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An Approach to Refinement of Irregular Clouds of Points Using Generalized Finite Differences

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  • Luis Gavete
  • María Lucía Gavete
  • Francisco Ureña
  • Juan José Benito

Abstract

This paper describes a fully automatic adaptive refinement procedure performed in conjunction with the generalized finite difference method (GFDM) for solving a second-order partial differential equation (PDE) frequently encountered in engineering practice. A quadtree structure is used to organize the clouds of points. The adaptive procedure is based on the existing differences between the gradients of close points. The relative error between two successive adaptation processes is taken as the criterion to stop the algorithm. Using this adaptive procedure, the high gradient regions are easily detected and refined. Some benchmark examples are presented showing the accuracy of the method.

Suggested Citation

  • Luis Gavete & María Lucía Gavete & Francisco Ureña & Juan José Benito, 2015. "An Approach to Refinement of Irregular Clouds of Points Using Generalized Finite Differences," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, July.
    • Handle: RePEc:hin:jnlmpe:283757
    DOI: 10.1155/2015/283757
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