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## Vilmart, Gilles

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 Author ID: vilmart.gilles Published as: Vilmart, Gilles; Vilmart, G. External Links: MGP
 Documents Indexed: 35 Publications since 2006
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#### Co-Authors

 3 single-authored 15 Abdulle, Assyr 7 Chartier, Philippe 7 Zygalakis, Konstantinos C. 4 Hairer, Ernst 3 Lemou, Mohammed 2 Almuslimani, Ibrahim 2 Bai, Yun 2 Bertoli, Guillaume 2 Laurent, Adrien 2 Méhats, Florian 1 Besse, Christophe 1 Bréhier, Charles-Edouard 1 Castella, François 1 Crouseilles, Nicolas 1 Descombes, Stéphane 1 Durmus, Alain 1 Eftekhari, Armin 1 Huber, Martin E. 1 Makazaga, Joseba 1 Murua, Ander 1 Pavliotis, Grigorios A. 1 Roberts, Gareth O. 1 Vandereycken, Bart
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#### Serials

 8 SIAM Journal on Scientific Computing 4 Mathematics of Computation 3 BIT 3 SIAM Journal on Numerical Analysis 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Computational Physics 2 Numerische Mathematik 2 Foundations of Computational Mathematics 1 International Journal for Numerical Methods in Engineering 1 The Annals of Applied Probability 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Journal of Physics A: Mathematical and General 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Multiscale Modeling & Simulation 1 Discrete and Continuous Dynamical Systems. Series S 1 SIAM/ASA Journal on Uncertainty Quantification
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#### Fields

 35 Numerical analysis (65-XX) 14 Probability theory and stochastic processes (60-XX) 13 Partial differential equations (35-XX) 9 Dynamical systems and ergodic theory (37-XX) 8 Ordinary differential equations (34-XX) 4 Mechanics of deformable solids (74-XX) 3 Mechanics of particles and systems (70-XX) 1 Combinatorics (05-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Fluid mechanics (76-XX) 1 Operations research, mathematical programming (90-XX)

#### Citations contained in zbMATH Open

28 Publications have been cited 288 times in 212 Documents Cited by Year
Splitting methods with complex times for parabolic equations. Zbl 1180.65106
Castella, F.; Chartier, P.; Descombes, S.; Vilmart, G.
2009
Algebraic structures of B-series. Zbl 1201.65124
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
2010
Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics. Zbl 1327.65015
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
2015
Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1282.65146
Abdulle, Assyr; Vilmart, Gilles
2014
High order numerical approximation of the invariant measure of ergodic SDEs. Zbl 1310.65007
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
2014
A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems. Zbl 1251.65151
Abdulle, Assyr; Vilmart, Gilles
2012
Numerical integrators based on modified differential equations. Zbl 1122.65059
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
2007
High weak order methods for stochastic differential equations based on modified equations. Zbl 1246.65008
Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C.
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
2012
Weak second-order explicit stabilized methods for stiff stochastic differential equations. Zbl 1281.65005
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
2013
Multi-revolution composition methods for highly oscillatory differential equations. Zbl 1307.65100
Chartier, Philippe; Makazaga, Joseba; Murua, Ander; Vilmart, Gilles
2014
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
2013
Preprocessed discrete Moser-Veselov algorithm for the full dynamics of a rigid body. Zbl 1127.70002
Hairer, Ernst; Vilmart, Gilles
2006
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.
2013
Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1304.65245
Abdulle, Assyr; Bai, Yun; Vilmart, Gilles
2015
Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems. Zbl 1336.74063
Abdulle, A.; Huber, M. E.; Vilmart, G.
2015
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
2011
Fast Langevin based algorithm for MCMC in high dimensions. Zbl 1373.60053
Durmus, Alain; Roberts, Gareth O.; Vilmart, Gilles; Zygalakis, Konstantinos C.
2017
A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations. Zbl 07161200
Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles
2020
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.
2014
Postprocessed integrators for the high order integration of ergodic SDEs. Zbl 1327.65018
Vilmart, Gilles
2015
Reducing round-off errors in rigid body dynamics. Zbl 1140.70002
Vilmart, Gilles
2008
Weak second order multirevolution composition methods for highly oscillatory stochastic differential equations with additive or multiplicative noise. Zbl 1320.65019
Vilmart, Gilles
2014
Optimal explicit stabilized integrator of weak order 1 for stiff and ergodic stochastic differential equations. Zbl 1392.65013
Abdulle, Assyr; Almuslimani, Ibrahim; Vilmart, Gilles
2018
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
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
2016
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
2019
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
2020
A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations. Zbl 07161200
Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles
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
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
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
2018
Fast Langevin based algorithm for MCMC in high dimensions. Zbl 1373.60053
Durmus, Alain; Roberts, Gareth O.; Vilmart, Gilles; Zygalakis, Konstantinos C.
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
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
2016
Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics. Zbl 1327.65015
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
2015
Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1304.65245
Abdulle, Assyr; Bai, Yun; Vilmart, Gilles
2015
Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems. Zbl 1336.74063
Abdulle, A.; Huber, M. E.; Vilmart, G.
2015
Postprocessed integrators for the high order integration of ergodic SDEs. Zbl 1327.65018
Vilmart, Gilles
2015
Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems. Zbl 1282.65146
Abdulle, Assyr; Vilmart, Gilles
2014
High order numerical approximation of the invariant measure of ergodic SDEs. Zbl 1310.65007
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
2014
Multi-revolution composition methods for highly oscillatory differential equations. Zbl 1307.65100
Chartier, Philippe; Makazaga, Joseba; Murua, Ander; Vilmart, Gilles
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.
2014
Weak second order multirevolution composition methods for highly oscillatory stochastic differential equations with additive or multiplicative noise. Zbl 1320.65019
Vilmart, Gilles
2014
Weak second-order explicit stabilized methods for stiff stochastic differential equations. Zbl 1281.65005
Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C.
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
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.
2013
A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems. Zbl 1251.65151
Abdulle, Assyr; Vilmart, Gilles
2012
High weak order methods for stochastic differential equations based on modified equations. Zbl 1246.65008
Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C.
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
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
2011
Algebraic structures of B-series. Zbl 1201.65124
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
2010
Splitting methods with complex times for parabolic equations. Zbl 1180.65106
Castella, F.; Chartier, P.; Descombes, S.; Vilmart, G.
2009
Reducing round-off errors in rigid body dynamics. Zbl 1140.70002
Vilmart, Gilles
2008
Numerical integrators based on modified differential equations. Zbl 1122.65059
Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles
2007
Preprocessed discrete Moser-Veselov algorithm for the full dynamics of a rigid body. Zbl 1127.70002
Hairer, Ernst; Vilmart, Gilles
2006
all top 5

#### Cited by 298 Authors

 25 Abdulle, Assyr 22 Vilmart, Gilles 14 Chartier, Philippe 8 Zhao, Xiaofei 7 Lemou, Mohammed 6 Méhats, Florian 5 Bai, Yun 5 Blanes, Sergio 5 Crouseilles, Nicolas 5 Ebrahimi-Fard, Kurusch 5 Hong, Jialin 5 Huber, Martin E. 5 Manchon, Dominique 5 Murua, Ander 5 Shang, Xiaocheng 4 Bogfjellmo, Geir 4 Ostermann, Alexander 4 Seydaoğlu, Muaz 4 Tang, Xiao 4 Xiao, Aiguo 4 Zygalakis, Konstantinos C. 3 Besse, Christophe 3 Bruned, Yvain 3 Burrage, Kevin 3 Casas, Fernando 3 D’Ambrosio, Raffaele 3 Dikhaminjia, Nana 3 Hairer, Martin 3 Hansen, Eskil 3 Koch, Othmar 3 McLachlan, Robert I. 3 Montijano, Juan Ignacio 3 Pollock, Sara 3 Rández, Luis 3 Rogava, Jemal L. 3 Sanz-Serna, Jesús María 3 Schmeding, Alexander 3 Stoltz, Gabriel 3 Sun, Liying 3 Tsiklauri, Mikheil 3 Wang, Xu 3 Zhu, Yunrong 2 Auzinger, Winfried 2 Bader, Philipp 2 Biscay, Rolando J. 2 Bréhier, Charles-Edouard 2 Calvo, Manuel 2 Chen, Chuchu 2 Curry, Charles 2 Dahmen, Rafael 2 Durmus, Alain 2 Einkemmer, Lukas 2 Engquist, Bjorn E. 2 Erdoğan, Utku 2 Escorihuela-Tomàs, Alejandro 2 Frénod, Emmanuel 2 Hairer, Ernst 2 Henning, Patrick 2 Hoang, Viet Ha 2 Hofstätter, Harald 2 Jackiewicz, Zdzislaw 2 Kleefeld, Andreas 2 Komori, Yoshio 2 Kropat, Erik 2 Kvaerno, Anne 2 Laburta, María Pilar 2 Laurent, Adrien 2 Leimkuhler, Benedict J. 2 Lu, Jianfeng 2 Majka, Mateusz B. 2 Meyer-Nieberg, Silja 2 Mijatović, Aleksandar 2 Modin, Klas 2 Mora, Carlos M. 2 Munthe-Kaas, Hans Z. 2 O’Sullivan, Stephen 2 Owren, Brynjulf 2 Paternoster, Beatrice 2 Sandu, Adrian 2 Szpruch, Lukasz 2 Tan, Wee Chin 2 Thalhammer, Mechthild 2 Verdier, Olivier 2 Wang, Lijin 2 Weber, Gerhard-Wilhelm 2 Weng, Lihui 2 Zhang, Yong 1 Abd Hamid, Fatin 1 Almuslimani, Ibrahim 1 Anmarkrud, Sverre 1 Antoine, Xavier 1 Anton, Cristina A. 1 Arjmand, Doghonay 1 Asante-Asamani, E. O. 1 Aylwin, Rubén 1 Bach, Francis R. 1 Bailleul, Ismaël F. 1 Bal, Guillaume 1 Bao, Weizhu 1 Barrio, Roberto ...and 198 more Authors
all top 5

#### Cited in 75 Serials

 19 Journal of Computational Physics 14 BIT 13 Numerische Mathematik 12 Journal of Computational and Applied Mathematics 10 Multiscale Modeling & Simulation 9 Mathematics of Computation 9 SIAM Journal on Numerical Analysis 9 Applied Numerical Mathematics 9 SIAM Journal on Scientific Computing 9 Foundations of Computational Mathematics 8 Numerical Algorithms 5 Discrete and Continuous Dynamical Systems. Series S 4 Oberwolfach Reports 3 Advances in Computational Mathematics 3 Discrete and Continuous Dynamical Systems. Series B 3 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Applied Mathematics and Computation 2 International Journal for Numerical Methods in Engineering 2 Mathematics and Computers in Simulation 2 Journal of Scientific Computing 2 Optimization Methods & Software 2 Journal of Machine Learning Research (JMLR) 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 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 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 Physics Letters. A 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 The Annals of Statistics 1 Inventiones Mathematicae 1 Journal of Algebra 1 Journal of the American Statistical Association 1 Numerical Functional Analysis and Optimization 1 Advances in Applied Mathematics 1 Journal of Complexity 1 Numerical Methods for Partial Differential Equations 1 SIAM Journal on Matrix Analysis and Applications 1 The Annals of Applied Probability 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 SIAM Review 1 Stochastic Processes and their Applications 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Celestial Mechanics and Dynamical Astronomy 1 Journal of Nonlinear Science 1 Potential Analysis 1 Journal of Mathematical Sciences (New York) 1 Computational and Applied Mathematics 1 Georgian Mathematical Journal 1 Discrete and Continuous Dynamical Systems 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 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 Journal of Noncommutative Geometry 1 Communications in Computational Physics 1 Networks and Heterogeneous Media 1 Electronic Journal of Statistics 1 SIAM Journal on Imaging Sciences 1 Journal of Geometric Mechanics 1 Statistics and Computing 1 Journal of Computational Dynamics 1 SIAM/ASA Journal on Uncertainty Quantification 1 Annales de l’Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (AIHPD) 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
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#### Cited in 38 Fields

 176 Numerical analysis (65-XX) 75 Partial differential equations (35-XX) 58 Probability theory and stochastic processes (60-XX) 32 Dynamical systems and ergodic theory (37-XX) 30 Ordinary differential equations (34-XX) 16 Mechanics of deformable solids (74-XX) 16 Statistical mechanics, structure of matter (82-XX) 12 Associative rings and algebras (16-XX) 10 Mechanics of particles and systems (70-XX) 10 Fluid mechanics (76-XX) 8 Combinatorics (05-XX) 8 Quantum theory (81-XX) 7 Computer science (68-XX) 6 Statistics (62-XX) 4 General and overarching topics; collections (00-XX) 4 Approximations and expansions (41-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Topological groups, Lie groups (22-XX) 3 Functional analysis (46-XX) 3 Operator theory (47-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Optics, electromagnetic theory (78-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Information and communication theory, circuits (94-XX) 2 Real functions (26-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral equations (45-XX) 2 Operations research, mathematical programming (90-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX)