, Int. J. Numer. Meth. Eng. 44, 461–487.;2-%23
  63. O. Coulaud, E. Sonnendrücker, E. Dillon, P. Bertrand, A. Ghizzo (1999): Parallelisation of Semi-Lagrangian Vlasov Codes, J. Plasma Phys. 61, 435–448.


  64. E. Frénod et E. Sonnendrücker (1998): Homogenization of the Vlasov Equation and of the Vlasov-Poisson System with a Strong External Magnetic Field, Asymptotic Analysis 18 (3-4), 193-213.
  65. F. Assous, P. Ciarlet Jr, E. Sonnendrücker (1998): Resolution of the Maxwell equations in a domain with reentrant corners, Modelisation Math. Anal. Numer. 32 (3), 359–389.


  66. P. Ciarlet Jr, E. Sonnendrücker (1997): A Decomposition of the Electromagnetic Field. Application to the Darwin Model, Math. Models and Methods Appl. Sci. 7 (8), 1085–1120.


  67. P.-A. Raviart, E. Sonnendrücker (1996): A Hierarchy of Approximate Models for the Maxwell Equations, Numer. Math. 73, p. 329–372.
  68. F. Assous, P. Ciarlet Jr, E. Sonnendrücker (1996): Résolution des équations de Maxwell dans un domaine avec un coin rentrant, C. R. Acad. Sci. Paris, t. 323, Série I, p. 203–208.


  69. E. Sonnendrücker, J.J. Ambrosiano, S.T. Brandon (1995): A finite element formulation of the Darwin PIC model for use on unstructured grids, J. Comput. Phys. 121, p. 81–297.
  70. P.-A. Raviart, E. Sonnendrücker (1995): Approximate Models for the Maxwell Equations J. Comput. Appl. Math. 63, p. 69-81.
  71. P.-A. Raviart, E. Sonnendrücker (1995): Modèles quasistatique et de Darwin pour les équations de Maxwell, C. R. Acad. Sci. Paris, t. 320, Série I, 307–313.

Refereed articles in conference proceedings:

  1. Afeyan, B., Casas, F., Crouseilles, N., Dodhy, A., Faou, E., Mehrenberger, M., Sonnendrücker, E. (2014): Simulations of Kinetic Electrostatic Electron Nonlinear (KEEN) Waves with Two-Grid, Variable Velocity Resolution and High-Order Time-Splitting. The European Physical Journal D 68.10, 1–21.,
  2. M. Mehrenberger, C. Steiner, L. Marradi, N. Crouseilles, E. Sonnendrücker and B. Afeyan (2013): Vlasov on GPU, ESAIM: Proc. 43, 37–58.
  3. J.-P. Braeunig, N.Crouseilles, M. Mehrenberger, E. Sonnendrücker, (2012): Guiding-center simulations on curvilinear meshes. Discrete and Continuous Dynamical Systems Series S, 5 (2), pp. 271–282. doi:10.3934/dcdss.2012.5.271.
  4. A. Ratnani and E. Sonnendr¨c                ker 2012: Isogeometric analysis in reduced magnetohydrodynamics. Comput. Sci. Disc. 5 014007
  5. N. Crouseilles, M. Gutnic, G. Latu, E. Sonnendrücker (2008): Comparison of two Eulerian solvers for the four-dimensional Vlasov equation. I. Commun. Nonlinear Sci. Numer. Simul. 13, no. 1, 88–93.
  6. N. Crouseilles, M. Gutnic, G. Latu, E. Sonnendrücker (2008): Comparison of two Eulerian solvers for the four-dimensional Vlasov equation. II. Commun. Nonlinear Sci. Numer. Simul. 13, no. 1, 94–99.
  7. V. Grandgirard, Y. Sarazin, X. Garbet, G. Dif-Pradalier, P. Ghendrih, N. Crouseilles, G. Latu, E. Sonnendrücker, N. Besse (2008): Computing ITG turbulence with a full-f semi-Lagrangian code, Communications in Nonlinear Science and Numerical Simulation, pp 81-87, Vol. 13(1).
  8. N. Crouseilles, G. Latu, E. Sonnendrücker (2007): Hermite splines interpolation on patches for a parallel Vlasov beam simulations, Nuclear instruments and Methods in Physics Research A., pp 129-132, Vol. 557(1).
  9. Guillaume Latu, Nicolas Crouseilles, Virginie Grandgirard, Eric Sonnendrücker (2007): Gyrokinetic Semi-Lagrangian Parallel Simulation using a Hybrid OpenMP/MPI Programming, Recent Advances in PVM an MPI, Springer, LNCS, pp 356-364, Vol. 4757.
  10. Hyam Abboud, Sébastien Jund, Stéphanie Salmon, Eric Sonnendrücker, Hamdi Zorgati (2007): Two-scale simulation of Maxwell’s equations, ESAIM: PROC Volume 16 CEMRACS 2005 - Computational Aeroacoustics and Computational Fluid Dynamics in Turbulent Flows, 211 – 223.,
  11. N. Crouseilles, G. Latu, J.-L. Lemaire, E. Sonnendrücker (2006): Semi-Lagrangian Vlasov codes for the transport of intense particle beams in the 4D transverse phase-space, Beam Dynamics Newsletter, Num. 41.
  12. V. Grandgirard, Y. Sarazin, X. Garbet, G. Dif-Pradalier, P. Ghendrih, N. Crouseilles, G. Latu, E. Sonnendrücker, N. Besse, P. Bertrand (2006): GYSELA, a full-f global gyrokinetic Semi-Lagrangian code for ITG turbulence simulations, Proceedings of Theory of Fusion Plasmas, Varenna.
  13. N. Besse, F. Filbet, M. Gutnic, I. Paun, E. Sonnendrücker (2003): An adaptive numerical method for the Vlasov equation based on a multi-resolution analysis, in Numerical Mathematics and Advanced Applications, ENUMATH 2001, F. Brezzi, A. Buffa, S. Corsaro, A. Murli (Eds), (Springer, 2003).
  14. F. Filbet, E. Sonnendrücker (2003): Numerical methods for the Vlasov equation, in Numerical Mathematics and Advanced Applications, ENUMATH 2001, F. Brezzi, A. Buffa, S. Corsaro, A. Murli (Eds), (Springer, 2003).
  15. F. Filbet, E. Sonnendrücker, J.-L. Lemaire (2002): Direct Axisymmetric Vlasov Simulations of space charged dominated beams. Lecture Notes in Computer Sciences, ICCS 2002, part 3, 305–314.
  16. F. Kemm, C.-D. Munz, R. Schneider, E. Sonnendrücker (2001): Divergence corrections in the numerical simulation of electromagnetic wave propagation. Hyperbolic problems: theory, numerics, applications, Vol. I, II (Magdeburg, 2000), 603–612, Internat. Ser. Numer. Math., 140, 141, Birkhäuser, Basel, 2001.
  17. F. Assous, P. Ciarlet, Jr., P.-A.Raviart, J. Segré, E. Sonnendrücker (1998): The solution of Maxwell’s equations in a non-convex polyhedron. I. Saddle-point approach and singularities. Mathematical and numerical aspects of wave propagation (Golden, CO, 1998), 364–368, SIAM, Philadelphia, PA, 1998
  18. E. Sonnendrücker, A. Friedman, D.P. Grote (1999): Progress towards simulating heavy ion beams for Inertial Fusion Energy based on 1) A Darwin model field solver, and 2) A semi-Lagrangian Vlasov solver. Proceedings of the 1999 Particle Accelerator Conference, (Editors: A. Luccio, W. MacKay)
  19. C.-D. Munz, S. Roller, E. Sonnendrücker (1999): A numerical approach to multiple scale problems based on asymptotic analysis. Numerical treatment of multi-scale problems (Kiel, 1997), 134–145, Notes Numer. Fluid Mech., 70, Vieweg, Braunschweig, 1999.

Internal reports:

  1. Jean-Philippe Braeunig, Nicolas Crouseilles, Virginie Grandgirard, Guillaume Latu, Michel Mehrenberger, Eric Sonnendrücker (2009): Some numerical aspects of the conservative PSM scheme in a 4D drift-kinetic code,
  2. E. Sonnendrücker, A. Friedman, E.P. Lee: A model for incorporating module impedance and multi-beam effects into WARP, HIFAN Note 1001, Lawrence Berkeley National Laboratory.
  3. E. Sonnendrücker, A. Friedman, D.P. Grote, S.M. Lund: Simulation of charged particle beams using a semi-Lagrangian Vlasov method, HIFAN Note 999, Lawrence Berkeley National Laboratory.
  4. E. Sonnendrücker, J.J. Barnard, A. Friedman, S.M. Lund: Vlasov simulations of halo formation in mismatched beams, HIFAN Note 1002, Lawrence Berkeley National Laboratory.

Edition of books:

  1. Three Courses on Partial Differential Equations, Series: IRMA Lectures in Mathematics and Theoretical Physics, de Gruyter, Berlin 2003.
  2. Numerical methods for hyperbolic and kinetic equations, European Mathematical Society, 2005. Co-édition avec S. Cordier, T. Goudon et M. Gutnic.