All-at-once multigrid methods for Poisson and Stokes control problems

Dr. Stefan Takacs

Dec. 3, 2013, 1:45 p.m. S2 059

In this talk we consider standard Poisson and Stokes control problems of
tracking type. The optimality
system (KKT system) characterising the solution of such a
PDE-constrained optimisation problem is a
large-scale sparse linear system. This system is symmetric but not
positive definite. Therefore, standard
iterative solvers are typically not the best choice.

We are interested in fast iteration schemes with convergence rates
bounded away from 1 by a constant
which is independent of the discretization parameter (the grid size) and
of problem parameters, like
in the regularization parameter in the model problem. To achieve this
goal, we propose an all-at-once
multigrid approach.

The main focus of the talk is on the convergence theory. We will
introduce an abstract framework which
allows to develop the convergence theory in a systematic way.