Erlangen 2018 – wissenschaftliches Programm
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P: Fachverband Plasmaphysik
P 1: Helmholtz Graduate School I - Theory
P 1.4: Vortrag
Montag, 5. März 2018, 11:45–12:10, A 0.112
Splitting Schemes and Compatible Spaces for Linearized MHD — •Mustafa Gaja1,2, Emmanuel Franck3, Eric Sonnendruecker1,2, Ahmed Ratnani1,2, Jalal Lakhlili1, and Mariarosa Mazza1 — 1Max Planck Institute fuer Plasma Physik, Garching, Germany — 2Technische Universitaet Muenchen, Muenchen, Germany — 3Inria Nancy Grand Est and IRMA, Strasbourg, France
We investigate the linearized Magnetohydrodynamics (MHD) model for the evolution of the perpendicular components of the velocity and the magnetic fields in the context of tokamaks via the novel technique of Isogeometric Analysis (IgA) with high degree B-Splines. The discretization is based on compatible finite element spaces that preserve the natural properties (i.e, divergence-free condition) of the resulting operators to avoid spurious modes and related numerical instabilities. The geometry is planar and is written to be easily generalized to a torus case. We present results on the compatible discretization and couple this investigation with a hamiltonian splitting in time which allows to deconstruct the system into ’building-blocks’ operators that could be inverted individually. Such operators, Laplacian like and Mass operators (H1 and L2 projectors, respectively) for example, are inverted using a robust and optimal ad-hoc multigrid (MG) designed using the Generalized Locally Toeplitz (GLT) theory. This MG is used as a preconditioner for Krylov-Type solvers where the GLT theory is used to construct an efficient smoother for the MG that eliminates the pathology ensuing from using high order B-Splines discretization.