Bremen 2017 – wissenschaftliches Programm
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P: Fachverband Plasmaphysik
P 6: Helmholtz Graduate School I
P 6.7: Poster
Montag, 13. März 2017, 16:30–18:30, HS Foyer
Optimal and Robust Multigrid Solver for Elliptic Problems with Application to Anisotropic Diffusion — •Mustafa Gaja1, Ahmed Ratnani1, Emmanuel Franck2, Mariarosa Mazza1, Jalal Lakhlili1, and Eric Sonnendruecker1 — 1Max Planck Institute For Plasma Physics, Germany — 2Inria Nancy Grand Est and IRMA Strasbourg, France
We investigate devising a robust and an optimal multigrid (MG) solver for the linear system arising from applying Isogeometric Analysis using B-Splines as basis functions for elliptic problems. The Laplacian and the Mass operators (H1 and L2 projectors, respectively) are inverted using MG as a solver and the acquired Toeplitz matrices from applying the Generalized Locally Toeplitz (GLT) theory as a preconditioner. The latter is used to construct an efficient preconditioner that eliminates the pathology ensuing from using high order B-Splines discretization. The goal is to have building blocks that are used for more complicated systems, thanks to physics based preconditioning and splitting schemes. We present the obtained results and show how we apply the method for anisotropic diffusion and present the corresponding results.