
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 NavierStokes 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 Krylovspace 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 saddlepoint system. We present the ingredients of this method (smoothers, coarselevel construction) and pinpoint a major problem, the stability of the coarselevel 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. 
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