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

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

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

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

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

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

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

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