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Implicitly extrapolated geometric multigrid on disk-like domains for the gyrokinetic Poisson equation from fusion plasma applications

Kühn, Martin Joachim and Kruse, Carola and Rüde, Ulrich (2020) Implicitly extrapolated geometric multigrid on disk-like domains for the gyrokinetic Poisson equation from fusion plasma applications. In: Sparse Days 2020. Sparse Days 2020, Toulouse, France. (Unpublished)

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Abstract

In the context of Tokamak fusion plasma, the gyrokinetic Poisson equation has to be solved on disk-like domains which correspond to the poloidal cross-section of the Tokamak geometry. In its simpliest form, this cross section takes a circular form but deformed geometries were found to be advantageous and are more realistic. We propose a taylored solver for the gyrokinetic Poisson equation on disklike geometries described by curvilinear coordinates. Our solver also copes with an anisotropic, locally refined mesh to model the edge part of the Tokamak and a rapidly dropping density profile. Multigrid methods can achieve optimal complexity for many problems and are among the most efficient solvers for elliptic model problems. Multigrid methods for geometries described by curvilinear coordinates are however less common. We present a taylored geometric multigrid algorithm using optimized line smoothers to enable parallel scalability. We propose an implicit extrapolation scheme for our algorithm to increase the order of convergence by using nonstandard numerical integration rules for P1 finite elements. We also use problem-specific finite differences, which numerically show the same order of convergence as their finite elements' counterpart, enabling a matrix-free implementation with a low memory footprint.

Item URL in elib:https://elib.dlr.de/138678/
Document Type:Conference or Workshop Item (Speech)
Title:Implicitly extrapolated geometric multigrid on disk-like domains for the gyrokinetic Poisson equation from fusion plasma applications
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Kühn, Martin JoachimMartin.Kuehn (at) dlr.dehttps://orcid.org/0000-0002-0906-6984
Kruse, CarolaParallel Algorithms Team, CERFACS (Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique), 42 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, Francehttps://orcid.org/0000-0002-4142-7356
Rüde, UlrichLehrstuhl für Informatik 10 (Systemsimulation), Universität Erlangen-Nürnberg, Nürnberghttps://orcid.org/0000-0001-8796-8599
Date:November 2020
Journal or Publication Title:Sparse Days 2020
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Status:Unpublished
Keywords:fusion plasma, disk-like, cross section, multigrid, extrapolation
Event Title:Sparse Days 2020
Event Location:Toulouse, France
Event Type:international Conference
Organizer:Cerfacs
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 - Vorhaben SISTEC (old)
Location: Köln-Porz
Institutes and Institutions:Institute for Software Technology
Institute for Software Technology > High-Performance Computing
Deposited By: Kühn, Martin Joachim
Deposited On:07 Dec 2020 09:48
Last Modified:20 Jun 2021 15:54

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