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Preconditioned iterative methods for Navier-Stokes control problems. (English) Zbl 1349.76087

Summary: PDE-constrained optimization problems are a class of problems which have attracted much recent attention in scientific computing and applied science. In this paper we discuss preconditioned iterative methods for a class of (time-independent) Navier-Stokes control problems, one of the main problems of this type in the field of fluid dynamics. Having detailed the Picard-type iteration we use to solve the problems and derived the structure of the matrix system to be solved at each step, we utilize the theory of saddle point systems to develop efficient preconditioned iterative solution techniques for these problems. We also require theory of solving convection-diffusion control problems, as well as a commutator argument to justify one of the components of the preconditioner.

MSC:

76D55 Flow control and optimization for incompressible viscous fluids
49M25 Discrete approximations in optimal control
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
65K10 Numerical optimization and variational techniques

Software:

IFISS
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Full Text: DOI

References:

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