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Computational Mechanics

, Volume 40, Issue 6, pp 949–963 | Cite as

An improved finite point method for tridimensional potential flows

  • Enrique Ortega
  • Eugenio OñateEmail author
  • Sergio Idelsohn
Original Paper

Abstract

At the local level, successful meshless techniques such as the Finite Point Method must have two main characteristics: a suitable geometrical support and a robust numerical approximation built on the former. In this article we develop the second condition and present an alternative procedure to obtain shape functions and their derivatives from a given cloud of points regardless of its geometrical features. This procedure, based on a QR factorization and an iterative adjust of local approximation parameters, allows obtaining a satisfactory minimization problem solution, even in the most difficult cases where usual approaches fail. It is known that high-order meshless constructions need to include a large number of points in the local support zone and this fact turns the approximation more dependent on the size, shape and spatial distribution of the local cloud of points. The proposed procedure also facilitates the construction of high-order approximations on generic geometries reducing their dependence on the geometrical support where they are based. Apart from the alternative solution to the minimization problem, the behaviour of high-order Finite Point approximations and the overall performance of the proposed methodology are shown by means of several numerical tests.

Keywords

Weighting Function Shape Function Local Approximation Move Little Square Star Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Verlag 2007

Authors and Affiliations

  • Enrique Ortega
    • 1
  • Eugenio Oñate
    • 1
    Email author
  • Sergio Idelsohn
    • 1
  1. 1.International Center for Numerical Methods in Engineering (CIMNE)Universidad Politécnica de CataluñaBarcelonaEspaña

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