A piecewise polynomial harmonic nonlinear interpolatory reconstruction operator on non uniform grids—adaptation around jump discontinuities and elimination of gibbs phenomenon

In this paper, we analyze the behavior of a nonlinear reconstruction operator called PPH around discontinuities. The acronym PPH stands for Piecewise Polynomial Harmonic, since it uses piecewise polynomials defined by means of an adaption based on the use of the weighted Harmonic mean. This study is...

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Detalhes bibliográficos
Autores: Ortiz Herranz, Pedro, Trillo Moya, Juan Carlos
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Recursos:Universidad Politécnica de Cartagena(UPCT)
Repositorio:Repositorio Digital UPCT
OAI Identifier:oai:repositorio.upct.es:10317/10576
Acesso em linha:http://hdl.handle.net/10317/10576
https://www.mdpi.com/2227-7390/9/4/335
Access Level:acceso abierto
Palavra-chave:Interpolation
Reconstruction
Nonlinearity
Nonuniform
σ quasi-uniform
Adaption
Discontinuities
Gibbs effects
Matemática Aplicada
1206.07 Interpolación, Aproximación y Ajuste de Curvas
12 Matemáticas
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oai_identifier_str oai:repositorio.upct.es:10317/10576
network_acronym_str ES
network_name_str España
repository_id_str
spelling A piecewise polynomial harmonic nonlinear interpolatory reconstruction operator on non uniform grids—adaptation around jump discontinuities and elimination of gibbs phenomenonOrtiz Herranz, PedroTrillo Moya, Juan CarlosInterpolationReconstructionNonlinearityNonuniformσ quasi-uniformAdaptionDiscontinuitiesGibbs effectsMatemática Aplicada1206.07 Interpolación, Aproximación y Ajuste de Curvas12 MatemáticasIn this paper, we analyze the behavior of a nonlinear reconstruction operator called PPH around discontinuities. The acronym PPH stands for Piecewise Polynomial Harmonic, since it uses piecewise polynomials defined by means of an adaption based on the use of the weighted Harmonic mean. This study is carried out in the general case of nonuniform grids, although for some results we restrict to σ quasi-uniform grids. In particular we analyze the numerical order of approximation close to jump discontinuities and the elimination of the Gibbs effects. We show, both theoretically and with numerical examples, that the numerical order is reduced but not completely lost as it is the case in their linear counterparts. Moreover we observe that the reconstruction is free of any Gibbs effects for sufficiently small grid sizes.This research was funded by the FUNDACIÓN SÉNECA, AGENCIA DE CIENCIA Y TECNOLOGÍA DE LA REGIÓN DE MURCIA grant number 20928/PI/18, and by the Spanish national research project PID2019-108336GB-I00.MDPIFundación Séneca202220222021info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10317/10576https://www.mdpi.com/2227-7390/9/4/335reponame:Repositorio Digital UPCTinstname:Universidad Politécnica de Cartagena(UPCT)InglésInvestigación de las propiedades de un operador de reconstrucción no lineal en mallados no uniformeshttp://hdl.handle.net/10317/1050020928/PI/18PID2019-108336GB-I00Atribución-NoComercial-SinDerivadas 3.0 Españahttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:repositorio.upct.es:10317/105762026-05-15T06:39:02Z
dc.title.none.fl_str_mv A piecewise polynomial harmonic nonlinear interpolatory reconstruction operator on non uniform grids—adaptation around jump discontinuities and elimination of gibbs phenomenon
title A piecewise polynomial harmonic nonlinear interpolatory reconstruction operator on non uniform grids—adaptation around jump discontinuities and elimination of gibbs phenomenon
spellingShingle A piecewise polynomial harmonic nonlinear interpolatory reconstruction operator on non uniform grids—adaptation around jump discontinuities and elimination of gibbs phenomenon
Ortiz Herranz, Pedro
Interpolation
Reconstruction
Nonlinearity
Nonuniform
σ quasi-uniform
Adaption
Discontinuities
Gibbs effects
Matemática Aplicada
1206.07 Interpolación, Aproximación y Ajuste de Curvas
12 Matemáticas
title_short A piecewise polynomial harmonic nonlinear interpolatory reconstruction operator on non uniform grids—adaptation around jump discontinuities and elimination of gibbs phenomenon
title_full A piecewise polynomial harmonic nonlinear interpolatory reconstruction operator on non uniform grids—adaptation around jump discontinuities and elimination of gibbs phenomenon
title_fullStr A piecewise polynomial harmonic nonlinear interpolatory reconstruction operator on non uniform grids—adaptation around jump discontinuities and elimination of gibbs phenomenon
title_full_unstemmed A piecewise polynomial harmonic nonlinear interpolatory reconstruction operator on non uniform grids—adaptation around jump discontinuities and elimination of gibbs phenomenon
title_sort A piecewise polynomial harmonic nonlinear interpolatory reconstruction operator on non uniform grids—adaptation around jump discontinuities and elimination of gibbs phenomenon
dc.creator.none.fl_str_mv Ortiz Herranz, Pedro
Trillo Moya, Juan Carlos
author Ortiz Herranz, Pedro
author_facet Ortiz Herranz, Pedro
Trillo Moya, Juan Carlos
author_role author
author2 Trillo Moya, Juan Carlos
author2_role author
dc.contributor.none.fl_str_mv Fundación Séneca
dc.subject.none.fl_str_mv Interpolation
Reconstruction
Nonlinearity
Nonuniform
σ quasi-uniform
Adaption
Discontinuities
Gibbs effects
Matemática Aplicada
1206.07 Interpolación, Aproximación y Ajuste de Curvas
12 Matemáticas
topic Interpolation
Reconstruction
Nonlinearity
Nonuniform
σ quasi-uniform
Adaption
Discontinuities
Gibbs effects
Matemática Aplicada
1206.07 Interpolación, Aproximación y Ajuste de Curvas
12 Matemáticas
description In this paper, we analyze the behavior of a nonlinear reconstruction operator called PPH around discontinuities. The acronym PPH stands for Piecewise Polynomial Harmonic, since it uses piecewise polynomials defined by means of an adaption based on the use of the weighted Harmonic mean. This study is carried out in the general case of nonuniform grids, although for some results we restrict to σ quasi-uniform grids. In particular we analyze the numerical order of approximation close to jump discontinuities and the elimination of the Gibbs effects. We show, both theoretically and with numerical examples, that the numerical order is reduced but not completely lost as it is the case in their linear counterparts. Moreover we observe that the reconstruction is free of any Gibbs effects for sufficiently small grid sizes.
publishDate 2021
dc.date.none.fl_str_mv 2021
2022
2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10317/10576
https://www.mdpi.com/2227-7390/9/4/335
url http://hdl.handle.net/10317/10576
https://www.mdpi.com/2227-7390/9/4/335
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Investigación de las propiedades de un operador de reconstrucción no lineal en mallados no uniformes
http://hdl.handle.net/10317/10500
20928/PI/18
PID2019-108336GB-I00
dc.rights.none.fl_str_mv Atribución-NoComercial-SinDerivadas 3.0 España
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial-SinDerivadas 3.0 España
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:Repositorio Digital UPCT
instname:Universidad Politécnica de Cartagena(UPCT)
instname_str Universidad Politécnica de Cartagena(UPCT)
reponame_str Repositorio Digital UPCT
collection Repositorio Digital UPCT
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869415350935748608
score 15.300719

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