Section de MathématiquesAbout
I am a PhD student in mathematics at University of Geneva. I work under the supervision of Gilles Vilmart in the numerical analysis research group. My research is about the order reduction of the Strang splitting method when applied to partial differential equation with inhomogeneous boundary conditions.
Preprints and Master Thesis
- Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with oblique boundary conditions, Guillaume Bertoli, Christophe Besse and Gilles Vilmart, Mathematics of computation, 2021.
- Strang splitting method for semilinear parabolic problems with inhomogeneous boundary conditions: a correction based on the flow of the nonlinearity, Guillaume Bertoli and Gilles Vilmart, SIAM journal of scientific computing, 2020.
- Splitting methods for the Schrödinger equation with absorbing boundary conditions, Guillaume Bertoli under the supervision of Gilles Vilmart, Master Thesis, 2017.
Teaching
- Assistant for the exercice sessions of the course "Analyse numérique".
- Assistant for the exercice sessions of the course "Analyse numérique et analyse fonctionnelle des EDP".
- Scientific divulgation for the Mathscope.
Presentations and Poster sessions
- Splitting methods and the Baker-Campbell-Hausdorff formula presentation for the graduate seminar at University of Geneva in 2018
- An Introduction to Stochastic Differential Equations and their numerical analysis in the Leysin workshop in collaboration with Adrien Laurent and Marco Sutti
- Poster presentation in Scicade 2019 for the paper "Strang splitting method for semilinear parabolic problems with inhomogeneous boundary conditions: a correction based on the flow of the nonlinearity"
- "Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with oblique boundary conditions" in the visio-conference Canum 2020
Distinctions and competitions
- Edouard Gans Prize 2017 for the best master thesis in mathematics at University of Geneva
- Science Me Divulgation competition in 2018 with Adrien Laurent and Fathi Ben Aribi