All-at-once solution of time-dependent Stokes control

Authors:
Martin Stoll;Andy Wathen
Affiliations:
Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany;Numerical Analysis Group, Mathematical Institute, 24-29 St Giles', Oxford, OX1 3LB, United Kingdom
Venue:
Journal of Computational Physics
Year:
2013

Citing 16
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Abstract

The solution of time-dependent PDE-constrained optimization problems subject to unsteady flow equations presents a challenge to both algorithms and computing power. In this paper we present an all-at-once approach where we solve for all time-steps of the discretized unsteady Stokes problem at once. The most desirable feature of this approach is that for all steps of an iterative scheme we only need approximate solutions of the discretized Stokes operator. This leads to an efficient scheme which exhibits mesh-independent behaviour.