Null-space preconditioners for saddle point systems
Pestana, Jennifer and Rees, Tyrone (2016) Null-space preconditioners for saddle point systems. SIAM Journal on Matrix Analysis and Applications, 37 (3). pp. 1103-1128. ISSN 0895-4798 (https://doi.org/10.1137/15M1021349)
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Abstract
The null-space method is a technique that has been used for many years to reduce a saddle point system to a smaller, easier to solve, symmetric positive-definite system. This method can be understood as a block factorization of the system. Here we explore the use of preconditioners based on incomplete versions of a particular null-space factorization, and compare their performance with the equivalent Schur-complement based preconditioners. We also describe how to apply the non-symmetric preconditioners proposed using the conjugate gradient method (CG) with a non-standard inner product. This requires an exact solve with the (1,1) block, and the resulting algorithm is applicable in other cases where Bramble-Pasciak CG is used. We verify the efficiency of the newly proposed preconditioners on a number of test cases from a range of applications.
ORCID iDs
Pestana, Jennifer ORCID: https://orcid.org/0000-0003-1527-3178 and Rees, Tyrone;-
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Item type: Article ID code: 56709 Dates: DateEvent18 August 2016Published18 August 2016Published Online16 June 2016Accepted13 May 2015SubmittedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 21 Jun 2016 15:12 Last modified: 06 Sep 2024 00:46 URI: https://strathprints.strath.ac.uk/id/eprint/56709