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Author ID: vilmart.gilles Recent zbMATH articles by "Vilmart, Gilles"
Published as: Vilmart, Gilles; Vilmart, G.
External Links: MGP

Publications by Year

Citations contained in zbMATH Open

36 Publications have been cited 467 times in 316 Documents Cited by Year
Algebraic structures of B-series. Zbl 1201.65124
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
54
2010
Splitting methods with complex times for parabolic equations. Zbl 1180.65106
Castella, F.; Chartier, P.; Descombes, S.; Vilmart, G.
46
2009
High order numerical approximation of the invariant measure of ergodic SDEs. Zbl 1310.65007
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
28
2014
Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics. Zbl 1327.65015
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
27
2015
High weak order methods for stochastic differential equations based on modified equations. Zbl 1246.65008
Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C.
22
2012
Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1282.65146
Abdulle, Assyr; Vilmart, Gilles
22
2014
A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems. Zbl 1251.65151
Abdulle, Assyr; Vilmart, Gilles
21
2012
Weak second-order explicit stabilized methods for stiff stochastic differential equations. Zbl 1281.65005
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
20
2013
Numerical integrators based on modified differential equations. Zbl 1122.65059
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
19
2007
Optimal explicit stabilized integrator of weak order 1 for stiff and ergodic stochastic differential equations. Zbl 1392.65013
Abdulle, Assyr; Almuslimani, Ibrahim; Vilmart, Gilles
16
2018
Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete spacetime analysis. Zbl 1426.76208
Abdulle, Assyr; Vilmart, Gilles
15
2012
PIROCK: A swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise. Zbl 1297.65110
Abdulle, Assyr; Vilmart, Gilles
15
2013
Multi-revolution composition methods for highly oscillatory differential equations. Zbl 1307.65100
Chartier, Philippe; Makazaga, Joseba; Murua, Ander; Vilmart, Gilles
14
2014
Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1304.65245
Abdulle, Assyr; Bai, Yun; Vilmart, Gilles
13
2015
A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations. Zbl 07161200
Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles
13
2020
Postprocessed integrators for the high order integration of ergodic SDEs. Zbl 1327.65018
Vilmart, Gilles
11
2015
Fast Langevin based algorithm for MCMC in high dimensions. Zbl 1373.60053
Durmus, Alain; Roberts, Gareth O.; Vilmart, Gilles; Zygalakis, Konstantinos C.
10
2017
An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems. Zbl 1352.65462
Abdulle, A.; Bai, Y.; Vilmart, G.
9
2014
High order integrator for sampling the invariant distribution of a class of parabolic stochastic PDEs with additive space-time noise. Zbl 1346.60105
Bréhier, Charles-Edouard; Vilmart, Gilles
9
2016
Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems. Zbl 1336.74063
Abdulle, A.; Huber, M. E.; Vilmart, G.
9
2015
Drift-preserving numerical integrators for stochastic Poisson systems. Zbl 1480.65014
Cohen, David; Vilmart, Gilles
9
2022
Preprocessed discrete Moser-Veselov algorithm for the full dynamics of a rigid body. Zbl 1127.70002
Hairer, Ernst; Vilmart, Gilles
8
2006
Weak second order multirevolution composition methods for highly oscillatory stochastic differential equations with additive or multiplicative noise. Zbl 1320.65019
Vilmart, Gilles
8
2014
Mean-square \(A\)-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations. Zbl 1367.65011
Abdulle, A.; Vilmart, G.; Zygalakis, K. C.
8
2013
The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods. Zbl 1230.65122
Abdulle, Assyr; Vilmart, Gilles
6
2011
Reducing round-off errors in rigid body dynamics. Zbl 1140.70002
Vilmart, Gilles
5
2008
Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs. Zbl 1433.60078
Laurent, Adrien; Vilmart, Gilles
5
2020
Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds. Zbl 1487.60112
Laurent, Adrien; Vilmart, Gilles
5
2022
Strang splitting method for semilinear parabolic problems with inhomogeneous boundary conditions: a correction based on the flow of the nonlinearity. Zbl 1447.65058
Bertoli, Guillaume; Vilmart, Gilles
4
2020
Explicit stabilized integrators for stiff optimal control problems. Zbl 1460.49021
Almuslimani, Ibrahim; Vilmart, Gilles
4
2021
Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations. (Convergence accélérée vers l’équilibre et variance asymptotique réduite pour la dynamique de Langevin à l’aide de perturbations de Stratonovich.) Zbl 07066212
Abdulle, Assyr; Pavliotis, Grigorios A.; Vilmart, Gilles
3
2019
Asymptotic preserving numerical schemes for multiscale parabolic problems. (Schémas numériques Asymptotic Preserving pour les problèmes paraboliques multi-échelles.) Zbl 1387.65096
Crouseilles, Nicolas; Lemou, Mohammed; Vilmart, Gilles
2
2016
Multirevolution integrators for differential equations with fast stochastic oscillations. Zbl 1428.60097
Laurent, Adrien; Vilmart, Gilles
2
2020
Explicit stabilised gradient descent for faster strongly convex optimisation. Zbl 1462.90089
Eftekhari, Armin; Vandereycken, Bart; Vilmart, Gilles; Zygalakis, Konstantinos C.
2
2021
Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions. Zbl 1500.65059
Bertoli, Guillaume; Besse, Christophe; Vilmart, Gilles
2
2021
Highly oscillatory problems with time-dependent vanishing frequency. Zbl 1411.74046
Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles
1
2019
Drift-preserving numerical integrators for stochastic Poisson systems. Zbl 1480.65014
Cohen, David; Vilmart, Gilles
9
2022
Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds. Zbl 1487.60112
Laurent, Adrien; Vilmart, Gilles
5
2022
Explicit stabilized integrators for stiff optimal control problems. Zbl 1460.49021
Almuslimani, Ibrahim; Vilmart, Gilles
4
2021
Explicit stabilised gradient descent for faster strongly convex optimisation. Zbl 1462.90089
Eftekhari, Armin; Vandereycken, Bart; Vilmart, Gilles; Zygalakis, Konstantinos C.
2
2021
Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions. Zbl 1500.65059
Bertoli, Guillaume; Besse, Christophe; Vilmart, Gilles
2
2021
A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations. Zbl 07161200
Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles
13
2020
Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs. Zbl 1433.60078
Laurent, Adrien; Vilmart, Gilles
5
2020
Strang splitting method for semilinear parabolic problems with inhomogeneous boundary conditions: a correction based on the flow of the nonlinearity. Zbl 1447.65058
Bertoli, Guillaume; Vilmart, Gilles
4
2020
Multirevolution integrators for differential equations with fast stochastic oscillations. Zbl 1428.60097
Laurent, Adrien; Vilmart, Gilles
2
2020
Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations. (Convergence accélérée vers l’équilibre et variance asymptotique réduite pour la dynamique de Langevin à l’aide de perturbations de Stratonovich.) Zbl 07066212
Abdulle, Assyr; Pavliotis, Grigorios A.; Vilmart, Gilles
3
2019
Highly oscillatory problems with time-dependent vanishing frequency. Zbl 1411.74046
Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles
1
2019
Optimal explicit stabilized integrator of weak order 1 for stiff and ergodic stochastic differential equations. Zbl 1392.65013
Abdulle, Assyr; Almuslimani, Ibrahim; Vilmart, Gilles
16
2018
Fast Langevin based algorithm for MCMC in high dimensions. Zbl 1373.60053
Durmus, Alain; Roberts, Gareth O.; Vilmart, Gilles; Zygalakis, Konstantinos C.
10
2017
High order integrator for sampling the invariant distribution of a class of parabolic stochastic PDEs with additive space-time noise. Zbl 1346.60105
Bréhier, Charles-Edouard; Vilmart, Gilles
9
2016
Asymptotic preserving numerical schemes for multiscale parabolic problems. (Schémas numériques Asymptotic Preserving pour les problèmes paraboliques multi-échelles.) Zbl 1387.65096
Crouseilles, Nicolas; Lemou, Mohammed; Vilmart, Gilles
2
2016
Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics. Zbl 1327.65015
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
27
2015
Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1304.65245
Abdulle, Assyr; Bai, Yun; Vilmart, Gilles
13
2015
Postprocessed integrators for the high order integration of ergodic SDEs. Zbl 1327.65018
Vilmart, Gilles
11
2015
Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems. Zbl 1336.74063
Abdulle, A.; Huber, M. E.; Vilmart, G.
9
2015
High order numerical approximation of the invariant measure of ergodic SDEs. Zbl 1310.65007
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
28
2014
Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1282.65146
Abdulle, Assyr; Vilmart, Gilles
22
2014
Multi-revolution composition methods for highly oscillatory differential equations. Zbl 1307.65100
Chartier, Philippe; Makazaga, Joseba; Murua, Ander; Vilmart, Gilles
14
2014
An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems. Zbl 1352.65462
Abdulle, A.; Bai, Y.; Vilmart, G.
9
2014
Weak second order multirevolution composition methods for highly oscillatory stochastic differential equations with additive or multiplicative noise. Zbl 1320.65019
Vilmart, Gilles
8
2014
Weak second-order explicit stabilized methods for stiff stochastic differential equations. Zbl 1281.65005
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
20
2013
PIROCK: A swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise. Zbl 1297.65110
Abdulle, Assyr; Vilmart, Gilles
15
2013
Mean-square \(A\)-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations. Zbl 1367.65011
Abdulle, A.; Vilmart, G.; Zygalakis, K. C.
8
2013
High weak order methods for stochastic differential equations based on modified equations. Zbl 1246.65008
Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C.
22
2012
A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems. Zbl 1251.65151
Abdulle, Assyr; Vilmart, Gilles
21
2012
Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete spacetime analysis. Zbl 1426.76208
Abdulle, Assyr; Vilmart, Gilles
15
2012
The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods. Zbl 1230.65122
Abdulle, Assyr; Vilmart, Gilles
6
2011
Algebraic structures of B-series. Zbl 1201.65124
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
54
2010
Splitting methods with complex times for parabolic equations. Zbl 1180.65106
Castella, F.; Chartier, P.; Descombes, S.; Vilmart, G.
46
2009
Reducing round-off errors in rigid body dynamics. Zbl 1140.70002
Vilmart, Gilles
5
2008
Numerical integrators based on modified differential equations. Zbl 1122.65059
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
19
2007
Preprocessed discrete Moser-Veselov algorithm for the full dynamics of a rigid body. Zbl 1127.70002
Hairer, Ernst; Vilmart, Gilles
8
2006
all top 5

Cited by 418 Authors

30 Abdulle, Assyr
24 Vilmart, Gilles
17 Chartier, Philippe
10 Blanes, Sergio
9 Lemou, Mohammed
9 Zhao, Xiaofei
8 Bruned, Yvain
8 Casas, Fernando
8 D’Ambrosio, Raffaele
8 Ebrahimi-Fard, Kurusch
8 Méhats, Florian
8 Zygalakis, Konstantinos C.
7 Bréhier, Charles-Edouard
7 Hong, Jialin
6 Crouseilles, Nicolas
6 Laurent, Adrien
6 Manchon, Dominique
6 McLachlan, Robert I.
6 Shang, Xiaocheng
5 Bai, Yun
5 Chen, Chuchu
5 Escorihuela-Tomàs, Alejandro
5 Huber, Martin E.
5 Murua, Ander
5 Sanz-Serna, Jesús María
4 Almuslimani, Ibrahim
4 Bogfjellmo, Geir
4 Burrage, Kevin
4 De Souza, Giacomo Rosilho
4 Di Giovacchino, Stefano
4 Kleefeld, Andreas
4 Munthe-Kaas, Hans Z.
4 Ostermann, Alexander
4 Seydaoğlu, Muaz
4 Stoltz, Gabriel
4 Tang, Xiao
4 Thalhammer, Mechthild
4 Xiao, Aiguo
3 Besse, Christophe
3 Curry, Charles
3 Dikhaminjia, Nana
3 Hairer, Martin
3 Hansen, Eskil
3 Koch, Othmar
3 Komori, Yoshio
3 Kvaerno, Anne
3 Leimkuhler, Benedict J.
3 Li, Qin
3 Lu, Jianfeng
3 Majka, Mateusz B.
3 Montijano, Juan Ignacio
3 Paternoster, Beatrice
3 Pereyra, Marcelo
3 Pollock, Sara
3 Rández, Luis
3 Rogava, Jemal L.
3 Scalone, Carmela
3 Schmeding, Alexander
3 Schratz, Katharina
3 Sun, Liying
3 Szpruch, Lukasz
3 Tsiklauri, Mikheil
3 Verdier, Olivier
3 Wang, Xu
3 Wright, Stephen J.
3 Zhu, Yunrong
2 Arjmand, Doghonay
2 Auzinger, Winfried
2 Bader, Philipp
2 Bailleul, Ismaël F.
2 Bernier, Joackim
2 Bi, Chunjia
2 Biscay, Rolando J.
2 Blumenthal, Adrian
2 Calvo, Manuel
2 Chen, Shi
2 Chung, Tsz Shun Eric
2 Dahmen, Rafael
2 Debrabant, Kristian
2 Durmus, Alain
2 Eftekhari, Armin
2 Einkemmer, Lukas
2 Ekre, Fredrik
2 Engquist, Bjorn E.
2 Erdoğan, Utku
2 Frénod, Emmanuel
2 González, Cesáreo
2 Guo, Liming
2 Hairer, Ernst
2 Henning, Patrick
2 Hoang, Viet Ha
2 Hochbruck, Marlis
2 Hofstätter, Harald
2 Jackiewicz, Zdzislaw
2 Jänicke, Ralf
2 Keil, Tim
2 Kock, Joachim
2 Kropat, Erik
2 Laburta, María Pilar
2 Larsson, Fredrik
...and 318 more Authors
all top 5

Cited in 97 Serials

32 Journal of Computational Physics
19 BIT
16 Journal of Computational and Applied Mathematics
15 SIAM Journal on Scientific Computing
14 Applied Numerical Mathematics
13 Mathematics of Computation
13 Numerische Mathematik
12 Multiscale Modeling & Simulation
11 Foundations of Computational Mathematics
10 SIAM Journal on Numerical Analysis
8 Numerical Algorithms
7 Journal of Scientific Computing
6 Discrete and Continuous Dynamical Systems. Series B
6 Discrete and Continuous Dynamical Systems. Series S
5 Oberwolfach Reports
5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
5 Journal of Computational Dynamics
4 Advances in Computational Mathematics
3 Computers & Mathematics with Applications
3 Applied Mathematics and Computation
3 Numerical Methods for Partial Differential Equations
3 International Journal of Computer Mathematics
3 Journal of Machine Learning Research (JMLR)
3 SIAM Journal on Imaging Sciences
3 Statistics and Computing
3 Forum of Mathematics, Sigma
2 Computer Methods in Applied Mechanics and Engineering
2 International Journal for Numerical Methods in Engineering
2 Mathematics and Computers in Simulation
2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
2 Stochastic Processes and their Applications
2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
2 SIAM Journal on Optimization
2 Computational and Applied Mathematics
2 Optimization Methods & Software
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Communications in Computational Physics
2 Advances in Applied Mathematics and Mechanics
2 Numerical Algebra, Control and Optimization
2 Stochastic and Partial Differential Equations. Analysis and Computations
1 Acta Mechanica
1 Advances in Applied Probability
1 Communications in Mathematical Physics
1 Computer Physics Communications
1 Mathematical Methods in the Applied Sciences
1 Physics Letters. A
1 Advances in Mathematics
1 Annales de l’Institut Fourier
1 The Annals of Statistics
1 Bulletin of the London Mathematical Society
1 Inventiones Mathematicae
1 Journal of Algebra
1 Journal of the American Statistical Association
1 Journal of Differential Equations
1 Journal of the London Mathematical Society. Second Series
1 Journal of the Mathematical Society of Japan
1 Mathematische Annalen
1 Numerical Functional Analysis and Optimization
1 Advances in Applied Mathematics
1 Journal of Computational Mathematics
1 Journal of Complexity
1 Computational Mechanics
1 Applied Mathematics Letters
1 SIAM Journal on Matrix Analysis and Applications
1 The Annals of Applied Probability
1 European Journal of Operational Research
1 SIAM Review
1 Celestial Mechanics and Dynamical Astronomy
1 Journal of Nonlinear Science
1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
1 Potential Analysis
1 Journal of Mathematical Sciences (New York)
1 Georgian Mathematical Journal
1 Electronic Journal of Probability
1 Discrete and Continuous Dynamical Systems
1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics
1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
1 Journal of the European Mathematical Society (JEMS)
1 Communications in Nonlinear Science and Numerical Simulation
1 Mathematical Modelling and Analysis
1 Journal of Numerical Mathematics
1 International Journal of Computational Methods
1 International Journal of Geometric Methods in Modern Physics
1 Acta Numerica
1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
1 Journal of Noncommutative Geometry
1 Networks and Heterogeneous Media
1 Electronic Journal of Statistics
1 Journal of Geometric Mechanics
1 Forum of Mathematics, Pi
1 Mathematical Sciences
1 SIAM/ASA Journal on Uncertainty Quantification
1 Annales de l’Institut Henri Poincaré D. Combinatorics, Physics and their Interactions
1 Journal de l’École Polytechnique – Mathématiques
1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys
1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1 SIAM Journal on Mathematics of Data Science
all top 5

Cited in 40 Fields

256 Numerical analysis (65-XX)
100 Partial differential equations (35-XX)
94 Probability theory and stochastic processes (60-XX)
39 Dynamical systems and ergodic theory (37-XX)
37 Ordinary differential equations (34-XX)
22 Associative rings and algebras (16-XX)
19 Mechanics of deformable solids (74-XX)
18 Statistical mechanics, structure of matter (82-XX)
14 Computer science (68-XX)
14 Fluid mechanics (76-XX)
12 Combinatorics (05-XX)
11 Statistics (62-XX)
11 Mechanics of particles and systems (70-XX)
10 Approximations and expansions (41-XX)
10 Quantum theory (81-XX)
8 Operations research, mathematical programming (90-XX)
6 Topological groups, Lie groups (22-XX)
6 Functional analysis (46-XX)
5 General and overarching topics; collections (00-XX)
5 Nonassociative rings and algebras (17-XX)
5 Global analysis, analysis on manifolds (58-XX)
4 Operator theory (47-XX)
4 Systems theory; control (93-XX)
3 Linear and multilinear algebra; matrix theory (15-XX)
3 Category theory; homological algebra (18-XX)
3 Optics, electromagnetic theory (78-XX)
3 Classical thermodynamics, heat transfer (80-XX)
2 Harmonic analysis on Euclidean spaces (42-XX)
2 Abstract harmonic analysis (43-XX)
2 Integral equations (45-XX)
2 Calculus of variations and optimal control; optimization (49-XX)
2 Biology and other natural sciences (92-XX)
2 Information and communication theory, circuits (94-XX)
1 History and biography (01-XX)
1 Commutative algebra (13-XX)
1 Algebraic geometry (14-XX)
1 Special functions (33-XX)
1 Differential geometry (53-XX)
1 Astronomy and astrophysics (85-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

Citations by Year