Block-triangular preconditioners for PDE-constrained optimization

Tyrone Rees, Martin Stoll

Research output: Contribution to journalArticlepeer-review

58 Scopus citations

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 that 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 that gives convergence bounds in the non-standard inner product and illustrates their competitiveness on a number of computed examples. Copyright © 2010 John Wiley & Sons, Ltd.
Original languageEnglish (US)
Pages (from-to)977-996
Number of pages20
JournalNumerical Linear Algebra with Applications
Volume17
Issue number6
DOIs
StatePublished - Nov 26 2010
Externally publishedYes

Fingerprint

Dive into the research topics of 'Block-triangular preconditioners for PDE-constrained optimization'. Together they form a unique fingerprint.

Cite this