Speaker
Description
Optimal control problems with PDEs as constraints arise very often in scientific and industrial applications. Due to the difficulties arising in their numerical solution, researchers have put a great effort into devising robust solvers for this class of problems. An example of a highly challenging problem attracting significant attention is the distributed control of incompressible viscous fluid flow problems. In this case, the physics is described by the incompressible Navier--Stokes equations. Since the PDEs given in the constraints are non-linear, in order to obtain a solution of Navier--Stokes control problems one has to iteratively solve linearizations of the problems until a prescribed tolerance on the non-linear residual is achieved.
In this talk, we present efficient and robust preconditioned iterative methods for the solution of the stationary incompressible Navier--Stokes control problem, when employing a Gauss--Newton linearization of the first-order optimality conditions. The iterative solver is based on an augmented Lagrangian preconditioner. By employing saddle-point theory, we derive suitable approximations of the $(1,1)$-block and the Schur complement. Numerical experiments show the effectiveness and robustness of our approach, for a range of problem parameters.
