View in EDS PDF Full Text

Efficient ILU preconditioning and inexact-Newton-GMRES to solve the 2D steady shallow water equations.

Saved in:
Bibliographic Details
Title: Efficient ILU preconditioning and inexact-Newton-GMRES to solve the 2D steady shallow water equations.
Authors: Heniche, M.1 mourad_heniche@inrs-eau.uquebec.ca, Secretan, Y.1, Leclerc, M.1
Source: Communications in Numerical Methods in Engineering. Feb2001, Vol. 17 Issue 2, p69-75. 7p. 3 Charts, 4 Graphs.
Subjects: Factorization, Factorization of operators, Newton-Raphson method, Finite element method, Hydraulics, Fluid mechanics
Abstract: This paper presents a practical use of incomplete lower–upper factorization (ILU) preconditioning inexact-Newton-GMRES(m) for solving the steady shallow water equations. An efficient algorithm to store in a compact row format the ILU preconditioning matrix is proposed. Numerical experiments shows a linear variation of both CPU time and storage versus the matrix dimension until more than a million. Two examples are performed where the first one shows that an increment of solution norm based convergence is inaccurate. The second one reveal the importance of mesh numbering and unknowns ordering on convergence rate. An empirical criterion for choosing a good mesh numbering is also proposed. It is found that the Sloan numbering method enhances efficiency of the solver. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
Copyright of Communications in Numerical Methods in Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Links:
  – Type: pdflink
Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 13440368
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Efficient ILU preconditioning and inexact-Newton-GMRES to solve the 2D steady shallow water equations.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Heniche%2C+M%2E%22">Heniche, M.</searchLink><relatesTo>1</relatesTo><i> mourad_heniche@inrs-eau.uquebec.ca</i><br /><searchLink fieldCode="AR" term="%22Secretan%2C+Y%2E%22">Secretan, Y.</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Leclerc%2C+M%2E%22">Leclerc, M.</searchLink><relatesTo>1</relatesTo>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Communications+in+Numerical+Methods+in+Engineering%22">Communications in Numerical Methods in Engineering</searchLink>. Feb2001, Vol. 17 Issue 2, p69-75. 7p. 3 Charts, 4 Graphs.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Factorization%22">Factorization</searchLink><br /><searchLink fieldCode="DE" term="%22Factorization+of+operators%22">Factorization of operators</searchLink><br /><searchLink fieldCode="DE" term="%22Newton-Raphson+method%22">Newton-Raphson method</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Hydraulics%22">Hydraulics</searchLink><br /><searchLink fieldCode="DE" term="%22Fluid+mechanics%22">Fluid mechanics</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper presents a practical use of incomplete lower–upper factorization (ILU) preconditioning inexact-Newton-GMRES(m) for solving the steady shallow water equations. An efficient algorithm to store in a compact row format the ILU preconditioning matrix is proposed. Numerical experiments shows a linear variation of both CPU time and storage versus the matrix dimension until more than a million. Two examples are performed where the first one shows that an increment of solution norm based convergence is inaccurate. The second one reveal the importance of mesh numbering and unknowns ordering on convergence rate. An empirical criterion for choosing a good mesh numbering is also proposed. It is found that the Sloan numbering method enhances efficiency of the solver. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Communications in Numerical Methods in Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=13440368
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1002/1099-0887(200102)17:2<69::AID-CNM388>3.0.CO;2-A
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 7
        StartPage: 69
    Subjects:
      – SubjectFull: Factorization
        Type: general
      – SubjectFull: Factorization of operators
        Type: general
      – SubjectFull: Newton-Raphson method
        Type: general
      – SubjectFull: Finite element method
        Type: general
      – SubjectFull: Hydraulics
        Type: general
      – SubjectFull: Fluid mechanics
        Type: general
    Titles:
      – TitleFull: Efficient ILU preconditioning and inexact-Newton-GMRES to solve the 2D steady shallow water equations.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Heniche, M.
      – PersonEntity:
          Name:
            NameFull: Secretan, Y.
      – PersonEntity:
          Name:
            NameFull: Leclerc, M.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 02
              Text: Feb2001
              Type: published
              Y: 2001
          Identifiers:
            – Type: issn-print
              Value: 10698299
          Numbering:
            – Type: volume
              Value: 17
            – Type: issue
              Value: 2
          Titles:
            – TitleFull: Communications in Numerical Methods in Engineering
              Type: main
ResultId 1