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- W638340508 abstract "Active flow control plays acentral role in many industrial applications such as e.g. controlof crystal growth processes, where the flow in the melt has asignificant impact on the quality of the crystal. Optimal controlof the flow by electro-magnetic fields and/or boundary temperaturesleads to optimisation problems with PDE constraints, which arefrequently governed by the time-dependent Navier-Stokes equations.The mathematical formulation is a minimisation problem with PDEconstraints. By exploiting the special structure of the first ordernecessary optimality conditions, the so called Karush-Kuhn-Tucker(KKT)-system, this thesis develops a special hierarchical solutionapproach for such equations, based on the distributed control ofthe Stokes – and Navier – Stokes. The numerical costs forsolving the optimisation problem are only about 20-50 times higherthan a pure forward simulation, independent of the refinementlevel. Utilising modern multigrid techniques in space, it ispossible to solve a forward simulation with optimal complexity,i.e., an appropriate solver for a forward simulation needs O(N)operations, N denoting the total number of unknowns for a givencomputational mesh in space and time. Such solvers typically applyappropriate multigrid techniques for the linear subproblems inspace. As a consequence, the developed solution approach for theoptimal control problem has complexity O(N) as well. This isachieved by a combination of a space-time Newton approach for thenonlinearity and a monolithic space-time multigrid approach for'global' linear subproblems. A second inner monolithic multigridmethod is applied for subproblems in space, utilising localPressure-Schur complement techniques to treat the saddle-pointstructure. The numerical complexity of this algorithm distinguishesthis approach from adjoint-based steepest descent methods used tosolve optimisation problems in many practical applications, whichin general do not satisfy this complexity requirement." @default.
- W638340508 created "2016-06-24" @default.
- W638340508 creator A5045296981 @default.
- W638340508 date "2011-12-21" @default.
- W638340508 modified "2023-09-23" @default.
- W638340508 title "A Hierarchical Flow Solver for Optimisation with PDE Constraints" @default.
- W638340508 doi "https://doi.org/10.17877/de290r-6950" @default.
- W638340508 hasPublicationYear "2011" @default.
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