Internship report : Simulation of plasma and Maxwell's equations using the port-Hamiltonian approach

Abstract

Report of a 4 months internship at ISAE Supaero. The purpose was to run simulations for Maxwell's equations and plasma physics and use the new Partionned Finite Element Method (PFEM) for port-Hamiltonian systems. The first four Chapters present a usual modelling of plasma equations, a geometric reduction and 1D spectral simulations based on N.M Trang Vu work. Then, PFEM use is detailed for 1D simulations and the advantages of this method are outlined. A more general framework is finally given for 3D simulations. Difficulties related to the complexity of Maxwell's equations are explained.