Construction of hierarchical matrices for the preconditioning of the three-dimensional Navier-Stokes equations

Publikationstyp
Doctoral Thesis
Date Issued
2025
Sprache
English
Author(s)
Grams, Jonas David 
Advisor
Le Borne, Sabine  orcid-logo
Referee
Börm, Steffen  
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2024-12-20
Institute
Mathematik E-10  
TORE-DOI
10.15480/882.14508
TORE-URI
https://tore.tuhh.de/handle/11420/53603
Citation
Technische Universität Hamburg (2025)
Solving saddle point problems, e.g. obtained from the discretization of the Navier-Stokes equations, with Krylov subspace methods is a difficult task due to often unfavorable (spectral) properties of the system matrix. A popular preconditioning technique for those kinds of systems are block preconditioners relying on approximations to the upper left system matrix block and the so-called Schur complement. These approximations can be obtained by hierarchical matrix LU factorizations but require the explicit computation of an approximate Schur complement. We present improvements in the construction of the required hierarchical matrices leading to a speed-up for the preconditioner set-up.
Subjects
hierarchical matrices
preconditioning
saddle point problems
Navier-Stokes equations
cluster strategies
DDC Class
510: Mathematics
Lizenz
https://creativecommons.org/licenses/by/4.0/
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