1. Introduction to Scientific Computing II Multigrid Dr. Miriam Mehl Institut für Informatik Scientific Computing In Computer Science

2. Relaxation Methods – Properties convergence depends on  method  frequency of the error  stepsize h

3. Jacobi – Details fast for  middle frequencies slow for  high and low frequencies

4. Damped Jacobi – Details fast for  high frequencies slow for  low frequencies

5. Multigrid – Principle fine grid  eliminate high frequencies coarse grids  eliminate low frequencies(!)  equation for the error(!)  error smooth => representable

6. Multigrid – Algorithm iterate (J/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

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

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

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

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

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

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

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

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