Peridynamic least squares minimization

Madenci E., Dorduncu M., Gu X.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, vol.348, pp.846-874, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 348
  • Publication Date: 2019
  • Doi Number: 10.1016/j.cma.2019.01.032
  • Journal Name: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.846-874
  • Keywords: Peridynamic, Least squares minimization, Nonlocal, Derivatives, Integral form, CONVERGENCE, SCHEME
  • Erciyes University Affiliated: Yes

Abstract

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. (C) 2018 Elsevier B.V. All rights reserved.