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.
Fil: Amore, Paolo. Universidad de Colima. Facultad de Ciencias; México
Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina
Fil: Boyd, John. P.. University of Michigan; Estados Unidos
Fil: Boris, Rösler. Universidad de Colima. Facultad de Ciencias; México
Materia
FINITE DIFFERENCE
HELMHOLTZ EQUATION
RICHARDSON EXTRAPOLATION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/81590
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
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, RöslerFINITE DIFFERENCEHELMHOLTZ EQUATIONRICHARDSON EXTRAPOLATIONhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We 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.Fil: Amore, Paolo. Universidad de Colima. Facultad de Ciencias; MéxicoFil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; ArgentinaFil: Boyd, John. P.. University of Michigan; Estados UnidosFil: Boris, Rösler. Universidad de Colima. Facultad de Ciencias; MéxicoAcademic Press Inc Elsevier Science2016-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/81590Amore, Paolo; Fernández, Francisco Marcelo; Boyd, John. P.; Boris, Rösler; High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences; Academic Press Inc Elsevier Science; Journal of Computational Physics; 312; 5-2016; 252-2710021-9991CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021999116000796info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1509.02795info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jcp.2015.12.059info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:23:45Zoai:ri.conicet.gov.ar:11336/81590instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:23:46.002CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
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
FINITE DIFFERENCE
HELMHOLTZ EQUATION
RICHARDSON EXTRAPOLATION
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 FINITE DIFFERENCE
HELMHOLTZ EQUATION
RICHARDSON EXTRAPOLATION
topic FINITE DIFFERENCE
HELMHOLTZ EQUATION
RICHARDSON EXTRAPOLATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
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.
Fil: Amore, Paolo. Universidad de Colima. Facultad de Ciencias; México
Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina
Fil: Boyd, John. P.. University of Michigan; Estados Unidos
Fil: Boris, Rösler. Universidad de Colima. Facultad de Ciencias; México
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
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://hdl.handle.net/11336/81590
Amore, Paolo; Fernández, Francisco Marcelo; Boyd, John. P.; Boris, Rösler; High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences; Academic Press Inc Elsevier Science; Journal of Computational Physics; 312; 5-2016; 252-271
0021-9991
CONICET Digital
CONICET
url http://hdl.handle.net/11336/81590
identifier_str_mv Amore, Paolo; Fernández, Francisco Marcelo; Boyd, John. P.; Boris, Rösler; High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences; Academic Press Inc Elsevier Science; Journal of Computational Physics; 312; 5-2016; 252-271
0021-9991
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021999116000796
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1509.02795
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jcp.2015.12.059
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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