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Block and joint ℋ︁‐matrix preconditioners for the Oseen equations
Author(s) -
Le Borne Sabine
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610354
Subject(s) - block (permutation group theory) , schur complement , block matrix , lu decomposition , saddle point , domain decomposition methods , diagonal , matrix (chemical analysis) , mathematics , factorization , matrix decomposition , rank (graph theory) , triangular matrix , linear system , algorithm , finite element method , combinatorics , mathematical analysis , geometry , pure mathematics , eigenvalues and eigenvectors , physics , materials science , composite material , quantum mechanics , invertible matrix , thermodynamics
For saddle point problems in fluid dynamics, many preconditioners in the literature exploit the block structure of the problem to construct block diagonal or block triangular preconditioners. The performance of such preconditioners depends on whether fast, approximate solvers for the linear systems on the block diagonal as well as for the Schur complement are available. We will construct these efficient preconditioners using hierarchical matrix techniques in which fully populated matrices are approximated by blockwise low rank approximations. We will compare such block preconditioners with those obtained through a completely different approach where the given block structure is not used but a domain‐decomposition based ℋ‐LU factorization is constructed for the complete system matrix. Preconditioners resulting from these two approaches will be discussed and compared through numerical results. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)