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Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations Abdulle, Assyr; Pavliotis, Grigorios A.; Vilmart, Gilles 2019
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Highly oscillatory problems with time-dependent vanishing frequency Chartier, Philippe; Lemou, Mohammed; Méhats, Florian; Vilmart, Gilles 2019
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Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations Abdulle, Assyr; Almuslimani, Ibrahim; Vilmart, Gilles 2018
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Fast Langevin based algorithm for MCMC in high dimensions Durmus, Alain; Roberts, Gareth O.; Vilmart, Gilles; Zygalakis, Konstantinos C. 2017
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Computing the long term evolution of the solar system with geometric numerical integrators Fiorelli, Shaula; Vilmart, Gilles 2017
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Asymptotic Preserving numerical schemes for multiscale parabolic problems Crouseilles, Nicolas; Lemou, Mohammed; Vilmart, Gilles 2016
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High Order Integrator for Sampling the Invariant Distribution of a Class of Parabolic Stochastic PDEs with Additive Space-Time Noise Bréhier, Charles-Edouard; Vilmart, Gilles 2016
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Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems Abdulle, Assyr; Bai, Yun; Vilmart, Gilles 2015
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Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 2015
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Rigid body dynamics Vilmart, Gilles 2015
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Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems Abdulle, Assyr; Huber, Martin; Vilmart, Gilles 2015
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Postprocessed Integrators for the High Order Integration of Ergodic SDEs Vilmart, Gilles 2015
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Multi-revolution composition methods for highly oscillatory differential equations Chartier, Philippe; Makazaga, Joseba; Murua, Ander; Vilmart, Gilles 2014
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Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems Abdulle, Assyr; Vilmart, Gilles 2014
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Weak Second Order Multirevolution Composition Methods for Highly Oscillatory Stochastic Differential Equations with Additive or Multiplicative Noise Vilmart, Gilles 2014
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High Order Numerical Approximation of the Invariant Measure of Ergodic SDEs Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 2014
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An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems Abdulle, Assyr; Bai, Yun; Vilmart, Gilles 2014
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PIROCK: A swiss-knife partitioned implicit–explicit orthogonal Runge–Kutta Chebyshev integrator for stiff diffusion–advection–reaction problems with or without noise Abdulle, Assyr; Vilmart, Gilles 2013
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Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 2013
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Weak Second Order Explicit Stabilized Methods for Stiff Stochastic Differential Equations Abdulle, Assyr; Vilmart, Gilles; Zygalakis, Konstantinos C. 2013
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A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems Abdulle, Assyr; Vilmart, Gilles 2012
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Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete space-time analysis Abdulle, Assyr; Vilmart, Gilles 2012
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High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations Abdulle, Assyr; Cohen, David; Vilmart, Gilles; Zygalakis, Konstantinos C. 2012
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The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods Abdulle, Assyr; Vilmart, Gilles 2011
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Algebraic structures of B-series Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles 2010
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Splitting methods with complex times for parabolic equations Castella, F.; Chartier, P.; Descombes, S.; Vilmart, Gilles 2009
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The role of symplectic integrators in optimal control Chyba, Monique; Hairer, Ernst; Vilmart, Gilles 2009
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Reducing round-off errors in rigid body dynamics Vilmart, Gilles 2008
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Étude d'intégrateurs géométriques pour des équations différentielles Vilmart, Gilles 2008
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Numerical integrators based on modified differential equations Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles 2007
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Modified differential equations Chartier, Philippe; Hairer, Ernst; Vilmart, Gilles 2007
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Preprocessed Discrete Moser-Veselov algorithm for the full dynamics of the rigid body Hairer, Ernst; Vilmart, Gilles 2006