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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/96795
Ver los metadatos del registro completo
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 |