University of Twente Student Theses


On the Multigrid Method for Anisotropic Diffusion

Oudsten, M.A. den (2023) On the Multigrid Method for Anisotropic Diffusion.

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Abstract:In this thesis the convergence of the multigrid method with Jacobi, Gauss-Seidel and Incomplete Line LU (ILLU) smoothers is analysed numerically for anisotropic diffusion problems. For this, an eigenvalue analysis is performed on the multigrid method in two dimensions. This shows that the method, using either the Jacobi or ILLU smoother, is not always robust for strongly anisotropic problems. To ensure convergence for the multigrid method with the ILLU smoother for strongly anisotropic problems, a bound on the relation between the grid size and the anisotropy is proposed. Also, a more robust iterative scheme is proposed and analysed. This iterative scheme based on the multigrid method is robust when solving the anisotropic diffusion problem using either the Jacobi, Gauss-Seidel or ILLU smoother.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics MSc (60348)
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