Multigrid smoothers for saddle point systems / eingereicht von Lisa Claus, M. Sc. Wuppertal, Juni 2019
Inhalt
- Acknowledgments
- Contents
- Introduction
- Partial differential equations
- Definition and classification of partial differential equations
- Discretization methods
- Classification of the linear systems arising from systems of PDEs
- Multigrid methods
- Basic iterative methods
- Geometric multigrid methods
- Local Fourier analysis
- Classical Algebraic multigrid methods
- New class of algebraic multigrid methods
- Parallel multigrid methods
- Construction of geometric multigrid smoothers for the Stokes equations
- The Stokes equations
- Multigrid components for the Stokes equations on staggered grids
- Computational work
- LFA for the Stokes equations
- Numerical results
- Algorithm development
- Automatic construction of algebraic multigrid smoothers
- Model problem - Maxwell's equations
- Automatic construction of AMG smoothers
- Evaluating the smoothers
- Constructing an interpolation operator
- Conclusions & Outlook
- List of Figures
- List of Tables
- List of Notations
- Bibliography