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 language | English (US) |
|---|---|
| Pages (from-to) | 977-996 |
| Number of pages | 20 |
| Journal | Numerical Linear Algebra with Applications |
| Volume | 17 |
| Issue number | 6 |
| DOIs | |
| State | Published - Nov 26 2010 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: Contract/grant sponsor: King Abdullah University of Science and Technology (KAUST); contract/grant number: KUK-C1-013-04
This publication acknowledges KAUST support, but has no KAUST affiliated authors.