Performance comparison of nodally integrated galerkin meshfree methods and nodally collocated strong form meshfree methods

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

Abstract

For a truly meshfree technique, Galerkin meshfree methods rely chiefly on nodal integration of the weak form. In the case of Strong Form Collocation meshfree methods, direct collocation at the nodes can be employed. In this paper, performance of these node-based Galerkin and collocation meshfree methods is compared in terms of accuracy, efficiency, and stability. Considering both accuracy and efficiency, the overall effectiveness in terms of CPU time versus error is also assessed. Based on the numerical experiments, nodally integrated Galerkin meshfree methods with smoothed gradients and variationally consistent integration yield the most effective solution technique, while direct collocation of the strong form at nodal locations has comparable effectiveness.

Original languageEnglish (US)
Title of host publicationComputational Methods in Applied Sciences
PublisherSpringer Netherland
Pages145-164
Number of pages20
DOIs
StatePublished - Jan 1 2018

Publication series

NameComputational Methods in Applied Sciences
Volume46
ISSN (Print)1871-3033

Fingerprint

Meshfree Method
Performance Comparison
Galerkin methods
Galerkin Method
Collocation Method
Collocation
Program processors
Nodal Integration
Meshfree
CPU Time
Vertex of a graph
Galerkin
Experiments
Numerical Experiment
Gradient
Form

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Modeling and Simulation
  • Biomedical Engineering
  • Computer Science Applications
  • Fluid Flow and Transfer Processes
  • Computational Mathematics
  • Electrical and Electronic Engineering

Cite this

Hillman, M. C., & Chen, J. S. (2018). Performance comparison of nodally integrated galerkin meshfree methods and nodally collocated strong form meshfree methods. In Computational Methods in Applied Sciences (pp. 145-164). (Computational Methods in Applied Sciences; Vol. 46). Springer Netherland. https://doi.org/10.1007/978-3-319-60885-3_7
Hillman, Michael Charles ; Chen, J. S. / Performance comparison of nodally integrated galerkin meshfree methods and nodally collocated strong form meshfree methods. Computational Methods in Applied Sciences. Springer Netherland, 2018. pp. 145-164 (Computational Methods in Applied Sciences).
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Hillman, MC & Chen, JS 2018, Performance comparison of nodally integrated galerkin meshfree methods and nodally collocated strong form meshfree methods. in Computational Methods in Applied Sciences. Computational Methods in Applied Sciences, vol. 46, Springer Netherland, pp. 145-164. https://doi.org/10.1007/978-3-319-60885-3_7

Performance comparison of nodally integrated galerkin meshfree methods and nodally collocated strong form meshfree methods. / Hillman, Michael Charles; Chen, J. S.

Computational Methods in Applied Sciences. Springer Netherland, 2018. p. 145-164 (Computational Methods in Applied Sciences; Vol. 46).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Hillman MC, Chen JS. Performance comparison of nodally integrated galerkin meshfree methods and nodally collocated strong form meshfree methods. In Computational Methods in Applied Sciences. Springer Netherland. 2018. p. 145-164. (Computational Methods in Applied Sciences). https://doi.org/10.1007/978-3-319-60885-3_7