Gilles Vilmart is a post-doc at EPFL, Chair of Computational Mathematics and Numerical Analysis (ANMC) at the Mathematics Institute of Computational Science and Engineering (MATHICSE), under supervision of A. Abdulle. He obtained his PhD in Mathematics from the University of Geneva and the University of Rennes at INRIA in Dec. 2008 under the supervision of E. Hairer and P. Chartier (thèse en cotutelle internationale).
University of Geneva (2006-2009), Ecole Normale Supérieure de Cachan, antenne de Bretagne (2002-2006).
- Computational methods and numerical analysis for multiscale methods
- Numerical geometric methods for ordinary differential equations, Hamiltonian systems, optimal control, rigid body motion.
- Algebraic structures involved in numerical analysis of ODEs: B-series and generalisations, modified equations.
Splitting methods with complex times for parabolic equations, BIT 49 (2009) 487-508, (with F. Castella, P. Chartier and S. Descombes).
The role of sympectic integrators in optimal control, Optim. Control Appl. Meth. (2009) 30(4):367-382 (with M. Chyba and E. Hairer).
- Reducing round-off errors in rigid body dynamics, J.Comput. Phys. 227 (2008) 7083-7088.
Numerical integrators based on modified differential equations, Math. Comp. 76 (2007) 1941-1953 (with P. Chartier and E. Hairer).
- Preprocessed Discrete Moser-Veselov algorithm for the full dynamics of the rigid body, J. Phys. A: Math. Gen. 39 (2006) 13225-13235 (with E. Hairer).