A unified stability analysis of meshless particle methods

Ted Belytschko*, Yong Guo, Wing K Liu, Shao Ping Xiao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

288 Scopus citations

Abstract

A unified stability analysis of meshless methods with Eulerian and Lagrangian kernels is presented. Three types of instabilities were identified in one dimension: an instability due to rank deficiency, a tensile instability and a material instability which is also found in continua. The stability of particle methods with Eulerian and Lagrangian kernels is markedly different: Lagrangian kernels do not exhibit the tensile instability. In both kernels, the instability due to rank deficiency can be suppressed by stress points. In two dimensions the stabilizing effect of stress points is dependent on their locations. It was found that the best approach to stable particle discretizations is to use Lagrangian kernels with stress points. The stability of the least-squares stabilization was also studied.

Original languageEnglish (US)
Pages (from-to)1359-1400
Number of pages42
JournalInternational Journal for Numerical Methods in Engineering
Volume48
Issue number9
DOIs
StatePublished - Jan 1 2000

Keywords

  • Kernel
  • Particle methods
  • Stability

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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