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Publications
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Adrien Laurent and Gilles Vilmart, Multirevolution integrators for differential equations with fast stochastic oscillations, SIAM J. Sci. Comput 42 (2020), 115-139. Abstract.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Gilles Vilmart, Postprocessed integrators for the high order
integration of ergodic SDEs, SIAM J. Sci. Comput. 37 (2015), 201-220. Abstract.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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
- 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
- Gilles Vilmart, Rigid body dynamics (17 pages), Encyclopedia of Applied and Computational Mathematics, Springer, 2013.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Philippe Chartier, Ernst Hairer, and Gilles Vilmart, Algebraic
structures of B-series, Found.
Comput. Math. 10(7) (2010) 407–427. Abstract
- François Castella, Philippe Chartier, Stéphane Descombes,
and Gilles Vilmart, Splitting methods
with complex times for parabolic equations, BIT 49 (2009) 487-508. Abstract
- 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
- Gilles Vilmart, Reducing round-off errors
in rigid body dynamics, J.Comput.
Phys. 227 (2008) 7083-7088. Abstract
- Philippe Chartier, Ernst Hairer, and Gilles Vilmart, Modified
differential equations, ESAIM
Proceedings, Vol 21, 16-20, Sep. 2007. Abstract
- Philippe Chartier, Ernst Hairer, and Gilles Vilmart, Numerical
integrators based on modified differential equations, Math.
Comp. 76 (2007) 1941-1953. Abstract
- 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
- Monique Chyba, Ernst Hairer, and Gilles Vilmart, Symplectic
integrators in sub-Riemannian geometry: the Martinet case, INRIA Research Report No. 6017, Nov. 2006. Abstract
- Philippe Chartier, Ernst Hairer, and Gilles Vilmart, A
substitution law for B-series vector fields, INRIA Research
Report No. 5498, Feb. 2005. Abstract
Vulgarisation scientifique
Last update:
14-Fév-2023