Geodesic
Joint domain-decomposition \(\mathcal H\)-LU preconditioners for saddle point problems
Electronic transactions on numerical analysis, Tome 26 (2007), pp. 285-298
For saddle point problems in fluid dynamics, several popular preconditioners exploit the block structure of the problem to construct block triangular preconditioners. The performance of such preconditioners depends on whether fast, approximate solvers for the linear systems on the block diagonal (representing convection-diffusion problems) as well as for the Schur complement (in the pressure variables) are available. In this paper, we will introduce a completely different approach in which we ignore this given block structure. We will instead compute an approximate LU-factorization of the complete system matrix using hierarchical matrix techniques. In particular, we will use domain-decomposition clustering with an additional local pivoting strategy to order the complete index set.
Classification : 65F05, 65F30, 65F50
Keywords: hierarchical matrices, data-sparse approximation, oseen equations, preconditioning, factorization 
@article{ETNA_2007__26__a10,
     author = {Le Borne,  Sabine and Oliveira,  Suely},
     title = {Joint domain-decomposition \(\mathcal {H\)-LU} preconditioners for saddle point problems},
     journal = {Electronic transactions on numerical analysis},
     pages = {285--298},
     year = {2007},
     volume = {26},
     zbl = {1171.65371},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2007__26__a10/}
}
TY  - JOUR
AU  - Le Borne,  Sabine
AU  - Oliveira,  Suely
TI  - Joint domain-decomposition \(\mathcal H\)-LU preconditioners for saddle point problems
JO  - Electronic transactions on numerical analysis
PY  - 2007
SP  - 285
EP  - 298
VL  - 26
UR  - http://geodesic.mathdoc.fr/item/ETNA_2007__26__a10/
LA  - en
ID  - ETNA_2007__26__a10
ER  - 
%0 Journal Article
%A Le Borne,  Sabine
%A Oliveira,  Suely
%T Joint domain-decomposition \(\mathcal H\)-LU preconditioners for saddle point problems
%J Electronic transactions on numerical analysis
%D 2007
%P 285-298
%V 26
%U http://geodesic.mathdoc.fr/item/ETNA_2007__26__a10/
%G en
%F ETNA_2007__26__a10
Le Borne,  Sabine; Oliveira,  Suely. Joint domain-decomposition \(\mathcal H\)-LU preconditioners for saddle point problems. Electronic transactions on numerical analysis, Tome 26 (2007), pp. 285-298. http://geodesic.mathdoc.fr/item/ETNA_2007__26__a10/