Algebraic multigrid method by smoothed agglomeration for a Stokes problem
Ales Janka (EPFL Lausanne)
We introduce an algebraic multigrid method by smoothed agglomeration for solving indefinite linear systems of equations encountered, for example, when treating the discretized Stokes problem.
First, we describe the idea of smoothed agglomeration on a simpler case of symmetric positive definite problems, together with an overview of available theoretical convergence results. Then we consider different ways of constructing efficient multigrid solvers for indefinite systems. Instead of treating pressure and velocity separately, we finally opt for a monolitic multigrid method with indefinite problems on each multigrid level.
The monolithic multigrid strategy allows us to achieve a black-box method with a robust behaviour even for very elongated geometries, where standard pressure mass-matrix or pressure laplace preconditioners of the pressure Schur complement become inefficient. Related numerical experiments will be presented.