Markus Wabro : Algebraic Multigrid Methods for the Oseen Equations
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 special preconditioners
for Krylov-space methods, e.g. as introduced by Elman, Silvester, Wathen et.al.).
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" situation
s, i.e., when flows for complex 3D geometries have to be simulated.