View in EDS

Least square finite volume particle method for solving PDEs.

Saved in:
Bibliographic Details
Title: Least square finite volume particle method for solving PDEs.
Authors: Zhang, Zhen1 (AUTHOR), Liu, Xiaoxing1 (AUTHOR) liuxx85@mail.sysu.edu.cn
Source: Computers & Mathematics with Applications. May2026, Vol. 210, p137-152. 16p.
Subjects: Finite volume method, Particle methods (Numerical analysis), Numerical analysis, Taylor's series, Partial differential equations, Meshfree methods, Least squares, Gaussian quadrature formulas
Abstract: Although arbitrary-order accuracy can be achieved in meshless particle methods by combining Taylor-series expansion with least-squares techniques, this approach incurs high computational costs due to the inversion of high-order matrices. In this study, we develop a novel meshless method called least-square finite volume particle (LSFVP) method for solving PDEs efficiently. The particles are modeled as squares in two-dimensional space. The integral form of the PDEs is discretized for each finite volume particle using the LSFVP framework. The original second-order derivative is conceptually transformed into a first-order derivative. The least square method is employed to estimate the flux across particle surfaces, while Gauss integration ensures the overall second-order accuracy in evaluating surface flux integrals. Several numerical examples are presented to validate the proposed LSFVP method. [ABSTRACT FROM AUTHOR]
Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science 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 Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 192989075
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Least square finite volume particle method for solving PDEs.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Zhen%22">Zhang, Zhen</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Xiaoxing%22">Liu, Xiaoxing</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> liuxx85@mail.sysu.edu.cn</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Computers+%26+Mathematics+with+Applications%22">Computers & Mathematics with Applications</searchLink>. May2026, Vol. 210, p137-152. 16p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Finite+volume+method%22">Finite volume method</searchLink><br /><searchLink fieldCode="DE" term="%22Particle+methods+%28Numerical+analysis%29%22">Particle methods (Numerical analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Taylor's+series%22">Taylor's series</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Meshfree+methods%22">Meshfree methods</searchLink><br /><searchLink fieldCode="DE" term="%22Least+squares%22">Least squares</searchLink><br /><searchLink fieldCode="DE" term="%22Gaussian+quadrature+formulas%22">Gaussian quadrature formulas</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Although arbitrary-order accuracy can be achieved in meshless particle methods by combining Taylor-series expansion with least-squares techniques, this approach incurs high computational costs due to the inversion of high-order matrices. In this study, we develop a novel meshless method called least-square finite volume particle (LSFVP) method for solving PDEs efficiently. The particles are modeled as squares in two-dimensional space. The integral form of the PDEs is discretized for each finite volume particle using the LSFVP framework. The original second-order derivative is conceptually transformed into a first-order derivative. The least square method is employed to estimate the flux across particle surfaces, while Gauss integration ensures the overall second-order accuracy in evaluating surface flux integrals. Several numerical examples are presented to validate the proposed LSFVP method. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Computers & Mathematics with Applications is the property of Pergamon Press - An Imprint of Elsevier Science 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=192989075
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.camwa.2026.02.020
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 16
        StartPage: 137
    Subjects:
      – SubjectFull: Finite volume method
        Type: general
      – SubjectFull: Particle methods (Numerical analysis)
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Taylor's series
        Type: general
      – SubjectFull: Partial differential equations
        Type: general
      – SubjectFull: Meshfree methods
        Type: general
      – SubjectFull: Least squares
        Type: general
      – SubjectFull: Gaussian quadrature formulas
        Type: general
    Titles:
      – TitleFull: Least square finite volume particle method for solving PDEs.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Zhang, Zhen
      – PersonEntity:
          Name:
            NameFull: Liu, Xiaoxing
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 15
              M: 05
              Text: May2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 08981221
          Numbering:
            – Type: volume
              Value: 210
          Titles:
            – TitleFull: Computers & Mathematics with Applications
              Type: main
ResultId 1