inria-00576894, version 1

Generalized Filtering Decomposition

Laura Grigori () ¹, Frédéric Nataf () ²

N° RR-7569 (2011)

• 1:  GRAND-LARGE (INRIA Saclay - Ile de France)
• http://grand-large.lri.fr/index.php/Main_Page
  INRIA – CNRS : UMR8623 – Université Paris XI - Paris Sud PCRI - Université de Paris-Sud, Bâtiment 650, 91405 ORSAY Cedex France
• 2:  Laboratoire Jacques-Louis Lions (LJLL)
• http://www.ann.jussieu.fr
  CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI B.C. 187 75252 Paris Cedex 05 France

Bibliographic reference

• Type of document: Research reports
• Domain:

  Computer Science/Distributed, Parallel, and Cluster Computing

  Computer Science/Numerical Analysis

• Title: Generalized Filtering Decomposition
• Abstract: This paper introduces a new preconditioning technique that is suitable for matrices arising from the discretization of a system of PDEs on unstructured grids. The preconditioner satisfies a so-called filtering property, which ensures that the input matrix is identical with the preconditioner on a given filtering vector. This vector is chosen to alleviate the effect of low frequency modes on convergence and so decrease or eliminate the plateau which is often observed in the convergence of iterative methods. In particular, the paper presents a general approach that allows to ensure that the filtering condition is satisfied in a matrix decomposition. The input matrix can have an arbitrary sparse structure. Hence, it can be reordered using nested dissection, to allow a parallel computation of the preconditioner and of the iterative process.
• ACM Classification: G.: Mathematics of Computing/G.1: NUMERICAL ANALYSIS/G.1.3: Numerical Linear Algebra/G.1.3.4: Linear systems (direct and iterative methods)
• Full text language: English
• Report type: Research Report
• Page number: 8
• Publication date: 2011-03-15
• Keywords: linear solvers – Krylov subspace methods – preconditioning – filtering property – block incomplete decomposition
• Writing date: 2010-05-03
• Internal note: RR-7569
• ANR Project: 8656

Attached file list to this document: 

TEX

RR-7569.tex(28.2 KB)

paperTFFD2004.bib(20.5 KB)

Logo-INRIA-couleur.ps(35.1 KB)

RR.sty(20.7 KB)

rap-rech1.ps(19.5 KB)

logo_saclay.ps(32.3 KB)

Logo-INRIA-picto.ps(24.4 KB)

RR-7569.bbl(3.4 KB)

PDF

RR-7569.pdf(189.8 KB)

PS

RR-7569.ps(667.2 KB)

• inria-00576894, version 1
• http://hal.inria.fr/inria-00576894
• oai:hal.inria.fr:inria-00576894
• From: Laura Grigori <>
• Submitted on: Tuesday, 15 March 2011 15:45:50
• Updated on: Tuesday, 15 March 2011 21:35:20