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Fast iterative solvers for large matrix systems arising from time-dependent Stokes control problems

Pearson, John W (2016) Fast iterative solvers for large matrix systems arising from time-dependent Stokes control problems. Applied Numerical Mathematics, 108 . pp. 87-101. ISSN 0168-9274. (doi:10.1016/j.apnum.2016.05.002)

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In this manuscript we consider the development of fast iterative solvers for Stokes control problems, an important class of PDE-constrained optimization problems. In particular we wish to develop effective preconditioners for the matrix systems arising from finite element discretizations of time-dependent variants of such problems. To do this we consider a suitable rearrangement of the matrix systems, and exploit the saddle point structure of many of the relevant sub-matrices involved - we may then use this to construct representations of these sub-matrices based on good approximations of their (1,1)-block and Schur complement. We test our recommended iterative methods on a distributed control problem with Dirichlet boundary conditions, and on a time-periodic problem.

Item Type: Article
DOI/Identification number: 10.1016/j.apnum.2016.05.002
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 16:59 UTC
Last Modified: 29 May 2019 14:28 UTC
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