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Performance Comparison of Nodally Integrated Galerkin Meshfree Methods and Nodally Collocated Strong Form Meshfree Methods

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Advances in Computational Plasticity

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 46))

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.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA, 16802-1408, USA

    M. Hillman

  2. Department of Structural Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA, 92093-0085, USA

    J. S. Chen

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  1. M. Hillman
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Correspondence to J. S. Chen .

Editor information

Editors and Affiliations

  1. CIMNE, Universitat Politècnica de Catalunya, Barcelona, Spain

    Eugenio Oñate

  2. Swansea University, Swansea, United Kingdom

    Djordje Peric

  3. Swansea University, Swansea, United Kingdom

    Eduardo de Souza Neto

  4. CIMNE, Universitat Politècnica de Catalunya, Barcelona, Spain

    Michele Chiumenti

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Hillman, M., Chen, J.S. (2018). Performance Comparison of Nodally Integrated Galerkin Meshfree Methods and Nodally Collocated Strong Form Meshfree Methods. In: Oñate, E., Peric, D., de Souza Neto, E., Chiumenti, M. (eds) Advances in Computational Plasticity. Computational Methods in Applied Sciences, vol 46. Springer, Cham. https://doi.org/10.1007/978-3-319-60885-3_7

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  • DOI: https://doi.org/10.1007/978-3-319-60885-3_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60884-6

  • Online ISBN: 978-3-319-60885-3

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