Abstract
AbstractFor 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 ℋ︁‐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)
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