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

Martin Joachim Kühn (1, 2) , Carola Kruse (2) , Ulrich Rüde (3, 2)

1 German Aerospace Center (DLR), Institute for Software Technology, Department for High-Performance Computing, Cologne, Germany
2 CERFACS - Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique
3 Friedrich-Alexander Universität Erlangen-Nürnberg, Chair for Computer Science 10 - System simulation

The gyrokinetic Poisson equation arises as a subproblem of Tokamak fusion reactor simulations. It is often posed on disk-like cross sections of the Tokamak that are represented in generalized polar coordinates. On the resulting curvilinear anisotropic meshes, we discretize the differential equation by finite differences or low order finite elements. Using an implicit extrapolation technique similar to multigrid tau-extrapolation, the approximation order can be increased. This technique can be naturally integrated in a matrix-free geometric multigrid algorithm. Special smoothers are developed to deal with the mesh anisotropy arising from the curvilinear coordinate system and mesh grading.

Mots clés: fusion plasma; disk-like; cross section; multigrid; extrapolation

Domaines: Analyse numérique [math.NA]

Martin Joachim Kühn, Carola Kruse, Ulrich Rüde. Implicitly extrapolated geometric multigrid on disk-like domains for the gyrokinetic Poisson equation from fusion plasma applications. 2020. ⟨hal-03003307⟩