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Domain decomposition based H-LU preconditioning
Publikationstyp
Journal Article
Date Issued
2009-03-03
Sprache
English
Author(s)
Journal
Volume
112
Issue
4
Start Page
565
End Page
600
Citation
Numerische Mathematik 112 (4): 565-600 (2009-06-01)
Publisher DOI
Scopus ID
Hierarchical 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 this paper, we develop a new approach to construct the necessary partition based on domain decomposition. Compared to standard geometric bisection based H-matrices, this new approach yields H-LU factorizations of finite element stiffness matrices with significantly improved storage and computational complexity requirements. These rigorously proven and numerically verified improvements result from an H-matrix block structure which is naturally suited for parallelization and in which large subblocks of the stiffness matrix remain zero in an LU factorization. We provide numerical results in which a domain decomposition based H-LU factorization is used as a preconditioner in the iterative solution of the discrete (three-dimensional) convection-diffusion equation. © 2009 Springer-Verlag.
DDC Class
510: Mathematik