Seminar

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The numerical reconstruction of solutions to kinetic models remains a formidable task. Challenges include numerical stability, conservation, accuracy, and complexity reduction. In this talk we will discuss the numerical treatment of two fundamental kinetic models: the Vlasov-Poisson system, and the Landau equation. Specifically, we will introduce several techniques that are currently in development. These include a discontinuous Galerkin, a representation theory, and a semi-Lagrangian approach. Other relevant aspects, such as positivity preservation, error estimates, Schur’s lemma, low-rank methods, implementation challenges, and the extension to the relativistic Landau will be discussed. The goal is for this presentation is to be a conversational and friendly introduction to the subject. We will focus on the “philosophy” behind these techniques as opposed to their technical aspects.