

Preprint 62/2004
-matrix preconditioners in convection-dominated problems
Sabine Le Borne and Lars Grasedyck
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Submission date: 28. Sep. 2004
Pages: 11
published in: SIAM journal on matrix analysis and applications, 27 (2006) 4, p. 1172-1183
DOI number (of the published article): 10.1137/040615845
Bibtex
MSC-Numbers: 65F05, 65F30, 65F50
Keywords and phrases: hierarchical matrices, preconditioning, convection-dominant problems
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Abstract:
Hierarchical matrices provide a data-sparse way to approximate
fully populated matrices. In this paper we exploit
-matrix techniques to approximate the LU-decompositions of
stiffness matrices
as they appear in (finite element or finite difference)
discretizations of convection-dominated elliptic partial
differential equations.
These sparse
-matrix approximations may then be used as
preconditioners in iterative methods. Whereas the approximation
of the matrix inverse by an
-matrix requires some modification
in the underlying index clustering when applied to convection-dominant
problems, the
-LU-decomposition works well in the
standard
-matrix setting even in the convection dominant case.
We will complement our theoretical analysis with some numerical
examples.