Graduate Seminar - 9/25, 12:00PM Duncan Hall 1064

Heiko K. Weichelt

Department of Mathematics, Chemnitz University of Technology, Germany
Research Group Computational Methods in Systems and Control Theory (CSC)
Max-Planck-Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany

"Numerical Solution of the Feedback Control Problem for Coupled Flow Problems: Ideas, Approaches, and Numerical Results"

In order to explore boundary feedback stabilization of coupled flow problems we consider the Navier-Stokes equations that describe instationary, incompressible flows coupled with a diffusion convection equation. Using a standard finite element discretization we get a differential-algebraic system of differential index two. We show how to reduce this index with a projection method to get a generalized state space system, where a linear quadratic control approach can be applied. This leads to large-scale saddle point systems which have to be solved in a threefold nested iteration. For obtaining a fast iterative solution of those non-symmetric systems we derive efficient preconditioners based on the approaches due to Wathen et al. [Elman/Silvester/Wathen 2005, Stoll/Wathen 2011]. Finally we show recent numerical results regarding the arising nested iteration. Joint work with Peter Benner and Jens Saak.