An Error-Based Low-Rank Correction for Pressure Schur Complement Preconditioners

Publikationstyp
Book Part
Date Issued
2023-12-14
Sprache
English
Author(s)
Beddig, Rebekka Salome 
Mathematik E-10  
Behrens, Jörn  
Universität Hamburg  
Le Borne, Sabine  orcid-logo
Mathematik E-10  
Simon, Konrad
TORE-URI
https://hdl.handle.net/11420/44822
First published in
Lecture notes in computational science and engineering  
Number in series
148
Start Page
77
End Page
92
Citation
In: Iske, A., Rung, T. (eds) Modeling, Simulation and Optimization of Fluid Dynamic Applications. Lecture Notes in Computational Science and Engineering, vol 148. Springer, Cham. (2023)
Publisher DOI
10.1007/978-3-031-45158-4_5
Scopus ID
2-s2.0-85180370472
Publisher
Springer
ISBN
978-3-031-45157-7
978-3-031-45158-4
We describe a multiplicative low-rank correction scheme for pressure Schur complement preconditioners to accelerate the iterative solution of the linearized Navier-Stokes equations. The application of interest is a model for buoyancydriven fluid flows described by the Boussinesq approximation which combines the Navier-Stokes equations enhanced with a Coriolis term and a temperature advection-diffusion equation. The update method is based on a low-rank approximation to the error between the identity and the preconditioned Schur complement. Numerical results on a cube and a shell geometry illustrate the action of the lowrank correction on spectra of preconditioned Schur complements using known preconditioning techniques, the least-squares commutator and the SIMPLE method. The computational costs of the update method are also investigated. The goal is to analyze whether such an update method can lead to accelerated solvers. Numerical experiments show that the update technique can reduce iteration counts in some cases but (counter-intutively) may increase iteration counts in other settings.
DDC Class
510: Mathematics