Zobrazit v EDS

A Localized Version of the Method of Fundamental Solutions in a Multi-level Context

Uloženo v:
Podrobná bibliografie
Název: A Localized Version of the Method of Fundamental Solutions in a Multi-level Context
Autoři: Gáspár, Csaba
Zdroj: Periodica Polytechnica Civil Engineering; Vol. 67 No. 3 (2023); 716-724 ; 1587-3773 ; 0553-6626
Informace o vydavateli: Budapest University of Technology and Economics
Rok vydání: 2023
Sbírka: Periodica Polytechnica (Budapest University of Technology and Economics)
Témata: method of fundamental solutions, local schemes, multi-level methods, quadtrees
Popis: The Method of Fundamental Solutions is applied to the Laplace equation. Instead of using the traditional approach with external source points and boundary collocation points, the original domain decomposed into a lot of smaller, overlapping subdomains, and the Method of Fundamental Solutions is used to the individual local subdomains. After eliminating the local source points, local schemes are obtained. Instead of constructing a global scheme, the local subproblems are solved sequentially, in an iterative way. This mimics a multiplicative Schwarz method with overlapping subdomains, which assures the convergence of the method. Combining the iteration with a simple Seidel-type method, the resulting iteration is used as a smoothing procedure of a multi-level method. The points belonging to the coarse and fine levels are defined by a quadtree-generated cell system controlled by the boundary of the original domain. The multi-level character of the obtained method makes it possible to reduce the necessary number of iterations, that is, the overall computational cost can be significantly reduced. Moreover, the solution of large and ill-conditioned systems is completely avoided. The method is illustrated through several numerical test examples.
Druh dokumentu: article in journal/newspaper
Popis souboru: application/pdf
Jazyk: English
Relation: https://pp.bme.hu/ci/article/view/21535/9732; https://pp.bme.hu/ci/article/view/21535
Dostupnost: https://pp.bme.hu/ci/article/view/21535
Rights: Copyright (c) 2023 Periodica Polytechnica Civil Engineering
Přístupové číslo: edsbas.180D4009
Databáze: BASE
FullText Text:
  Availability: 0
CustomLinks:
  – Url: https://pp.bme.hu/ci/article/view/21535#
    Name: EDS - BASE (s4221598)
    Category: fullText
    Text: View record from BASE
  – Url: https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=EBSCO&SrcAuth=EBSCO&DestApp=WOS&ServiceName=TransferToWoS&DestLinkType=GeneralSearchSummary&Func=Links&author=G%C3%A1sp%C3%A1r%20C
    Name: ISI
    Category: fullText
    Text: Nájsť tento článok vo Web of Science
    Icon: https://imagesrvr.epnet.com/ls/20docs.gif
    MouseOverText: Nájsť tento článok vo Web of Science
Header DbId: edsbas
DbLabel: BASE
An: edsbas.180D4009
RelevancyScore: 944
AccessLevel: 3
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 943.653564453125
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: A Localized Version of the Method of Fundamental Solutions in a Multi-level Context
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Gáspár%2C+Csaba%22">Gáspár, Csaba</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: Periodica Polytechnica Civil Engineering; Vol. 67 No. 3 (2023); 716-724 ; 1587-3773 ; 0553-6626
– Name: Publisher
  Label: Publisher Information
  Group: PubInfo
  Data: Budapest University of Technology and Economics
– Name: DatePubCY
  Label: Publication Year
  Group: Date
  Data: 2023
– Name: Subset
  Label: Collection
  Group: HoldingsInfo
  Data: Periodica Polytechnica (Budapest University of Technology and Economics)
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22method+of+fundamental+solutions%22">method of fundamental solutions</searchLink><br /><searchLink fieldCode="DE" term="%22local+schemes%22">local schemes</searchLink><br /><searchLink fieldCode="DE" term="%22multi-level+methods%22">multi-level methods</searchLink><br /><searchLink fieldCode="DE" term="%22quadtrees%22">quadtrees</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: The Method of Fundamental Solutions is applied to the Laplace equation. Instead of using the traditional approach with external source points and boundary collocation points, the original domain decomposed into a lot of smaller, overlapping subdomains, and the Method of Fundamental Solutions is used to the individual local subdomains. After eliminating the local source points, local schemes are obtained. Instead of constructing a global scheme, the local subproblems are solved sequentially, in an iterative way. This mimics a multiplicative Schwarz method with overlapping subdomains, which assures the convergence of the method. Combining the iteration with a simple Seidel-type method, the resulting iteration is used as a smoothing procedure of a multi-level method. The points belonging to the coarse and fine levels are defined by a quadtree-generated cell system controlled by the boundary of the original domain. The multi-level character of the obtained method makes it possible to reduce the necessary number of iterations, that is, the overall computational cost can be significantly reduced. Moreover, the solution of large and ill-conditioned systems is completely avoided. The method is illustrated through several numerical test examples.
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: article in journal/newspaper
– Name: Format
  Label: File Description
  Group: SrcInfo
  Data: application/pdf
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: NoteTitleSource
  Label: Relation
  Group: SrcInfo
  Data: https://pp.bme.hu/ci/article/view/21535/9732; https://pp.bme.hu/ci/article/view/21535
– Name: URL
  Label: Availability
  Group: URL
  Data: https://pp.bme.hu/ci/article/view/21535
– Name: Copyright
  Label: Rights
  Group: Cpyrght
  Data: Copyright (c) 2023 Periodica Polytechnica Civil Engineering
– Name: AN
  Label: Accession Number
  Group: ID
  Data: edsbas.180D4009
PLink https://erproxy.cvtisr.sk/sfx/access?url=https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.180D4009
RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    Subjects:
      – SubjectFull: method of fundamental solutions
        Type: general
      – SubjectFull: local schemes
        Type: general
      – SubjectFull: multi-level methods
        Type: general
      – SubjectFull: quadtrees
        Type: general
    Titles:
      – TitleFull: A Localized Version of the Method of Fundamental Solutions in a Multi-level Context
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Gáspár, Csaba
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2023
          Identifiers:
            – Type: issn-locals
              Value: edsbas
            – Type: issn-locals
              Value: edsbas.oa
          Titles:
            – TitleFull: Periodica Polytechnica Civil Engineering; Vol. 67 No. 3 (2023); 716-724
              Type: main
ResultId 1