Solving Elliptical Equations in 3D by Means of an Adaptive Refinement in Generalized Finite Differences

Solving Elliptical Equations in 3D by Means of an Adaptive Refinement in Generalized Finite Differences

We apply a 3D adaptive refinement procedure using meshless generalized finite difference method for solving elliptic partial differential equations. This adaptive refinement, based on an octree structure, allows adding nodes in a regular way in order to obtain smooth transitions with different nodal...

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Main Authors: Luis Gavete, Francisco Ureña, Juan Jose Benito, Miguel Ureña, Maria Lucia Gavete
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2018/9678473
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spelling doaj-3405dc9509854e099bb343744fd1eb8b2020-11-24T22:41:47ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472018-01-01201810.1155/2018/96784739678473Solving Elliptical Equations in 3D by Means of an Adaptive Refinement in Generalized Finite DifferencesLuis Gavete0Francisco Ureña1Juan Jose Benito2Miguel Ureña3Maria Lucia Gavete4ETSIME, Universidad Politécnica Madrid (UPM), Madrid, SpainETSII, Universidad Nacional de Educación a Distancia (UNED), Madrid, SpainETSII, Universidad Nacional de Educación a Distancia (UNED), Madrid, SpainETSII, Universidad Nacional de Educación a Distancia (UNED), Madrid, SpainETSIME, Universidad Politécnica Madrid (UPM), Madrid, SpainWe apply a 3D adaptive refinement procedure using meshless generalized finite difference method for solving elliptic partial differential equations. This adaptive refinement, based on an octree structure, allows adding nodes in a regular way in order to obtain smooth transitions with different nodal densities in the model. For this purpose, we define an error indicator as stop condition of the refinement, a criterion for choosing nodes with the highest errors, and a limit for the number of nodes to be added in each adaptive stage. This kind of equations often appears in engineering problems such as simulation of heat conduction, electrical potential, seepage through porous media, or irrotational flow of fluids. The numerical results show the high accuracy obtained.http://dx.doi.org/10.1155/2018/9678473
collection DOAJ
language English
format Article
sources DOAJ
author Luis Gavete
Francisco Ureña
Juan Jose Benito
Miguel Ureña
Maria Lucia Gavete
spellingShingle Luis Gavete
Francisco Ureña
Juan Jose Benito
Miguel Ureña
Maria Lucia Gavete
Solving Elliptical Equations in 3D by Means of an Adaptive Refinement in Generalized Finite Differences
Mathematical Problems in Engineering
author_facet Luis Gavete
Francisco Ureña
Juan Jose Benito
Miguel Ureña
Maria Lucia Gavete
author_sort Luis Gavete
title Solving Elliptical Equations in 3D by Means of an Adaptive Refinement in Generalized Finite Differences
title_short Solving Elliptical Equations in 3D by Means of an Adaptive Refinement in Generalized Finite Differences
title_full Solving Elliptical Equations in 3D by Means of an Adaptive Refinement in Generalized Finite Differences
title_fullStr Solving Elliptical Equations in 3D by Means of an Adaptive Refinement in Generalized Finite Differences
title_full_unstemmed Solving Elliptical Equations in 3D by Means of an Adaptive Refinement in Generalized Finite Differences
title_sort solving elliptical equations in 3d by means of an adaptive refinement in generalized finite differences
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2018-01-01
description We apply a 3D adaptive refinement procedure using meshless generalized finite difference method for solving elliptic partial differential equations. This adaptive refinement, based on an octree structure, allows adding nodes in a regular way in order to obtain smooth transitions with different nodal densities in the model. For this purpose, we define an error indicator as stop condition of the refinement, a criterion for choosing nodes with the highest errors, and a limit for the number of nodes to be added in each adaptive stage. This kind of equations often appears in engineering problems such as simulation of heat conduction, electrical potential, seepage through porous media, or irrotational flow of fluids. The numerical results show the high accuracy obtained.
url http://dx.doi.org/10.1155/2018/9678473
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AT franciscourena solvingellipticalequationsin3dbymeansofanadaptiverefinementingeneralizedfinitedifferences
AT juanjosebenito solvingellipticalequationsin3dbymeansofanadaptiverefinementingeneralizedfinitedifferences
AT miguelurena solvingellipticalequationsin3dbymeansofanadaptiverefinementingeneralizedfinitedifferences
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