1. Recherche
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hal-00811490v2  Article dans une revue
Assyr Abdulle, Yun Bai, Gilles Vilmart. Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems
Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2015, 8 (1), pp.91-118. <10.3934/dcdss.2015.8.91>
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hal-00739757v2  Article dans une revue
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
Journal of Computational Physics, Elsevier, 2013, 242, pp.869-888. <10.1016/j.jcp.2013.02.009>
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hal-00819565v1  Article dans une revue
Assyr Abdulle, Yun Bai, Gilles Vilmart. An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems
International Journal for Numerical Methods in Engineering, Wiley, 2014, 99 (7), pp.469-486. <10.1002/nme.4682>
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hal-01560573v1  Pré-publication, Document de travail
Shaula Fiorelli Vilmart, Gilles Vilmart. Computing the long term evolution of the solar system with geometric numerical integrators
to appear in Snapshots of modern mathematics from Oberwolfach, 2017. 2016
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hal-01174226v1  Pré-publication, Document de travail
Alain Durmus, Roberts Gareth, Gilles Vilmart, Konstantinos Zygalakis. Fast Langevin based algorithm for MCMC in high dimensions
33 pages. 2015
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inria-00113372v2  Rapport
Monique Chyba, Ernst Hairer, Gilles Vilmart. Symplectic integrators in sub-Riemannian geometry: the Martinet case
[Research Report] RR-6017, INRIA. 2006, pp.10
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hal-00777092v1  Article dans une revue
François Castella, Philippe Chartier, Stéphane Descombes, Gilles Vilmart. Splitting methods with complex times for parabolic equations
BIT Numerical Mathematics Numerical Mathematics, Springer, 2009, 49 (3), pp.487--508. <10.1007/s10543-009-0235-y>
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hal-00739754v2  Article dans une revue
Assyr Abdulle, Gilles Vilmart, Konstantinos Zygalakis. Weak second order explicit stabilized methods for stiff stochastic differential equations
SIAM J. Sci. Comput., Sociey for Industrial and Applied Mathematics, 2013, 35 (4), pp.1792-1814. <10.1137/12088954X>
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tel-00840733v1  HDR
Gilles Vilmart. Méthodes numériques géométriques et multi-échelles pour les équations différentielles (in English)
Analyse numérique [math.NA]. École normale supérieure de Cachan - ENS Cachan, 2013
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tel-00348112v1  Thèse
Gilles Vilmart. Study of geometric integrators for differential equations
Mathematics [math]. Université Rennes 1; University of Geneva, 2008. English
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hal-00772085v1  Article dans une revue
Monique Chyba, Ernst Hairer, Gilles Vilmart. The role of symplectic integrators in optimal control
Optim. Control Appl. Meth., 2009, 30 (4), pp.367-382. <10.1002/oca.855>
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hal-00912388v1  Pré-publication, Document de travail
Gilles Vilmart. Rigid body dynamics
Encyclopedia of Applied and Computational Mathematics, Springer. 2013
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inria-00598369v1  Article dans une revue
Philippe Chartier, Ernst Hairer, Gilles Vilmart. Algebraic Structures of B-series
Foundations of Computational Mathematics, Springer Verlag, 2010, 10 (4), pp.407-420. <10.1007/s10208-010-9065-1>
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hal-01012022v3  Article dans une revue
Gilles Vilmart. Postprocessed integrators for the high order integration of ergodic SDEs
SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2015, 37 (1), pp.A201-A220. <10.1137/140974328>
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hal-00965354v2  Article dans une revue
Assyr Abdulle, Gilles Vilmart, Konstantinos Zygalakis. Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics
SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2015, 53 (1), pp.1-16. <10.1137/140962644>
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hal-00858088v2  Article dans une revue
Assyr Abdulle, Gilles Vilmart, Konstantinos Zygalakis. High order numerical approximation of the invariant measure of ergodic SDEs
SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2014, 52 (4), pp.1600-1622. <10.1137/130935616>
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hal-01153448v2  Article dans une revue
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 Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2016, 38 (4), <10.1137/15M1021088>
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hal-00856672v4  Article dans une revue
Gilles Vilmart. Weak second order multi-revolution composition methods for highly oscillatory stochastic differential equations with additive or multiplicative noise
SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2014, 36 (4), pp.1770-1796. <10.1137/130935331>
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hal-00746563v1  Article dans une revue
Assyr Abdulle, David Cohen, Gilles Vilmart, Konstantinos Zygalakis. High weak order methods for stochastic differential equations based on modified equations
SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2012, 34 (3), pp.1800-1823. <10.1137/110846609>
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hal-00772086v1  Article dans une revue
Assyr Abdulle, Gilles Vilmart. The effect of numerical integration in the finite element method for nonmonotone nonlinear elliptic problems with application to numerical homogenization methods
Comptes rendus hebdomadaires des séances de l'Académie des sciences, Elsevier, 2011, 349, pp.1041-1046. <10.1016/j.crma.2011.09.005>
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hal-00739756v2  Article dans une revue
Assyr Abdulle, Gilles Vilmart, Konstantinos Zygalakis. Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations
BIT Numerical Mathematics, Springer Verlag, 2013, 53 (4), pp.827-840. <10.1007/s10543-013-0430-8>
hal-01187092v1  Article dans une revue
Nicolas Crouseilles, Mohammed Lemou, Gilles Vilmart. Asymptotic Preserving numerical schemes for multiscale parabolic problems
Comptes Rendus Mathématique, Elsevier Masson, 2016, 354 (3), pp.271-276. <10.1016/j.crma.2015.11.010>
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hal-00746811v2  Article dans une revue
Assyr Abdulle, Gilles Vilmart. Analysis of the finite element heterogeneous multiscale method for nonmonotone elliptic homogenization problems
Mathematics of Computation, American Mathematical Society, 2014, 83 (286), pp.513-536. <10.1090/S0025-5718-2013-02758-5>
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hal-00746821v1  Article dans une revue
Assyr Abdulle, Gilles Vilmart. Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete space-time analysis
Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2012, 22 (6), 40 p. <10.1142/S0218202512500029>
hal-00847907v1  Article dans une revue
Philippe Chartier, Ernst Hairer, Gilles Vilmart. Numerical integrators based on modified differential equations
Mathematics of Computation, American Mathematical Society, 2007, 76 (260), pp.1941-1953
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hal-00746826v1  Article dans une revue
Assyr Abdulle, Gilles Vilmart. A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems
Numerische Mathematik, Springer Verlag, 2012, 121, pp.397-431. <10.1007/s00211-011-0438-4>
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hal-00796581v2  Article dans une revue
Philippe Chartier, Joseba Makazaga, Ander Murua, Gilles Vilmart. Multi-revolution composition methods for highly oscillatory differential equations
Numerische Mathematik, Springer Verlag, 2014, 128 (1), pp.167-192. <10.1007/s00211-013-0602-0>
hal-00847919v1  Article dans une revue
Philippe Chartier, Ernst Hairer, Gilles Vilmart. Modified differential equations
ESAIM: Proceedings, EDP Sciences, 2007, 21, pp.16-20
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hal-01017106v3  Article dans une revue
Assyr Abdulle, Martin Huber, Gilles Vilmart. Linearized numerical homogenization method for nonlinear monotone parabolic multiscale problems
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, Society for Industrial and Applied Mathematics, 2015, <10.1137/140975504>

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