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H-FAINV: hierarchically factored approximate inverse preconditioners
Publikationstyp
Journal Article
Date Issued
2015-12-29
Sprache
English
Author(s)
Institut
TORE-URI
Volume
17
Issue
3
Start Page
135
End Page
150
Citation
Computing and Visualization in Science 3 (17): 135-150 (2015-06-01)
Publisher DOI
Scopus ID
Given a sparse matrix, its LU-factors, inverse and inverse factors typically suffer from substantial fill-in, leading to non-optimal complexities in their computation as well as their storage. In the past, several computationally efficient methods have been developed to compute approximations to these otherwise rather dense matrices. Many of these approaches are based on approximations through sparse matrices, leading to well-known ILU, sparse approximate inverse or factored sparse approximate inverse techniques and their variants. A different approximation approach is based on blockwise low rank approximations and is realized, for example, through hierarchical (𝓗H-) matrices. While 𝓗H-inverses and 𝓗H-LU factors have been discussed in the literature, this paper will consider the construction of an approximation of the factored inverse through 𝓗H-matrices (𝓗H-FAINV). We will describe a blockwise approach that permits to replace (exact) matrix arithmetic through approximate efficient 𝓗H-arithmetic. We conclude with numerical results in which we use approximate factored inverses as preconditioners in the iterative solution of the discretized convection–diffusion problem.
Subjects
Approximate factored inverse
Hierarchical matrices
Preconditioning
DDC Class
510: Mathematik