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

2. Multigrid – Recursive Algorithms
V-cycle: one recursive call
W-cycle: two recursive calls
F-cycle: V-cycle on each level

3. Two Grid – Multigrid Example: 2D Poisson 5-point-stencil h
two-grid analysis
V-cycle
1/32
0.042
1/64
0.044
1/128
1/256
0.043
1/512
1/1024
1/2048

4. Multigrid – Some Rules smoother optimal smoothing
not!!! optimal convergence
small number of smoothing iterations!

5. Multigrid – Some Rules grid coarsening standard: doubling of h
exceptions:
unisotropic operators
unstructured/adaptively refined grids

6. Multigrid – Some Rules restriction/interpolation
order of restriction + order of interpolation > order of discretisation

7. Multigrid – Some Rules
V-cycle
faster
W-cycle
more robust

8. Multigrid – Outlook adaptively refined grids unisotropic operators
line smoothers
semicoarsening
unstructured grids / general SLE
algebraic multigrid