The Mathematical Institute, University of Oxford, Eprints Archive

Preconditioned iterative methods for Navier-Stokes control problems

Pearson, John W. (2013) Preconditioned iterative methods for Navier-Stokes control problems. Technical Report. SIAM. (Submitted)

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Abstract

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 Navier-Stokes control problems, one of the main problems of this type in the field of fluid dynamics. Having detailed the Oseen-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.

Item Type:Technical Report (Technical Report)
Subjects:D - G > Fluid mechanics
H - N > Numerical analysis
O - Z > Systems theory
Research Groups:Numerical Analysis Group
ID Code:1751
Deposited By: Lotti Ekert
Deposited On:10 Sep 2013 09:37
Last Modified:29 May 2015 19:26

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