Peridynamic least squares minimization

Erdogan Madenci, Mehmet Dorduncu, Xin Gu

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


This study presents the peridynamic approximation of a field variable and its temporal and spatial derivatives based on least squares minimization. Such capability permits the conversion of local form of differentiation to its nonlocal analytical integral form. It enables the analysis of discrete and scattered data for numerical differentiation and approximation of the field variable without employing any special techniques. Also, it enables the numerical solution of differential field equations with single and multiple variables in a computational domain of either uniform or nonuniform discretization. The implicit solution to the discrete form of the differential equations can be achieved by employing standard techniques for solving sparse non-symmetric systems. The accuracy of this approach is demonstrated by considering numerical differentiation of discrete data, and solving ordinary and partial differential equations with particular characteristics.

Original languageEnglish (US)
Pages (from-to)846-874
Number of pages29
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - May 1 2019


  • Derivatives
  • Integral form
  • Least squares minimization
  • Nonlocal
  • Peridynamic

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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