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Fast iterative solvers for convection-diffusion control problems

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)

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. (Contact us about this Publication)
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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
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)

University of Kent Author Information

Pearson, John W.

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