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Low-rank update of preconditioners for saddle-point systems in fluid flow problems
Citation Link: https://doi.org/10.15480/882.13171
Publikationstyp
Doctoral Thesis
Date Issued
2024
Sprache
English
Author(s)
Beddig, Rebekka Salome
Advisor
Referee
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2024-03-15
Institute
TORE-DOI
Citation
Technische Universität Hamburg (2024)
We develop and analyze low-rank updates for preconditioners that are based on a (randomized) low-rank approximation of the error between the identity matrix and the preconditioned matrix. The low-rank updates are applied to different components of a block preconditioner for saddle-point systems that arise in the simulation of the rotating Boussinesq equations. A relaxation parameter improves the initial preconditioner as well as the low-rank updates. We analyze the complexity of the construction and application for different update schemes. An error analysis explains why low-rank corrections may deteriorate a given preconditioner. Numerical experiments illustrate the impact of various parameters on the effectiveness of the low-rank updates.
Subjects
preconditioner
low-rank update
saddle-point system
Schur complement
Boussinesq equations
fluid flow problems
DDC Class
510: Mathematics
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Beddig_Rebekka_Salome_Low-Rank_Updates_of_Preconditioners_for_Saddle_Point_Systems_in_Fluid_Flow_Problems.pdf
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