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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)

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)
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
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: John Pearson
Date Deposited: 30 Apr 2015 16:42 UTC
Last Modified: 29 May 2019 14:28 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/48156 (The current URI for this page, for reference purposes)
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