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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.