A block version of left-looking AINV preconditioner with one by one or two by two block pivots

Amin Rafiei, Matthias Bollhöfer and Fayssal Benkhaldoun

Applied Mathematics and Computation, 2019, vol. 350, issue C, 366-385

Abstract: In this paper, we present a block format of left-looking AINV preconditioner for a nonsymmetric matrix. This preconditioner has block 1 × 1 or 2 × 2 pivot entries. It is introduced based on a block format of Gaussian Elimination process which has been studied in [14]. We have applied the multilevel nested dissection reordering as the preprocessing and have compared this block preconditioner by the plain left-looking AINV preconditioner. If we mix the multilevel nested dissection by the maximum weighted matching process, then the numerical experiments indicate that the number of 2 × 2 pivot entries in the block preconditioner will grow up. In this case, the block preconditioner makes GMRES method convergent in a smaller number of iterations. In the numerical section, we have also compared the ILUT and block left-looking AINV preconditioners.

Keywords: Left-looking AINV; Maximum weighted matching; Multilevel nested dissection reordering; Block version of Gaussian Elimination process; ILUT preconditioner (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:350:y:2019:i:c:p:366-385

DOI: 10.1016/j.amc.2019.01.012

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