High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences

Autores
Amore, Paolo; Fernández, Francisco Marcelo; Boyd, John. P.; Boris, Rösler
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We apply second order finite differences to calculate the lowest eigenvalues of the Helmholtz equation, for complicated non-tensor domains in the plane, using different grids which sample exactly the border of the domain. We show that the results obtained applying Richardson and Padé-Richardson extrapolations to a set of finite difference eigenvalues corresponding to different grids allow us to obtain extremely precise values. When possible we have assessed the precision of our extrapolations comparing them with the highly precise results obtained using the method of particular solutions. Our empirical findings suggest an asymptotic nature of the FD series. In all the cases studied, we are able to report numerical results which are more precise than those available in the literature.
Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas
Materia
Física
Finite difference
Helmholtz equation
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/96795
Acceder
id SEDICI_588d0456223890887ba99b7e739295e6
oai_identifier_str oai:sedici.unlp.edu.ar:10915/96795
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differencesAmore, PaoloFernández, Francisco MarceloBoyd, John. P.Boris, RöslerFísicaFinite differenceHelmholtz equationWe apply second order finite differences to calculate the lowest eigenvalues of the Helmholtz equation, for complicated non-tensor domains in the plane, using different grids which sample exactly the border of the domain. We show that the results obtained applying Richardson and Padé-Richardson extrapolations to a set of finite difference eigenvalues corresponding to different grids allow us to obtain extremely precise values. When possible we have assessed the precision of our extrapolations comparing them with the highly precise results obtained using the method of particular solutions. Our empirical findings suggest an asymptotic nature of the FD series. In all the cases studied, we are able to report numerical results which are more precise than those available in the literature.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas2016-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf252-271http://sedici.unlp.edu.ar/handle/10915/96795enginfo:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/81590info:eu-repo/semantics/altIdentifier/issn/0021-9991info:eu-repo/semantics/altIdentifier/arxiv/1509.02795info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jcp.2015.12.059info:eu-repo/semantics/altIdentifier/hdl/11336/81590info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-15T11:12:20Zoai:sedici.unlp.edu.ar:10915/96795Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-15 11:12:20.282SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences
title High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences
spellingShingle High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences
Amore, Paolo
Física
Finite difference
Helmholtz equation
title_short High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences
title_full High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences
title_fullStr High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences
title_full_unstemmed High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences
title_sort High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences
dc.creator.none.fl_str_mv Amore, Paolo
Fernández, Francisco Marcelo
Boyd, John. P.
Boris, Rösler
author Amore, Paolo
author_facet Amore, Paolo
Fernández, Francisco Marcelo
Boyd, John. P.
Boris, Rösler
author_role author
author2 Fernández, Francisco Marcelo
Boyd, John. P.
Boris, Rösler
author2_role author
author
author
dc.subject.none.fl_str_mv Física
Finite difference
Helmholtz equation
topic Física
Finite difference
Helmholtz equation
dc.description.none.fl_txt_mv We apply second order finite differences to calculate the lowest eigenvalues of the Helmholtz equation, for complicated non-tensor domains in the plane, using different grids which sample exactly the border of the domain. We show that the results obtained applying Richardson and Padé-Richardson extrapolations to a set of finite difference eigenvalues corresponding to different grids allow us to obtain extremely precise values. When possible we have assessed the precision of our extrapolations comparing them with the highly precise results obtained using the method of particular solutions. Our empirical findings suggest an asymptotic nature of the FD series. In all the cases studied, we are able to report numerical results which are more precise than those available in the literature.
Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas
description We apply second order finite differences to calculate the lowest eigenvalues of the Helmholtz equation, for complicated non-tensor domains in the plane, using different grids which sample exactly the border of the domain. We show that the results obtained applying Richardson and Padé-Richardson extrapolations to a set of finite difference eigenvalues corresponding to different grids allow us to obtain extremely precise values. When possible we have assessed the precision of our extrapolations comparing them with the highly precise results obtained using the method of particular solutions. Our empirical findings suggest an asymptotic nature of the FD series. In all the cases studied, we are able to report numerical results which are more precise than those available in the literature.
publishDate 2016
dc.date.none.fl_str_mv 2016-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/96795
url http://sedici.unlp.edu.ar/handle/10915/96795
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/81590
info:eu-repo/semantics/altIdentifier/issn/0021-9991
info:eu-repo/semantics/altIdentifier/arxiv/1509.02795
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jcp.2015.12.059
info:eu-repo/semantics/altIdentifier/hdl/11336/81590
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
252-271
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
_version_ 1846064181204221952
score 13.22299

Publicaciones similares