The Mathematical Institute, University of Oxford, Eprints Archive

Block triangular preconditioners for PDE constrained
optimization

Stoll, Martin and Rees, Tyrone (2009) Block triangular preconditioners for PDE constrained
optimization.
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Abstract

In this paper we investigate the possibility of using a block triangular preconditioner for saddle point problems arising in PDE constrained optimization. In particular we focus on a conjugate gradient-type method introduced by Bramble and Pasciak which uses self adjointness of the preconditioned system in a non-standard inner product. We show when the Chebyshev semi-iteration is used as a preconditioner for the relevant matrix blocks involving the finite element mass matrix that the main drawback of the Bramble-Pasciak method – the appropriate scaling of the preconditioners – is easily overcome. We present an eigenvalue analysis for the block triangular preconditioners which gives convergence bounds in the non-standard inner product and illustrate their competitiveness on a number of computed examples.

Item Type:Article
Subjects:H - N > Numerical analysis
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:805
Deposited By:Dr M. Stoll
Deposited On:05 Sep 2009 07:49
Last Modified:15 Sep 2009 13:33

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