Volume 40, pp. 294-310, 2013.
Fast iterative solvers for convection-diffusion control problems
John W. Pearson and Andrew J. Wathen
Abstract
In this manuscript, we describe effective solvers for the optimal control
of stabilized convection-diffusion control problems. We employ the Local
Projection Stabilization, which results in the same matrix system whether
the discretize-then-optimize or optimize-then-discretize approach for this
problem is used. We then derive two effective preconditioners for this problem,
the first to be used with MINRES and the second to be used with the
Bramble-Pasciak Conjugate Gradient method. The key components of both
preconditioners
are an accurate mass matrix approximation, a good approximation of the Schur
complement,
and an appropriate multigrid process to enact this latter approximation. We
present numerical
results to illustrate that these preconditioners result in convergence in a
small number of iterations, which is robust with respect to the step-size
Full Text (PDF) [409 KB], BibTeX
Key words
PDE-constrained optimization, convection-diffusion control, preconditioning, Local Projection Stabilization, Schur complement.
AMS subject classifications
49M25, 65F08, 65F10, 65N30.
Links to the cited ETNA articles
| [25] | Vol. 34 (2008-2009), pp. 125-135 Andy Wathen and Tyrone Rees: Chebyshev semi-iteration in preconditioning for problems including the mass matrix |
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