Regularization-robust preconditioners for time-dependent PDE-constrained optimization problems

Pearson, John W and Stoll, Martin and Wathen, Andrew J (2012) Regularization-robust preconditioners for time-dependent PDE-constrained optimization problems. SIAM Journal on Matrix Analysis and Applications, 33 (4). pp. 1126-1152. ISSN 0895-4798. E-ISSN 1095-7162. (doi:https://doi.org/10.1137/110847949) (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)

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Official URL
http://dx.doi.org/10.1137/110847949

Abstract

In this article, we motivate, derive, and test effective preconditioners to be used with the MINRES algorithm for solving a number of saddle point systems which arise in PDE-constrained optimization problems. We consider the distributed control problem involving the heat equation and the Neumann boundary control problem involving Poisson's equation and the heat equation. Crucial to the effectiveness of our preconditioners in each case is an effective approximation of the Schur complement of the matrix system. In each case, we state the problem being solved, propose the preconditioning approach, prove relevant eigenvalue bounds, and provide numerical results which demonstrate that our solvers are effective for a wide range of regularization parameter values, as well as mesh sizes and time-steps.

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 15:59 UTC
Last Modified: 01 May 2015 14:54 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/48151 (The current URI for this page, for reference purposes)
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