Introduction to Scientific Computing II Multigrid Dr. Miriam Mehl

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

Multigrid fine grid  reduce high frequencies error after beforesmoothing

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

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

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

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

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

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

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

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

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

Two Grid – Multigrid Example: 2D Poisson 5-point-stencil htwo-grid analysisV-cycle 1/ / / / / / /