Documents
Find a diverse range of documents, including essays, presentations, and reports I made as a student.
Internships
Finite-Volume Subcells correction on discontinuous Galerkin schemes.
Abstract. Building and implementing a new strategy for stabilizing discontinuous Galerkin numerical methods using a Finite-Volume subcells type approach for the Nonlinear Shallow-Water equations. We consider here an a priori approach, more precisely a monolithic subcell dG/FV convex property preserving scheme.
Advised by François Vilar & Fabien Marche.
Asymptotic analysis of PDEs sequences and homogenization theory.
Abstract. We consider two problems, including a Dirichlet problem on a variable open set. Ice fog forms when water vapour, mainly resulting from human activities, enters the atmosphere. This vapor condenses into droplets which quickly freeze, giving rise to particles of ice without a well-defined crystalline form. The objective is to model it as a homogenization problem.
Advised by Michel Bellieud.
From differential geometry to mathematical billiards.
Abstract. Studying one of the simplest dynamical system, the mathematical billiard where we characterize the periodic trajectories by their initial angle of shot (with Samuel Raë).
Advised by Daniel Massart.
Proof of Dirichlet Prime Number theorem.
Abstract. Demonstrating that, for a,b two integers, such that gcd(a,b)=1, the arithmetic progression {an+b} for n an integer contains an infinity of prime numbers. Such a proof contains various fields, like complex analysis or group theory.
Advised by Sylvain Brochard.
Projects
Hybrid High-Order method on Leray-Lions operators: studying a new non-conform finite-element method and its main discrete functional analysis results on Leray-Lions operators.
Report.
Müller’s SPH C++ implementation for fluid dynamics: building and implementing Smooth Particle Hydrodynamics method for a C++ simulation.
Report & Simulation.
Some results about measure theory: proving measure theory results, including differentiation of Radon measures, Besicovitch & Vitali covering theorems, Tietze & Lusin’s theorems.
Notes.
Projects for a posteriori estimates course: some results on a posteriori estimates and mesh adaption, some implementation on Fortran, Python and C++.
Reports.
Reports for analysis courses: some results on Hölderian functions and distribution theory.
Reports.
Reports for algebra courses: results on cube automorphism and euclidian ring, diophantine equations.
Reports.
Projects for machine learning and optimization course: database analysis and programming regression methods for machine learning on Python.
Reports.