We present and compare concepts for algebraic multigrid (AMG) solvers for the Oseen linearization of the Navier-Stokes equations for incompressible fluids.

The two main strategies in this area are the following. The first one is the segregated approach, where the equations for velocity and pressure are iteratively decoupled, and AMG is used for the solution of the resulting scalar problems (examples in this direction are Uzawa or SIMPLE schemes, or preconditioners for Krylov-space methods, e.g. as introduced by Silvester, Wathen et al., 2001).

The main topic of the talk will be the second strategy, the coupled approach, where an AMG method is developed for the whole saddle-point system. We present the ingredients of this method (smoothers, coarse level construction) and pinpoint a major problem, the stability of the coarse-level systems.

Finally, we will show how the different methods perform in "real life" situations, i.e. when flows in complex 3D domains have to be simulated.