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In this work we study optimal boundary control problems in energy
spaces, their construction of robust preconditioners and applications to
arterial blood ow. More precisely we consider the unconstrained optimal
Dirichlet and Neumann boundary control problems for the Poisson
equation. In both cases it turns out that the control can be eliminated
and thus a variational formulation in saddle point structure is
obtained. Further, the construction of corresponding robust
preconditioners for optimal boundary control problems is investigated.
We observe that the optimal boundary control problems are related to
biharmonic equation of rst kind. For the preconditioning we consider
either a preconditioner motivated from boundary element methods or a
multilevel preconditioner of BPX type. As an application we study the
optimal Dirichlet boundary control problem for arterial blood fow. In
particular, we are interested in the optimal in ow prole into an
arterial system, motivated for instance by an articial heart pump. Also,
we investigate on hemodynamic indicators, for the identication of
potential risk factors for aneurysms. Several numerical examples
illustrate the obtained theoretical results.