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

Luis Gavete, María Lucía Gavete, Francisco Ureña and Juan José Benito

Mathematical Problems in Engineering, 2015, vol. 2015, 1-9

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.

Date: 2015
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/MPE/2015/283757.pdf (application/pdf)
http://downloads.hindawi.com/journals/MPE/2015/283757.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:283757

DOI: 10.1155/2015/283757

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().