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  4. ℋ-Matrix preconditioners in convection-dominated problems
 
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ℋ-Matrix preconditioners in convection-dominated problems

Publikationstyp
Conference Paper
Date Issued
2006-07-31
Sprache
English
Author(s)
Le Borne, Sabine  orcid-logo
Grasedyck, Lars  
TORE-URI
http://hdl.handle.net/11420/10607
Journal
SIAM journal on matrix analysis and applications  
Volume
27
Issue
4
Start Page
1172
End Page
1183
Citation
SIAM Journal on Matrix Analysis and Applications 27 (4): 1172-1183 (2006-10-25)
Publisher DOI
10.1137/040615845
Scopus ID
2-s2.0-33750144295
Hierarchical matrices provide a data-sparse way to approximate fully populated matrices. In this paper we exploit ℋ-matrix techniques to approximate the LU-decompositions of stiffness matrices as they appear in (finite element or finite difference) discretizations of convectiondominated elliptic partial differential equations. These sparse ℋ-matrix approximations may then be used as preconditioners in iterative methods. Whereas the approximation of the matrix inverse by an ℋ-matrix requires some modification in the underlying index clustering when applied to convectiondominant problems, the ℋ-LU-decomposition works well in the standard ℋ-matrix setting even in the convection dominant case. We will complement our theoretical analysis with some numerical examples. © 2006 Society for Industrial and Applied Mathematics.
Subjects
Convectiondominant problems
Data-sparse approximation
Hierarchical matrices
Preconditioning
DDC Class
510: Mathematik
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