POINT INTERPOLATION METHODS BASED ON WEAKENED-WEAK FORMULATIONS

Authors

  • Naísses Z. Lima
  • Renato C. Mesquita

DOI:

https://doi.org/10.1590/S2179-10742013000200020

Keywords:

Meshless methods, point interpolation method, smoothed gradient, weakened-weak form

Abstract

This paper presents a study of meshless Point Interpolation Methods based on weakened-weak forms. The mathematical formulations of the methods are presented as well as the procedures for the support nodes selection called T-schemes. The numerical results are shown for four different types of electromagnetic static problems in order to ponctuate the characteristics of the approximation generated by these new methods.

References

[1] G. R. Liu, Mesh Free Methods: Moving Beyond the Finite Element Method, 2nd ed. CRC Press, 2009.
[2] T. Belytschko, Y. Y. Lu, and L. Gu, “Element-free Galerkin methods,” International Journal for Numerical Methods in
Engineering, vol. 37, no. 2, pp. 229 – 256, 1994.
[3] S. N. Atluri and S. Shen, “The meshless local Petrov-Galerkin (MLPG) method - A simple and less-costly alternative to
the finite element and boundary element methods,” CMES - Computer Modeling in Engineering and Sciences, vol. 3,
no. 1, pp. 11–51, 2002.
[4] N. Z. Lima, R. C. Mesquita, W. G. Facco, A. S. Moura, and E. J. Silva, “The nonconforming point interpolation method
applied to electromagnetic problems,” IEEE Transactions on Magnetics, vol. 48, pp. 619–622, 2012.
[5] G. Liu, “A g space theory and a weakened weak (w2) form for a unified formulation of compatible and incompatible
methods: Part i theory and part ii applications to solid mechanics problems,” International Journal for Numerical
Methods in Engineering, vol. 81, pp. 1093–1126, 2010.
[6] T. J. R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Dover Publications,
2000.
[7] J. G. Wang and G. R. Liu, “A point interpolation meshless method based on radial basis functions,” International
Journal for Numerical Methods in Engineering, vol. 54, pp. 1623–1648, 2002.
[8] S. Wu, G. Liu, H. Zhang, and G. Zhang, “A node-based smoothed point interpolation method (ns-pim) for thermoelastic
problems with solution bounds,” International Journal of Heat and Mass Transfer, vol. 52, pp. 1464–1471, 2009.
[9] S. Wu, G. Liu, X. Cui, T. Nguyen, and G. Zhang, “An edge-based smoothed point interpolation method (es-pim) for
heat transfer analysis of rapid manufacturing system,” International Journal of Heat and Mass Transfer, vol. 53, pp.
1938–1950, 2010.
[10] G. Zhang and G.-R. Liu, “A meshfree cell-based smoothed point interpolation method for solid mechanics problems,”
AIP Conference Proceedings, vol. 1233, no. 1, pp. 887–892, 2010.
[11] D. Meeker, “Force of an eight pole radial magnetic bearing,” http://www.femm.info/wiki/RadialMagneticBearing.

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Published

2013-08-01

How to Cite

Naísses Z. Lima, & Renato C. Mesquita. (2013). POINT INTERPOLATION METHODS BASED ON WEAKENED-WEAK FORMULATIONS. Journal of Microwaves, Optoelectronics and Electromagnetic Applications (JMOe), 12(2), 506-523. https://doi.org/10.1590/S2179-10742013000200020

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Section

Regular Papers

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