ome Particle methods for the Vlasov-Poisson system with a strong external magnetic field

par Kim Han Trinh

mercredi 15 juil. 2026, 14:00 → 17:30 Europe/Paris

Bâtiment 2A, amphi A (René Dabard). (Université de Rennes)

https://bbb.univ-rennes.fr/rooms/hjp-ggf-c4p-uja/join

The presentation will be given in English.

Composition of the committee:
- CAMPOS PINTO Martin, Reviewer, Max-Planck Institute of Plasma Physics
- CRESTETTO Anaïs, Examiner, University of Nantes
- CROUSEILLES Nicolas, Examiner, INRIA Rennes
- MEHRENBERGER Michel, Examiner, University of Aix-Marseille
- NAVORET Laurent, Reviewer, University of Strasbourg
- RODRIGUES Luis Miguel, PhD Supervisor, University of Rennes
- FILBET Francis, Co-supervisor, University of Toulouse

Abstract:

This thesis is devoted to the mathematical study of the numerical analysis and simulation of the Vlasov-Poisson systems with a strong external magnetic field. First, we propose and study a modified Crank-Nicolson time discretization to approximate the particle's motions, which serves as a pusher of the Particle-In-Cell (PIC) method for the Vlasov-Poisson system on complex geometries. In this regime, the explicit schemes are constrained by stability conditions linked to the small Larmor radius and high plasma frequency. To avoid this limitation, our approach is based on the asymptotic preserving framework,  providing consistent schemes with the guiding-center systems as the magnitude of the magnetic field becomes large. Second, we focus on the convergence analysis of the modified Crank-Nicolson scheme. This scheme removes classical strong restrictive stability constraints on discretization steps while capturing the large-scale dynamics, even when the discretization is too coarse to capture the fastest scales. Our error bounds are explicit regarding the discretization and stiffness parameters and match the numerical tests.