# Combinative preconditioning based on Relaxed Nested Factorization and Tangential Filtering preconditioner

1 GRAND-LARGE - Global parallel and distributed computing
CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LIFL - Laboratoire d'Informatique Fondamentale de Lille, LRI - Laboratoire de Recherche en Informatique
Abstract : The problem of solving block tridiagonal linear systems arising from the discretization of PDE is considered. The nested factorization preconditioner introduced by [J. R. Appleyard and I. M. Cheshire, {\it Nested Factorization}, SPE 12264, presented at the Seventh SPE Symposium on Reservoir Simulation, San Francisco, 1983] is an effective preconditioner for certain class of problems and a similar method is implemented in Schlumerger's Eclipse oil reservoir simulator. In this paper, a relaxed version of Nested Factorization preconditioner is proposed as a replacement to ILU(0). Indeed, the proposed preconditioner is SPD and leads to a stable splitting if the input matrix is S.P.D.\,. For ILU(0), equivalent properties hold if the input matrix is a M-matrix. Moreover it has no storage cost. Effective multiplicative/additive preconditioning is achieved in combination with Tangential filtering preconditioner with the filter vector chosen as vector of $ones$. Numerical tests are carried out with both additive and multiplicative combinations. With this setup the new preconditioner is as robust as the combination of ILU(0) with tangential filtering preconditioner.
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Reports

https://hal.inria.fr/inria-00392881
Contributor : Pawan Kumar <>
Submitted on : Tuesday, June 9, 2009 - 11:17:49 AM
Last modification on : Thursday, July 8, 2021 - 3:46:32 AM
Long-term archiving on: : Thursday, June 10, 2010 - 10:22:15 PM

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RR-6955.pdf
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• HAL Id : inria-00392881, version 1

### Citation

Pawan Kumar, Laura Grigori, Frédéric Nataf, Qiang Niu. Combinative preconditioning based on Relaxed Nested Factorization and Tangential Filtering preconditioner. [Research Report] RR-6955, INRIA. 2009. ⟨inria-00392881⟩

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