### Markus Gasteiger, MSc

**Phone:**-

**Fax:**+43 512 507 53899

**E-Mail:**This email address is being protected from spambots. You need JavaScript enabled to view it.

**Address:**

Technikerstraße 13

Office 705

A-6020 Innsbruck

# Collection and overview of collision terms

In this manuscript an overview of collision terms is given. These terms are used in kinetic modeling to describe the interactions between particles. We limit ourselves to terms relevant to plasma physics in this document. The collision operators are listed in a unified way, so that it is easier to compare them. Additionally, we also look at the theoretical background of such collision operators and from which base models they are build. In order to facilitate this, also the necessary basic physics knowledge is provided.

The document can be downloaded from here.

# ADI type preconditioners for the steady state inh. Vlasov eq.

The python codes, which were used to do the numerical experiments presented in

M. Gasteiger, L. Einkemmer, A. Ostermann, D. Tskhakaya

Alternating direction implicit type preconditioners for the steady state inhomogeneous Vlasov equation

Journal of Plasma Physics, Vol. 83:1, p. 705830107 (Cambridge, arXiv)

can be downloaded from here.

# Simulating time-dependent multi species plasmas

In the following we show a code that we use to compute the evolution of a plasma that consists of multiple particle species. We use a particle kinetic model based on the Vlasov-Poisson equation. The plasma system has one space and two velocity dimensions. Radial symmetric cylindrical coordinates are used for the velocity coordinate system. BGK-type collision operator re-thermalizes the velocity distribution.

The specific setup allows us to solve each species separately, which corresponds to a Lie-Trotter splitting scheme. For the specific time-integrator we use the GMRES function from Sundials Cvode library.

The code can be found here.

# Stencil operator programming library

This C++ library offers a framework to consistently define matrix-free functions of complex finite difference matrices. The library manages boundaries and data storage too. This allows for modifying parts of a complicated stencil in a simple way and still getting an efficient function in the end.

The code can be found here.