Gilles Vilmart

Publication Activity (10 Years)

Years Active: 2007-2022
Publications (10 Years): 16

Top Topics

Boundary Conditions

Numerical Scheme

Top Venues

SIAM J. Sci. Comput.

SIAM J. Numer. Anal.

Publications

Adrien Laurent, Gilles Vilmart
Order Conditions for Sampling the Invariant Measure of Ergodic Stochastic Differential Equations on Manifolds. Found. Comput. Math. 22 (3) (2022)
David Cohen, Gilles Vilmart
Drift-preserving numerical integrators for stochastic Poisson systems. Int. J. Comput. Math. 99 (1) (2022)
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) (2021)
Assyr Abdulle, Charles-Edouard Bréhier, Gilles Vilmart
Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs. CoRR (2021)
Ibrahim Almuslimani, Gilles Vilmart
Explicit Stabilized Integrators for Stiff Optimal Control Problems. SIAM J. Sci. Comput. 43 (2) (2021)
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) (2020)
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) (2020)
David Cohen, Gilles Vilmart
Drift-preserving numerical integrators for stochastic Poisson systems. CoRR (2020)
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) (2020)
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 (2020)
Adrien Laurent, Gilles Vilmart
Multirevolution Integrators for Differential Equations with Fast Stochastic Oscillations. SIAM J. Sci. Comput. 42 (1) (2020)
Adrien Laurent, Gilles Vilmart
Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds. CoRR (2020)
Ibrahim Almuslimani, Gilles Vilmart
Explicit stabilized integrators for stiff optimal control problems. CoRR (2019)
Philippe Chartier, Mohammed Lemou, Florian Méhats, Gilles Vilmart
Highly Oscillatory Problems with Time-Dependent Vanishing Frequency. SIAM J. Numer. Anal. 57 (2) (2019)
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) (2018)
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)
Gilles Vilmart
Postprocessed Integrators for the High Order Integration of Ergodic SDEs. SIAM J. Sci. Comput. 37 (1) (2015)
Assyr Abdulle, Gilles Vilmart, Konstantinos C. Zygalakis
Long Time Accuracy of Lie-Trotter Splitting Methods for Langevin Dynamics. SIAM J. Numer. Anal. 53 (1) (2015)
Assyr Abdulle, Martin E. Huber, Gilles Vilmart
Linearized Numerical Homogenization Method for Nonlinear Monotone Parabolic Multiscale Problems. Multiscale Model. Simul. 13 (3) (2015)
Assyr Abdulle, Gilles Vilmart, Konstantinos C. Zygalakis
High Order Numerical Approximation of the Invariant Measure of Ergodic SDEs. SIAM J. Numer. Anal. 52 (4) (2014)
Philippe Chartier, Joseba Makazaga, Ander Murua, Gilles Vilmart
Multi-revolution composition methods for highly oscillatory differential equations. Numerische Mathematik 128 (1) (2014)
Assyr Abdulle, Gilles Vilmart
Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Math. Comput. 83 (286) (2014)
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)
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 (2013)
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)
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)
Assyr Abdulle, Gilles Vilmart
A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems. Numerische Mathematik 121 (3) (2012)
Philippe Chartier, Ernst Hairer, Gilles Vilmart
Algebraic Structures of B-series. Found. Comput. Math. 10 (4) (2010)
Gilles Vilmart
Reducing round-off errors in rigid body dynamics. J. Comput. Phys. 227 (15) (2008)
Philippe Chartier, Ernst Hairer, Gilles Vilmart
Numerical integrators based on modified differential equations. Math. Comput. 76 (260) (2007)