A ROBUST TWO-LEVEL INCOMPLETE FACTORIZATION FOR (NAVIER-)STOKES SADDLE POINT MATRICES

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 r...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on matrix analysis and applications 2011-01, Vol.32 (4), p.1475-1499
Main Authors: WUBS, Fred W, THIES, Jonas
Format: Article
Language:English
Subjects:
Acceleration of convergence
Algebra
Applied mathematics
Arakawa C-grid
constraint preconditioning
electrical networks
Exact sciences and technology
F-matrix
grid-independent convergence
incomplete factorization
incompressible (Navier-)Stokes equations
indefinite matrix
Iterative methods
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematics
Methods
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations
saddle point problem
Sciences and techniques of general use
Velocity
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0895-4798
1095-7162
1095-7162
DOI:10.1137/100789439