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Gilles Vilmart
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2020 – today
- 2022
- [j25]Adrien Laurent, Gilles Vilmart:
Order Conditions for Sampling the Invariant Measure of Ergodic Stochastic Differential Equations on Manifolds. Found. Comput. Math. 22(3): 649-695 (2022) - [j24]David Cohen, Gilles Vilmart:
Drift-preserving numerical integrators for stochastic Poisson systems. Int. J. Comput. Math. 99(1): 4-20 (2022) - 2021
- [j23]Guillaume Bertoli, Christophe Besse, Gilles Vilmart:
Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions. Math. Comput. 90(332): 2705-2729 (2021) - [j22]Ibrahim Almuslimani, Gilles Vilmart:
Explicit Stabilized Integrators for Stiff Optimal Control Problems. SIAM J. Sci. Comput. 43(2): A721-A743 (2021) - [i5]Assyr Abdulle, Charles-Edouard Bréhier, Gilles Vilmart:
Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs. CoRR abs/2102.03209 (2021) - 2020
- [j21]Philippe Chartier, Mohammed Lemou, Florian Méhats, Gilles Vilmart:
A New Class of Uniformly Accurate Numerical Schemes for Highly Oscillatory Evolution Equations. Found. Comput. Math. 20(1): 1-33 (2020) - [j20]Adrien Laurent, Gilles Vilmart:
Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs. Math. Comput. 89(321): 169-202 (2020) - [j19]Adrien Laurent, Gilles Vilmart:
Multirevolution Integrators for Differential Equations with Fast Stochastic Oscillations. SIAM J. Sci. Comput. 42(1): A115-A139 (2020) - [j18]Guillaume Bertoli, Gilles Vilmart:
Strang Splitting Method for Semilinear Parabolic Problems With Inhomogeneous Boundary Conditions: A Correction Based on the Flow of the Nonlinearity. SIAM J. Sci. Comput. 42(3): A1913-A1934 (2020) - [i4]David Cohen, Gilles Vilmart:
Drift-preserving numerical integrators for stochastic Poisson systems. CoRR abs/2005.13991 (2020) - [i3]Adrien Laurent, Gilles Vilmart:
Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds. CoRR abs/2006.09743 (2020) - [i2]Guillaume Bertoli, Christophe Besse, Gilles Vilmart:
Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with oblique boundary conditions. CoRR abs/2011.05178 (2020)
2010 – 2019
- 2019
- [j17]Philippe Chartier, Mohammed Lemou, Florian Méhats, Gilles Vilmart:
Highly Oscillatory Problems with Time-Dependent Vanishing Frequency. SIAM J. Numer. Anal. 57(2): 925-944 (2019) - [i1]Ibrahim Almuslimani, Gilles Vilmart:
Explicit stabilized integrators for stiff optimal control problems. CoRR abs/1910.10584 (2019) - 2018
- [j16]Assyr Abdulle, Ibrahim Almuslimani, Gilles Vilmart:
Optimal Explicit Stabilized Integrator of Weak Order 1 for Stiff and Ergodic Stochastic Differential Equations. SIAM/ASA J. Uncertain. Quantification 6(2): 937-964 (2018) - 2016
- [j15]Charles-Edouard Bréhier, 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(4) (2016) - 2015
- [j14]Assyr Abdulle, Martin E. Huber, Gilles Vilmart:
Linearized Numerical Homogenization Method for Nonlinear Monotone Parabolic Multiscale Problems. Multiscale Model. Simul. 13(3): 916-952 (2015) - [j13]Assyr Abdulle, Gilles Vilmart, Konstantinos C. Zygalakis:
Long Time Accuracy of Lie-Trotter Splitting Methods for Langevin Dynamics. SIAM J. Numer. Anal. 53(1): 1-16 (2015) - [j12]Gilles Vilmart:
Postprocessed Integrators for the High Order Integration of Ergodic SDEs. SIAM J. Sci. Comput. 37(1) (2015) - 2014
- [j11]Assyr Abdulle, Gilles Vilmart:
Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Math. Comput. 83(286): 513-536 (2014) - [j10]Philippe Chartier, Joseba Makazaga, Ander Murua, Gilles Vilmart:
Multi-revolution composition methods for highly oscillatory differential equations. Numerische Mathematik 128(1): 167-192 (2014) - [j9]Assyr Abdulle, Gilles Vilmart, Konstantinos C. Zygalakis:
High Order Numerical Approximation of the Invariant Measure of Ergodic SDEs. SIAM J. Numer. Anal. 52(4): 1600-1622 (2014) - [j8]Gilles Vilmart:
Weak Second Order Multirevolution Composition Methods for Highly Oscillatory Stochastic Differential Equations with Additive or Multiplicative Noise. SIAM J. Sci. Comput. 36(4) (2014) - 2013
- [j7]Assyr Abdulle, 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. Comput. Phys. 242: 869-888 (2013) - [j6]Assyr Abdulle, Gilles Vilmart, Konstantinos C. Zygalakis:
Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations. SIAM J. Sci. Comput. 35(4) (2013) - 2012
- [j5]Assyr Abdulle, Gilles Vilmart:
A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems. Numerische Mathematik 121(3): 397-431 (2012) - [j4]Assyr Abdulle, David Cohen, Gilles Vilmart, Konstantinos C. Zygalakis:
High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations. SIAM J. Sci. Comput. 34(3) (2012) - 2010
- [j3]Philippe Chartier, Ernst Hairer, Gilles Vilmart:
Algebraic Structures of B-series. Found. Comput. Math. 10(4): 407-427 (2010)
2000 – 2009
- 2008
- [j2]Gilles Vilmart:
Reducing round-off errors in rigid body dynamics. J. Comput. Phys. 227(15): 7083-7088 (2008) - 2007
- [j1]Philippe Chartier, Ernst Hairer, Gilles Vilmart:
Numerical integrators based on modified differential equations. Math. Comput. 76(260): 1941-1953 (2007)
Coauthor Index
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