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Parallel black box ℋ-LU preconditioning for elliptic boundary value problems
Publikationstyp
Journal Article
Date Issued
2008-04-01
Sprache
English
Author(s)
Volume
11
Issue
4-6
Start Page
273
End Page
291
Citation
Computing and Visualization in Science 11 (4-6): 273-291 (2008-09-01)
Publisher DOI
Scopus ID
Hierarchical ( ℋ-) matrices provide a data-sparse way to approximate fully populated matrices. The two basic steps in the construction of an ℋ-matrix are (a) the hierarchical construction of a matrix block partition, and (b) the blockwise approximation of matrix data by low rank matrices. In the context of finite element discretisations of elliptic boundary value problems, ℋ-matrices can be used for the construction of preconditioners such as approximate ℋ-LU factors. In this paper, we develop a new black box approach to construct the necessary partition. This new approach is based on the matrix graph of the sparse stiffness matrix and no longer requires geometric data associated with the indices like the standard clustering algorithms. The black box clustering and a subsequent ℋ-LU factorisation have been implemented in parallel, and we provide numerical results in which the resulting black box ℋ-LU factorisation is used as a preconditioner in the iterative solution of the discrete (three-dimensional) convection-diffusion equation.
Subjects
Black box clustering
Hierarchical matrices
LU
Preconditioning
DDC Class
510: Mathematik