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Joint domain-decomposition H-LU preconditioners for saddle point problems
Publikationstyp
Journal Article
Date Issued
2007-12-01
Sprache
English
Author(s)
Volume
26
Start Page
285
End Page
298
Citation
Electronic Transactions on Numerical Analysis 26 (): 285-298 (2007-12-01)
Publisher Link
Scopus ID
Publisher
Kent State University
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. As a result, we obtain an H-matrix structure in which an H-LU factorization is computed more efficiently and with higher accuracy than for the corresponding block structure based clustering. H-LU preconditioners resulting from the block and joint approaches will be discussed and compared through numerical results.
Subjects
Data-sparse approximation
Factorization
Hierarchical matrices
Oseen equations
Preconditioning
DDC Class
510: Mathematik