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# H-FAINV: hierarchically factored approximate inverse preconditioners

Publikationstyp

Journal Article

Publikationsdatum

2015-12-29

Sprache

English

Institut

TORE-URI

Enthalten in

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.