### 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 language | English |
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Pages (from-to) | 273-281 |

Number of pages | 9 |

Journal | Computational Mechanics |

Volume | 53 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Computational Mechanics*,

*53*(2), 273-281. https://doi.org/10.1007/s00466-013-0906-z

}

*Computational Mechanics*, vol. 53, no. 2, pp. 273-281. https://doi.org/10.1007/s00466-013-0906-z

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Solving numerical difficulties for element-free Galerkin analyses

AU - Ju, Shen-Haw

AU - Hsu, H. H.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84893928405&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893928405&partnerID=8YFLogxK

U2 - 10.1007/s00466-013-0906-z

DO - 10.1007/s00466-013-0906-z

M3 - Article

VL - 53

SP - 273

EP - 281

JO - Computational Mechanics

JF - Computational Mechanics

SN - 0178-7675

IS - 2

ER -