An Approach to Refinement of Irregular Clouds of Points Using Generalized Finite Differences
Joint Authors
Gavete, Luis
Gavete, María Lucía
Ureña, Francisco
Benito, Juan José
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-07-26
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Gavete, Luis& Gavete, María Lucía& Ureña, Francisco& Benito, Juan José. 2015. An Approach to Refinement of Irregular Clouds of Points Using Generalized Finite Differences. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-9.
https://search.emarefa.net/detail/BIM-1073412
Modern Language Association (MLA)
Gavete, Luis…[et al.]. An Approach to Refinement of Irregular Clouds of Points Using Generalized Finite Differences. Mathematical Problems in Engineering No. 2015 (2015), pp.1-9.
https://search.emarefa.net/detail/BIM-1073412
American Medical Association (AMA)
Gavete, Luis& Gavete, María Lucía& Ureña, Francisco& Benito, Juan José. An Approach to Refinement of Irregular Clouds of Points Using Generalized Finite Differences. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-9.
https://search.emarefa.net/detail/BIM-1073412
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1073412