Null-space preconditioners for saddle point systems

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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 logoORCID: https://orcid.org/0000-0003-1527-3178 and Rees, Tyrone;
  • Item type:Article
    ID code:56709
    Dates:
    Date
    Event
    18 August 2016
    Published
    18 August 2016
    Published Online
    16 June 2016
    Accepted
    13 May 2015
    Submitted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:21 Jun 2016 15:12
    Last modified:02 Dec 2024 01:17
    URI:https://strathprints.strath.ac.uk/id/eprint/56709
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