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Geometric multigrid for the gyrokinetic Poisson equation from fusion plasma applications

Schwarz, Christina (2021) Geometric multigrid for the gyrokinetic Poisson equation from fusion plasma applications. Master's, Universität Erlangen-Nürnberg.

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Abstract

In order to face climate change and to preserve our ecosystem, we have to reduce the overall emission of carbon dioxide into the atmosphere. A promising addition to renewable energies is nuclear fusion. Delivering an almost infinite amount of clean and safe energy and with almost inexhaustible resources on earth, plasma fusion would solve all the world's climate and energy problems. However, being extremely complex, the reaction cannot be maintained for sufficient long time, yet, as it is extremely unstable. As the construction and operation of fusion reactors, e.g. tokamaks, is exceptionally expensive, numerical simulations are required in order to increase our knowledge about the fusion process. One existing code for plasma simulations in a tokamak is called GyselaX, in which a subroblem consists in solving a two dimensional Poisson equation on many cross-sections of the reactor geometry. The EoCoE (Energy Oriented Center of Excellence: toward exascale for energy) project, funded by the European Commission, aims for the improvement of the current solver for this equation in order to reduce the simulation times. In [1] and [2], a geometric multigrid approach using finite differences for the discretization and a combined line smoothing procedure has been developed. Additionally, an implicit extrapolation technique is used to increase the approximation order of the solution. In this master's thesis, this GmgPolar solver is detailed and implemented in C++. Moreover, several improvements have been applied to the solver and some parts of the code have been parallelised. As the full optimization and parallelisation exceeds the scope of this thesis, future work will be required, before comparing the solver with two other possible approaches and integrating it into GyselaX to reduce the simulation time. [1] Kühn, M. J.; Kruse, C.; Rüde, U. Energy-Minimizing, Symmetric Discretizations for Anisotropic Meshes and Energy Functional Extrapolation, SIAM J. Sci. Comput.Vol. 43(4), pp. A2448-A2473 (2021). [2] Kühn, M. J.; Kruse, C.; Rüde, U. Implicitly extrapolated geometric multigrid on disk-like domains for the gyrokinetic Poisson equation from fusion plasma applications, Preprint: https://hal.archives-ouvertes.fr/hal-03003307/, Submit-ted to Journal of Scientific Computing, 2021.

Item URL in elib:https://elib.dlr.de/146684/
Document Type:Thesis (Master's)
Additional Information:Betreuung der Arbeit im DLR und Zweitgutachten: Martin Joachim Kühn
Title:Geometric multigrid for the gyrokinetic Poisson equation from fusion plasma applications
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Schwarz, Christinachrissy-s96 (at) web.deUNSPECIFIED
Date:15 December 2021
Refereed publication:No
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Number of Pages:75
Status:Published
Keywords:Geometric multigrid, gyrokinetic, Poisson, fusion plasma, extrapolation, OpenMP
Institution:Universität Erlangen-Nürnberg
Department:Chair of Computer Science 10
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space System Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Space System Technology
DLR - Research theme (Project):R - Tasks SISTEC
Location: Köln-Porz
Institutes and Institutions:Institute for Software Technology > High-Performance Computing
Institute for Software Technology
Deposited By: Kühn, Dr. Martin Joachim
Deposited On:14 Dec 2021 10:52
Last Modified:21 Dec 2021 10:21

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