Efficient Solvers for Optimal Control Problems for the Stokes Equations in the Time-Harmonic Case

Dipl.-Ing. Wolfgang Krendl

June 7, 2011, 1:30 p.m. HS 14

As a special case for optimal control problems for the time-dependent Stokes equations with distributed control we will study the time harmonic one.

The main focus of the talk lies in the construction of efficient solvers for the discretized optimal system in the time-harmonic setting.

Substituting a multiharmonic ansatz in the variational formulation of the Kuhn Tucker system, will lead to a decoupled block system for the Fourier coefficients.

We will construct a block preconditioner which results in robust convergence rates for the Minimal Residual (MINRES) Method, for each of the indefinite blocks, with respect to the involved model parameters and the meshsize. Some numerical tests illustrate the theoretical results.