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Aspects of the use of orthogonal basis functions in the element-free Galerkin method

Zhuang, X.; Augarde, C.E.

Authors

X. Zhuang



Abstract

The element free Galerkin (EFG) method is probably the most widely used meshless method at present. In the EFG method, shape functions are derived from a moving least squares approximation using a polynomial basis, a calculation involving the inversion of a small matrix. A new implementation of the EFG method was published soon after the original where an alternative approach using an orthogonal basis was proposed to avoid matrix inversion in the formulation of the shape functions. In this paper we revisit this topic and show that the difficulties associated with the use of a polynomial basis remain present in the orthogonal case. We also show that certain terms in the derivative expressions are omitted in the new implementation of the EFG which can lead to errors. Finally we propose a new approach which avoids inversion while maintaining accuracy

Citation

Zhuang, X., & Augarde, C. (2010). Aspects of the use of orthogonal basis functions in the element-free Galerkin method. International Journal for Numerical Methods in Engineering, 81(3), 366-380. https://doi.org/10.1002/nme.2696

Journal Article Type Article
Publication Date 2010
Journal International Journal for Numerical Methods in Engineering
Print ISSN 0029-5981
Electronic ISSN 1097-0207
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 81
Issue 3
Pages 366-380
DOI https://doi.org/10.1002/nme.2696
Keywords Meshless, Element free Galerkin