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

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 extr...

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Autores principales: Amore, Paolo, Fernández, Francisco Marcelo, Boyd, John. P., Boris, Rösler
Formato: Articulo
Lenguaje:Inglés
Publicado: 2016
Materias:
Física
Finite difference
Helmholtz equation
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/96795
https://ri.conicet.gov.ar/11336/81590
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-96795
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
Finite difference
Helmholtz equation
spellingShingle Física
Finite difference
Helmholtz equation
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
topic_facet Física
Finite difference
Helmholtz equation
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.
format Articulo
Articulo
author Amore, Paolo
Fernández, Francisco Marcelo
Boyd, John. P.
Boris, Rösler
author_facet Amore, Paolo
Fernández, Francisco Marcelo
Boyd, John. P.
Boris, Rösler
author_sort Amore, Paolo
title High order eigenvalues for the Helmholtz equation in complicated non-tensor domains through Richardson extrapolation of second order finite differences
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
publishDate 2016
url http://sedici.unlp.edu.ar/handle/10915/96795
https://ri.conicet.gov.ar/11336/81590
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AT borisrosler highordereigenvaluesforthehelmholtzequationincomplicatednontensordomainsthroughrichardsonextrapolationofsecondorderfinitedifferences
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