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An Error-Based Low-Rank Correction for Pressure Schur Complement Preconditioners
Publikationstyp
Book part
Publikationsdatum
2023-12-14
Sprache
English
Author
Beddig, Rebekka Salome
Simon, Konrad
Volume
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
Scopus ID
Publisher
Springer
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