Lise-Marie Imbert-Gerard (University of Arizona)

"Numerical simulation of wave propagation in inhomogeneous plasmas"

Abstract: Several plasma wave phenomena play a major role in astrophysical and experimental applications, specifically wave absorption, mode conversion, and cyclotron damping. As it is often the case in plasma physics, hierarchies of models exist to describe various aspects of these phenomena, and this talk will focus on numerical simulations of a full wave model. The presentation will start with modeling aspects for the cold plasma model, leading to partial differential equations (PDEs) with variable coefficients, before turning to numerical methods specifically tailored to handle such PDEs: the so-called quasi-Trefftz methods.

Trefftz methods rely, in broad terms, on the idea of approximating solutions to PDEs via Galerkin-type methods with basis functions solving exactly the PDE locally, making explicit use of information about the ambient medium. They are of particular interest for wave propagation problems. But in general, for problems modeled by PDEs with variable coefficients, no exact solutions are available. Hence quasi-Trefftz methods have been introduced to address this problem: they rely not on exact solutions to the PDE but instead on high order approximate solutions constructed locally. We will discuss some of the fundamental properties of these numerical methods for aeroacoustic problems. The goal here will be to emphasize why they represent a promising alternative to more standard methods to tackle an important challenge related to the boundary layer of air flow around planes.

Finally we will highlight the main difficulty in developing quasi-Trefftz methods for electromagnetic wave propagation.