Block-triangular preconditioners for PDE-constrained optimization
KAUST Grant NumberKUK-C1-013-04
Online Publication Date2010-11-26
Print Publication Date2010-12
Permanent link to this recordhttp://hdl.handle.net/10754/597687
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AbstractIn 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.
CitationRees T, Stoll M (2010) Block-triangular preconditioners for PDE-constrained optimization. Numerical Linear Algebra with Applications 17: 977–996. Available: http://dx.doi.org/10.1002/nla.693.
SponsorsContract/grant sponsor: King Abdullah University of Science and Technology (KAUST); contract/grant number: KUK-C1-013-04