1. Introduction to Scientific Computing II Multigrid Dr. Miriam Mehl

2. Multigrid – Algorithm iterate (GS) on the fine grid restrict residual to the coarse grid solve coarse grid equation for the error interpolate error to the fine grid correct fine grid solution

3. Multigrid fine grid  reduce high frequencies error after beforesmoothing

4. Multigrid switch to coarse grid  restrict residual residual before restriction after

5. Multigrid solve coarse grid equation  recursive call of multigrid coarse grid solution

6. Multigrid solve coarse grid equation  recursive call of multigrid fine grid error coarse grid solution

7. Multigrid fine grid error interpolated coarse grid solution switch to fine grid – interpolate coarse grid solution

8. Multigrid switch to fine grid  apply coarse grid correction fine grid error before correction after correction

9. Multigrid fine grid  eliminate new high frequencies fine grid error before smoothing after smoothing

10. Multigrid – Degrees of Freedom smoother relation step sizes coarse – fine grid transfer operators – restriction – interpolation processing order of grid levels

11. Multigrid – Cycles V-cycle: one recursive call W-cycle: two recursive calls F-cycle: V-cycle on each level

12. Multigrid – Convergence two grid analysis h-independent convergence – for ‚good‘ components

13. Two Grid – Multigrid Example: 2D Poisson 5-point-stencil htwo-grid analysisV-cycle 1/320.042 1/640.0420.044 1/1280.0420.044 1/2560.0420.043 1/5120.0420.043 1/10240.042 1/20480.042