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Gilles Vilmart
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Splitting methods with complex times for parabolic equations
F Castella, P Chartier, S Descombes, G Vilmart
BIT Numerical Mathematics 49 (3), 487-508, 2009
942009
Algebraic structures of B-series
P Chartier, E Hairer, G Vilmart
Foundations of Computational Mathematics 10 (4), 407-427, 2010
902010
High order numerical approximation of the invariant measure of ergodic SDEs
A Abdulle, G Vilmart, KC Zygalakis
SIAM Journal on Numerical Analysis 52 (4), 1600-1622, 2014
762014
High weak order methods for stochastic differential equations based on modified equations
A Abdulle, D Cohen, G Vilmart, KC Zygalakis
SIAM Journal on Scientific Computing 34 (3), A1800-A1823, 2012
692012
Numerical integrators based on modified differential equations
P Chartier, E Hairer, G Vilmart
Mathematics of computation 76 (260), 1941-1953, 2007
622007
Long time accuracy of Lie--Trotter splitting methods for Langevin dynamics
A Abdulle, G Vilmart, KC Zygalakis
SIAM Journal on Numerical Analysis 53 (1), 1-16, 2015
582015
The role of symplectic integrators in optimal control
M Chyba, E Hairer, G Vilmart
Optimal control applications and methods 30 (4), 367-382, 2009
482009
Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems
A Abdulle, G Vilmart
Mathematics of Computation 83 (286), 513-536, 2014
47*2014
A substitution law for B-series vector fields
P Chartier, E Hairer, G Vilmart
INRIA, 2005
462005
Weak second order explicit stabilized methods for stiff stochastic differential equations
A Abdulle, G Vilmart, KC Zygalakis
SIAM Journal on Scientific Computing 35 (4), A1792-A1814, 2013
422013
Preprocessed discrete Moser–Veselov algorithm for the full dynamics of a rigid body
E Hairer, G Vilmart
Journal of Physics A: Mathematical and General 39 (42), 13225, 2006
392006
A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems
A Abdulle, G Vilmart
Numerische Mathematik 121 (3), 397-431, 2012
382012
Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems
A Abdulle, Y Bai, G Vilmart
Discrete & Continuous Dynamical Systems-S 8 (1), 91, 2015
342015
Coupling heterogeneous multiscale FEM with Runge–Kutta methods for parabolic homogenization problems: A fully discrete spacetime analysis
A Abdulle, G Vilmart
Mathematical Models and Methods in Applied Sciences 22 (06), 1250002, 2012
322012
A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations
P Chartier, M Lemou, F Méhats, G Vilmart
Foundations of Computational Mathematics 20 (1), 1-33, 2020
282020
PIROCK: A swiss-knife partitioned implicit–explicit orthogonal Runge–Kutta Chebyshev integrator for stiff diffusion–advection–reaction problems with or without noise
A Abdulle, G Vilmart
Journal of Computational Physics 242, 869-888, 2013
282013
Fast Langevin based algorithm for MCMC in high dimensions
A Durmus, GO Roberts, G Vilmart, KC Zygalakis
The Annals of Applied Probability 27 (4), 2195-2237, 2017
262017
Optimal explicit stabilized integrator of weak order 1 for stiff and ergodic stochastic differential equations
A Abdulle, I Almuslimani, G Vilmart
SIAM/ASA Journal on Uncertainty Quantification 6 (2), 937-964, 2018
252018
High order integrator for sampling the invariant distribution of a class of parabolic stochastic PDEs with additive space-time noise
CE Bréhier, G Vilmart
SIAM Journal on Scientific Computing 38 (4), A2283-A2306, 2016
252016
Postprocessed integrators for the high order integration of ergodic SDEs
G Vilmart
SIAM Journal on Scientific Computing 37 (1), A201-A220, 2015
222015
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