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

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

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 t...

Full description

Bibliographic Details
Main Authors: Luis Gavete, María Lucía Gavete, Francisco Ureña, Juan José Benito
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2015/283757
id doaj-8f7c90bffd1048e781532046b11cd6f2
record_format Article
spelling doaj-8f7c90bffd1048e781532046b11cd6f22020-11-24T23:47:57ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472015-01-01201510.1155/2015/283757283757An Approach to Refinement of Irregular Clouds of Points Using Generalized Finite DifferencesLuis Gavete0María Lucía Gavete1Francisco Ureña2Juan José Benito3UPM, ETSIME, Alenza 4, 28003 Madrid, SpainUPM, ETSIME, Alenza 4, 28003 Madrid, SpainUCLM, IMACI, Avenida Camilo José Cela, s/n, 13071 Ciudad Real, SpainUNED, ETSII, Apdo 60149, 28080 Madrid, SpainThis 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.http://dx.doi.org/10.1155/2015/283757
collection DOAJ
language English
format Article
sources DOAJ
author Luis Gavete
María Lucía Gavete
Francisco Ureña
Juan José Benito
spellingShingle Luis Gavete
María Lucía Gavete
Francisco Ureña
Juan José Benito
An Approach to Refinement of Irregular Clouds of Points Using Generalized Finite Differences
Mathematical Problems in Engineering
author_facet Luis Gavete
María Lucía Gavete
Francisco Ureña
Juan José Benito
author_sort Luis Gavete
title An Approach to Refinement of Irregular Clouds of Points Using Generalized Finite Differences
title_short An Approach to Refinement of Irregular Clouds of Points Using Generalized Finite Differences
title_full An Approach to Refinement of Irregular Clouds of Points Using Generalized Finite Differences
title_fullStr An Approach to Refinement of Irregular Clouds of Points Using Generalized Finite Differences
title_full_unstemmed An Approach to Refinement of Irregular Clouds of Points Using Generalized Finite Differences
title_sort approach to refinement of irregular clouds of points using generalized finite differences
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2015-01-01
description 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.
url http://dx.doi.org/10.1155/2015/283757
work_keys_str_mv AT luisgavete anapproachtorefinementofirregularcloudsofpointsusinggeneralizedfinitedifferences
AT marialuciagavete anapproachtorefinementofirregularcloudsofpointsusinggeneralizedfinitedifferences
AT franciscourena anapproachtorefinementofirregularcloudsofpointsusinggeneralizedfinitedifferences
AT juanjosebenito anapproachtorefinementofirregularcloudsofpointsusinggeneralizedfinitedifferences
AT luisgavete approachtorefinementofirregularcloudsofpointsusinggeneralizedfinitedifferences
AT marialuciagavete approachtorefinementofirregularcloudsofpointsusinggeneralizedfinitedifferences
AT franciscourena approachtorefinementofirregularcloudsofpointsusinggeneralizedfinitedifferences
AT juanjosebenito approachtorefinementofirregularcloudsofpointsusinggeneralizedfinitedifferences
_version_ 1725487997429743616

Similar Items