Pearson, John W, Wathen, Andrew J (2013) Fast iterative solvers for convection-diffusion control problems. Electronic Transactions on Numerical Analysis, 40 . pp. 294-310. ISSN 1068-9613. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:48156)
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Official URL: http://www.emis.ams.org/journals/ETNA/vol.40.2013/... |
Abstract
In this manuscript, we describe effective solvers for the optimal control of stabilized convectiondiffusion
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 h and the regularization parameter ? for
a range of problems.
Item Type: | Article |
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Subjects: |
Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations |
Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Depositing User: | John Pearson |
Date Deposited: | 30 Apr 2015 16:42 UTC |
Last Modified: | 16 Feb 2021 13:24 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/48156 (The current URI for this page, for reference purposes) |
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