Publications

  1. Q.M. Wargnier, Gilles Vilmart, Juan Martínez-Sykora, Biggo H. Hansteen, Bart de Pontieu, Time-Adaptive PIROCK Method with Error Control for Multi-Fluid and Single-Fluid MHD Systems, arXiv:2409.15552, submitted for publication (2024), 16 pages.
  2. Antoine Sandoz, Verena Ducret, Georg A. Gottwald, Gilles Vilmart, Karl Perron, SINDy for delay-differential equations: application to model bacterial zinc response, arXiv:2208.10826, Proc. R. Soc. A. (2023) 479:20220556, 18 pages. Abstract.
  3. Assyr Abdulle, Charles-Edouard Bréhier, and Gilles Vilmart, Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs, arXiv:2102.03209, IMA J. Numer. Anal. 43 (2023), 258-292. Abstract.
  4. Adrien Laurent and Gilles Vilmart, Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds, arXiv:2006.09743, Found. Comput. Math. 22 (2022) 649–695. Abstract.
  5. David Cohen and Gilles Vilmart, Drift-preserving numerical integrators for stochastic Poisson systems, arXiv:2005.13991, Int. J. Comput. Math. 99 (2022), 4-10. Abstract.
  6. Guillaume Bertoli, Christophe Besse, and Gilles Vilmart, Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions, arXiv:2011.05178, Math. Comp. 90 (2021) 2705-2729. Abstract.
  7. Ibrahim Almuslimani and Gilles Vilmart, Explicit stabilized integrators for stiff optimal control problems, arXiv:1910.10584, SIAM J. Sci. Comput. 43 (2021), A721-A743. Abstract.
  8. Armin Eftekhari, Bart Vandereycken, Gilles Vilmart, Konstantinos C. Zygalakis, Explicit stabilised gradient descent for faster strongly convex optimisation, arXiv:1805.07199, BIT Numer Math 61 (2021), 113-139, Abstract.
  9. Guillaume Bertoli and Gilles Vilmart, Strang splitting method for semilinear parabolic problems with inhomogeneous boundary conditions: a correction based on the flow of the nonlinearity, arXiv:1904.08826, SIAM J. Sci. Comput. 42 (2020), A1913-A1934. Abstract.
  10. Adrien Laurent and Gilles Vilmart, Multirevolution integrators for differential equations with fast stochastic oscillations, SIAM J. Sci. Comput 42 (2020), 115-139. Abstract.
  11. Adrien Laurent and Gilles Vilmart, Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs, arXiv:1707.02877, Math. Comp. 89 (2020), 169-202. Abstract.
  12. Philippe Chartier, Mohammed Lemou, Florian Méhats, and Gilles Vilmart, A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations, Found. Comput. Math. 20 (2020) 1–33. Abstract.
  13. Assyr Abdulle, Gregorios A. Pavliotis, and Gilles Vilmart, Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations, arXiv:1903.03024, C. R. Acad. Sci. Paris; Ser. I 357 (2019), 349-354. Abstract.
  14. Philippe Chartier, Mohammed Lemou, Florian Méhats, and Gilles Vilmart, Highly-oscillatory problems with time-dependent vanishing frequency, SIAM J. Numer. Anal. 57 (2019), 925-944. Abstract.
  15. Assyr Abdulle, Ibrahim Almuslimani, and Gilles Vilmart, Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations, SIAM/ASA J. Uncertain. Quantif. 6 (2018), no. 2, 937–964. Abstract.
  16. Alain Durmus, Gareth O. Robert, Gilles Vilmart, and Konstantinos C. Zygalakis, Fast Langevin based algorithm for MCMC in high dimensions, Ann. Appl. Probab. 27 (2017), 2195-2237. Abstract.
  17. Charles-Edouard Bréhier and Gilles Vilmart, High-order integrator for sampling the invariant distribution of a class of parabolic stochastic PDEs with additive space-time noise, SIAM J. Sci. Comput 38 (2016) A2283-A2306. Abstract.
  18. Nicolas Crouseilles, Mohammed Lemou, and Gilles Vilmart, Asymptotic Preserving numerical schemes for multiscale parabolic problems, C. R. Acad. Sci. Paris; Ser. I 354 (2016) 271–276. Abstract.
  19. Assyr Abdulle, Martin Huber, and Gilles Vilmart, Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems, SIAM Multiscale Model. Simul. 13 (2015), 916-952. Abstract.
  20. Gilles Vilmart, Postprocessed integrators for the high order integration of ergodic SDEs, SIAM J. Sci. Comput. 37 (2015), 201-220. Abstract.
  21. Assyr Abdulle, Gilles Vilmart, and Konstantinos C. Zygalakis, Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics, SIAM J. Numer. Anal. 53 (2015), 1-16. Abstract.
  22. Assyr Abdulle, Yun Bai, and Gilles Vilmart, Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems, DCDS-S 8 (2015), 91-118. Abstract.
  23. Gilles Vilmart, Weak second order multi-revolution composition methods for highly oscillatory stochastic differential equations with additive or multiplicative noise, SIAM J. Sci. Comput. 36 (2014), 1770-1796. Abstract.
  24. Assyr Abdulle, Gilles Vilmart, and Konstantinos C. Zygalakis, High order numerical approximation of the invariant measure of ergodic SDEs, SIAM J. Numer. Anal. 52 (2014), 1600-1622. Abstract.
  25. Assyr Abdulle, Yun Bai, and Gilles Vilmart, An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems, Int. J. Numer. Meth. Engng 99 (2014), 469-486. Abstract.
  26. Philippe Chartier, Joseba Makazaga, Ander Murua, and Gilles Vilmart, Multi-revolution composition methods for highly oscillatory differential equations, Numer. Math. 128 (2014), 167-192. Abstract
  27. Assyr Abdulle and Gilles Vilmart, Fully discrete analysis of the finite element heterogeneous multiscale method for nonlinear elliptic homogenization problems, Math. Comp. 83 (2014) 513-536. Abstract
  28. Gilles Vilmart, Rigid body dynamics (17 pages), Encyclopedia of Applied and Computational Mathematics, Springer, 2013.
  29. Assyr Abdulle, Gilles Vilmart, and Konstantinos C. Zygalakis, Weak second order explicit stabilized methods for stiff stochastic differential equations, SIAM J. Sci. Comput. 35 (2013):1792-1814. Abstract
  30. Assyr Abdulle, Gilles Vilmart, and Konstantinos C. Zygalakis, Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations, BIT 53 (2013) 827-840. Abstract
  31. Assyr Abdulle and Gilles Vilmart, PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise, J. Comp. Phys. 242 (2013), 869-888. Abstract
  32. Assyr Abdulle, David Cohen, Gilles Vilmart, and Konstantinos C. Zygalakis, High order weak methods for stochastic differential equations based on modified equations, SIAM J. Sci. Comput. 34 (2012):1800-1823. Abstract
  33. Assyr Abdulle and Gilles Vilmart, A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems, Numer. Math. 121 (2012) 397-431. Abstract
  34. Assyr Abdulle and Gilles Vilmart, Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete space-time analysis, Math. Models Methods Appl. Sci. 22 (2012) 1250002 (40 pages). Abstract
  35. Assyr Abdulle and Gilles Vilmart, The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods, C. R. Acad. Sci. Paris, Ser. I 349 (2011), 1041-1046. Abstract
  36. Philippe Chartier, Ernst Hairer, and Gilles Vilmart, Algebraic structures of B-series, Found. Comput. Math. 10(7) (2010) 407–427. Abstract
  37. François Castella, Philippe Chartier, Stéphane Descombes, and Gilles Vilmart, Splitting methods with complex times for parabolic equations, BIT 49 (2009) 487-508. Abstract
  38. Monique Chyba, Ernst Hairer, and Gilles Vilmart, The role of sympectic integrators in optimal control, Optim. Control Appl. Meth. (2009) 30(4):367-382. Abstract
  39. Gilles Vilmart, Reducing round-off errors in rigid body dynamics, J.Comput. Phys. 227 (2008) 7083-7088. Abstract
  40. Philippe Chartier, Ernst Hairer, and Gilles Vilmart, Modified differential equations, ESAIM Proceedings, Vol 21, 16-20, Sep. 2007. Abstract
  41. Philippe Chartier, Ernst Hairer, and Gilles Vilmart, Numerical integrators based on modified differential equations, Math. Comp. 76 (2007) 1941-1953. Abstract
  42. Ernst Hairer and Gilles Vilmart, Preprocessed Discrete Moser-Veselov algorithm for the full dynamics of the rigid body, J. Phys. A: Math. Gen. 39 (2006) 13225-13235. Abstract

Theses

Reports

Vulgarisation scientifique

 

Last update: 25-Sep-2024