Hierarchical solution concepts for flow control problems
Michael Hinze (Hamburg) and Stefan Turek (Dortmund)
Summary:
The goal of the project is the development of a
generally applicable hierarchical (multigrid) solution framework for flow control
problems which allows their numerical solution requiring a computational effort of only a
small multiple of that of the flow simulation itself. To achieve our goal we combine
- High performance scientific computing techniques in flow simulation,
- Discrete concepts in space and time which are tailored to the structure
of the first-order necessary optimality conditions of the underlying
optimization problem (Karush-Kuhn-Tucker system, short KKT system), and
- Sophisticated optimization algorithms combined with multigrid concepts
which allow to exploit the structure of the underlying optimization problem.
We investigate two different multigrid approaches. APPROACH I tackles the KKT system all-at-once, and APPROACH II exploits the structure of the KKT system and reduces it to a
nonlinear integral equation (variational inequality) for the control u, which then is tackled by a multigrid approach tailored to integral equations.
Within this first application period we concentrate on methodic and algorithmic aspects
which are validated at optimization problems for 2D time dependent flows with
prototypical character.
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