Solving numerical difficulties for element-free Galerkin analyses

Shen-Haw Ju, H. H. Hsu

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This study solves the numerical problems associated with the element-free Galerkin method (EFGM) to perform analyses efficiently in shared-memory computers. The truncation error is generally large for the moving least-squares approximation, and this can be overcome by using orthogonal basis functions, 16-byte floats, or the local origin. Then, the analysis accuracy is similar to that obtained with the reproducing kernel particle approximation. Determining the index array of the global stiffness matrix requires a large amount of computer memory. We thus propose a scheme to overcome this problem using slightly more computer time but much less computer memory. A binary search is also proposed to find the support domain nodes for Gaussian points, and this method is much more efficient than the linear search one. A Fortran module is developed to establish parallel solutions in the EFGM, and the programmer does not need to handle the global stiffness directly.

Original languageEnglish
Pages (from-to)273-281
Number of pages9
JournalComputational Mechanics
Volume53
Issue number2
DOIs
Publication statusPublished - 2014 Jan 1

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Element-free Galerkin
Element-free Galerkin Method
Galerkin methods
Data storage equipment
Linear search
Least squares approximations
Moving Least-squares Approximation
Binary search
Orthogonal Functions
Orthogonal Basis
Reproducing Kernel
Truncation Error
Stiffness matrix
Stiffness Matrix
Shared Memory
Basis Functions
Stiffness
Module
Approximation
Vertex of a graph

All Science Journal Classification (ASJC) codes

  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Solving numerical difficulties for element-free Galerkin analyses. / Ju, Shen-Haw; Hsu, H. H.

In: Computational Mechanics, Vol. 53, No. 2, 01.01.2014, p. 273-281.

Research output: Contribution to journalArticle

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