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2014 Multiscale Splitting Method for the Boltzmann-Poisson Equation: Application to the Dynamics of Electrons
Jürgen Geiser
Int. J. Differ. Equ. 2014: 1-8 (2014). DOI: 10.1155/2014/178625

Abstract

We present a model based on dynamics of electrons in a plasma using a simplified Boltzmann equation coupled with Poisson’s equation. The motivation arose from simulating active plasma resonance spectroscopy, which is used for plasma diagnostic techniques; see Braithwaite and Franklin (2009), Lapke et al. (2010), and Oberrath et al. (2011). Mathematically, we are interested in designing splitting methods for the model problem. While the full Boltzmann equation is delicate to solve, we decouple it into a transport and collision part, which are then solved in different ways. First we reduce it to a simplified transport-collision equation and start to analyse the abstract Cauchy problem using semigroup methods. Second, we pass to the coupled transport and collision model and apply the splitting ideas, resecting the different discretization schemes. The results are discussed first with numerical experiments and then we verify the underlying theoretical novelties.

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Jürgen Geiser. "Multiscale Splitting Method for the Boltzmann-Poisson Equation: Application to the Dynamics of Electrons." Int. J. Differ. Equ. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/178625

Information

Received: 15 August 2013; Revised: 20 January 2014; Accepted: 21 January 2014; Published: 2014
First available in Project Euclid: 20 January 2017

zbMATH: 1320.82063
MathSciNet: MR3178935
Digital Object Identifier: 10.1155/2014/178625

Rights: Copyright © 2014 Hindawi

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