A low-rank update for relaxed Schur complement preconditioners in fluid flow problems

Publikationstyp
Journal Article
Date Issued
2023-12
Sprache
English
Author(s)
Beddig, Rebekka S. 
Mathematik E-10  
Behrens, Jörn  
Universität Hamburg  
Le Borne, Sabine  orcid-logo
Mathematik E-10  
TORE-DOI
10.15480/882.8747
TORE-URI
https://hdl.handle.net/11420/43764
Journal
Numerical Algorithms  
Volume
94
Issue
4
Start Page
1597
End Page
1618
Citation
Numerical Algorithms 94 (4): 1597-1618 (2023-12)
Publisher DOI
10.1007/s11075-023-01548-3
Scopus ID
2-s2.0-85159093436
Publisher
Springer Science Business Media B.V.
The simulation of fluid dynamic problems often involves solving large-scale saddle-point systems. Their numerical solution with iterative solvers requires efficient preconditioners. Low-rank updates can adapt standard preconditioners to accelerate their convergence. We consider a multiplicative low-rank correction for pressure Schur complement preconditioners that is based on a (randomized) low-rank approximation of the error between the identity and the preconditioned Schur complement. We further introduce a relaxation parameter that scales the initial preconditioner. This parameter can improve the initial preconditioner as well as the update scheme. We provide an error analysis for the described update method. Numerical results for the linearized Navier–Stokes equations in a model for atmospheric dynamics on two different geometries illustrate the action of the update scheme. We numerically analyze various parameters of the low-rank update with respect to their influence on convergence and computational time.
Subjects
Low-rank update
Preconditioner
Saddle-point system
Schur complement
DDC Class
510: Mathematics
Publication version
acceptedVersion
Lizenz
https://creativecommons.org/licenses/by/4.0/
Loading...
Thumbnail Image
Name

s11075-023-01548-3.pdf

Type

Main Article

Size

703.99 KB

Format

Adobe PDF