Design and performant implementation of numerical methods for multiscale problems in plasma physics

Sever Hirstoaga 1, 2, 3
1 TONUS - TOkamaks and NUmerical Simulations
IRMA - Institut de Recherche Mathématique Avancée, Inria Nancy - Grand Est
3 ALPINES - Algorithms and parallel tools for integrated numerical simulations
INSMI - Institut National des Sciences Mathématiques et de leurs Interactions, Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
Abstract : This manuscript assembles my contributions in developing new mathematical and computational methods for analyzing the dynamics of charged particles, like electrons or ions, as a multiscale phenomenon. The underlying mechanisms of this general physical problem are described by Vlasov--Poisson systems. The objective of this work is to study these equations and to implement various efficient numerical methods to approximate their solutions. In Chapter 1, two strategies are proposed in order to cope with the multiscale issue. First, we obtain reduced models by means of asymptotic analysis in the frame of the two-scale convergence. Second, we treat the full model with a numerical method based on exponential integrator, by which the high frequency oscillations are exactly solved whereas the slower process is treated in an approximate way. In Chapter 2, we focus on the performance of Particle-in-Cell simulations for solving Vlasov--Poisson systems in six dimensional phase space. Mainly, we address specific data structures in order to optimize the memory accesses. In addition, we exploit efficiently parallelism patterns, like vectorization, multithreading, and multiprocessing. In Chapter 3, we develop a computational framework for modelling and simulating complex problems in plasma physics. More precisely, we study the problems of the diocotron instability in a non-neutral plasma and of the dynamics of two species of charged particles following an edge-localized mode event in a tokamak's scrape-off layer. In this direction, we propose and solve different kinetic and fluid equations to treat the modelling questions, while for the numerical aspect, an asymptotic preserving strategy turns out to be fruitful to deal with the multiscale issue.
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Sever Hirstoaga. Design and performant implementation of numerical methods for multiscale problems in plasma physics. Analysis of PDEs [math.AP]. Université de Strasbourg, IRMA UMR 7501, 2019. ⟨tel-02081304⟩

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