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Full Record Details
DOI
10.5286/raltr.2010022
Persistent URL
http://purl.org/net/epubs/work/53444
Record Status
Checked
Record Id
53444
Title
A robust two-level incomplete factorization for (Navier-)Stokes saddle point matrices
Contributors
FW Wubs
,
J Thies
Abstract
We present a new hybrid direct/iterative approach to the solution of a special class of saddle point matrices arising from the discretization of the steady incompressible Navier-Stokes equations on an Arakawa C-grid. The two-level method introduced here has the following properties: (i) it is very robust, even close to the point where the solution becomes unstable; (ii) a single parameter controls fill and convergence, making the method straightforward to use; (iii) the convergence rate is independent of the number of unknowns; (iv) it can be implemented on distributed memory machines in a natural way; (v) the matrix on the second level has the same structure and numerical properties as the original problem, so the method can be applied recursively; (vi) the iteration takes place in the divergence-free space, so the method qualifies as a ?constraint preconditioner?; (vii) the approach can also be applied to Poisson problems. This work is also relevant for problems in which similar saddle point matrices occur, for instance when simulating electrical networks, where one has to satisfy Kirchhoff?s conservation law for currents.
Organisation
CSE
,
CSE-NAG
,
STFC
Keywords
electrical networks
,
Saddle point problem
,
F-matrix
,
contraint preconditioning
,
incompressible (Navier-)Stokes equations
,
grid-independent convergence
,
indefinite matrix
,
incomplete factorization
,
Arakawa C-grid
Funding Information
Related Research Object(s):
Licence Information:
Language
English (EN)
Type
Details
URI(s)
Local file(s)
Year
Report
RAL Technical Reports
RAL-TR-2010-022. 2010.
wRAL2010022.pdf
2010
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