Numerical Treatment of Interfaces for Second-Order Wave Equations
- Autores
- Parisi, Maria Florencia; Iriondo, Mirta Susana; Cécere, Mariana Andrea; Reula, Oscar Alejandro
- Año de publicación
- 2014
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving the second-order wave equation. We show that it is possible to implement an interface scheme of “penalty” type for the second-order wave equation, similar to the ones used for first-order hyperbolic and parabolic equations, and the second-order scheme used by Mattsson et al. 2008. These schemes, known as SAT schemes for finite difference approximations and penalties for spectral ones, and ours share similar properties but in our case one needs to pass at the interface a smaller amount of data than previously known schemes. This is important for multi-block parallelizations in several dimensions, for it implies that one obtains the same solution quality while sharing among different computational grids only a fraction of the data one would need for a comparable (in accuracy) SAT or Mattsson et al.’s scheme. The semi-discrete approximation used here preserves the norm and uses standard finite-difference operators satisfying summation by parts. For the time integrator we use a semi-implicit IMEX Runge–Kutta method. This is crucial, since the explicit Runge–Kutta method would be impractical given the severe restrictions that arise from the stiff parts of the equations.
Fil: Parisi, Maria Florencia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Iriondo, Mirta Susana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomia Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomia Teórica y Experimental; Argentina
Fil: Cécere, Mariana Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Reula, Oscar Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina - Materia
-
Finite-Difference Methods
Partial Differential Equations
Ordinary And Partial Differential Equations
Boundary Value Problems - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/31793
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Numerical Treatment of Interfaces for Second-Order Wave EquationsParisi, Maria FlorenciaIriondo, Mirta SusanaCécere, Mariana AndreaReula, Oscar AlejandroFinite-Difference MethodsPartial Differential EquationsOrdinary And Partial Differential EquationsBoundary Value Problemshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving the second-order wave equation. We show that it is possible to implement an interface scheme of “penalty” type for the second-order wave equation, similar to the ones used for first-order hyperbolic and parabolic equations, and the second-order scheme used by Mattsson et al. 2008. These schemes, known as SAT schemes for finite difference approximations and penalties for spectral ones, and ours share similar properties but in our case one needs to pass at the interface a smaller amount of data than previously known schemes. This is important for multi-block parallelizations in several dimensions, for it implies that one obtains the same solution quality while sharing among different computational grids only a fraction of the data one would need for a comparable (in accuracy) SAT or Mattsson et al.’s scheme. The semi-discrete approximation used here preserves the norm and uses standard finite-difference operators satisfying summation by parts. For the time integrator we use a semi-implicit IMEX Runge–Kutta method. This is crucial, since the explicit Runge–Kutta method would be impractical given the severe restrictions that arise from the stiff parts of the equations.Fil: Parisi, Maria Florencia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Iriondo, Mirta Susana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomia Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomia Teórica y Experimental; ArgentinaFil: Cécere, Mariana Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Reula, Oscar Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaSpringer/plenum Publishers2014-06info: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/11336/31793Reula, Oscar Alejandro; Cécere, Mariana Andrea; Iriondo, Mirta Susana; Parisi, Maria Florencia; Numerical Treatment of Interfaces for Second-Order Wave Equations; Springer/plenum Publishers; Journal Of Scientific Computing; 60; 3; 6-2014; 875-8970885-7474CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/ 10.1007/s10915-014-9880-7info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10915-014-9880-7info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:09:48Zoai:ri.conicet.gov.ar:11336/31793instacron: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:34982025-09-03 10:09:48.524CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Numerical Treatment of Interfaces for Second-Order Wave Equations |
title |
Numerical Treatment of Interfaces for Second-Order Wave Equations |
spellingShingle |
Numerical Treatment of Interfaces for Second-Order Wave Equations Parisi, Maria Florencia Finite-Difference Methods Partial Differential Equations Ordinary And Partial Differential Equations Boundary Value Problems |
title_short |
Numerical Treatment of Interfaces for Second-Order Wave Equations |
title_full |
Numerical Treatment of Interfaces for Second-Order Wave Equations |
title_fullStr |
Numerical Treatment of Interfaces for Second-Order Wave Equations |
title_full_unstemmed |
Numerical Treatment of Interfaces for Second-Order Wave Equations |
title_sort |
Numerical Treatment of Interfaces for Second-Order Wave Equations |
dc.creator.none.fl_str_mv |
Parisi, Maria Florencia Iriondo, Mirta Susana Cécere, Mariana Andrea Reula, Oscar Alejandro |
author |
Parisi, Maria Florencia |
author_facet |
Parisi, Maria Florencia Iriondo, Mirta Susana Cécere, Mariana Andrea Reula, Oscar Alejandro |
author_role |
author |
author2 |
Iriondo, Mirta Susana Cécere, Mariana Andrea Reula, Oscar Alejandro |
author2_role |
author author author |
dc.subject.none.fl_str_mv |
Finite-Difference Methods Partial Differential Equations Ordinary And Partial Differential Equations Boundary Value Problems |
topic |
Finite-Difference Methods Partial Differential Equations Ordinary And Partial Differential Equations Boundary Value Problems |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving the second-order wave equation. We show that it is possible to implement an interface scheme of “penalty” type for the second-order wave equation, similar to the ones used for first-order hyperbolic and parabolic equations, and the second-order scheme used by Mattsson et al. 2008. These schemes, known as SAT schemes for finite difference approximations and penalties for spectral ones, and ours share similar properties but in our case one needs to pass at the interface a smaller amount of data than previously known schemes. This is important for multi-block parallelizations in several dimensions, for it implies that one obtains the same solution quality while sharing among different computational grids only a fraction of the data one would need for a comparable (in accuracy) SAT or Mattsson et al.’s scheme. The semi-discrete approximation used here preserves the norm and uses standard finite-difference operators satisfying summation by parts. For the time integrator we use a semi-implicit IMEX Runge–Kutta method. This is crucial, since the explicit Runge–Kutta method would be impractical given the severe restrictions that arise from the stiff parts of the equations. Fil: Parisi, Maria Florencia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina Fil: Iriondo, Mirta Susana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomia Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomia Teórica y Experimental; Argentina Fil: Cécere, Mariana Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina Fil: Reula, Oscar Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina |
description |
In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving the second-order wave equation. We show that it is possible to implement an interface scheme of “penalty” type for the second-order wave equation, similar to the ones used for first-order hyperbolic and parabolic equations, and the second-order scheme used by Mattsson et al. 2008. These schemes, known as SAT schemes for finite difference approximations and penalties for spectral ones, and ours share similar properties but in our case one needs to pass at the interface a smaller amount of data than previously known schemes. This is important for multi-block parallelizations in several dimensions, for it implies that one obtains the same solution quality while sharing among different computational grids only a fraction of the data one would need for a comparable (in accuracy) SAT or Mattsson et al.’s scheme. The semi-discrete approximation used here preserves the norm and uses standard finite-difference operators satisfying summation by parts. For the time integrator we use a semi-implicit IMEX Runge–Kutta method. This is crucial, since the explicit Runge–Kutta method would be impractical given the severe restrictions that arise from the stiff parts of the equations. |
publishDate |
2014 |
dc.date.none.fl_str_mv |
2014-06 |
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/11336/31793 Reula, Oscar Alejandro; Cécere, Mariana Andrea; Iriondo, Mirta Susana; Parisi, Maria Florencia; Numerical Treatment of Interfaces for Second-Order Wave Equations; Springer/plenum Publishers; Journal Of Scientific Computing; 60; 3; 6-2014; 875-897 0885-7474 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/31793 |
identifier_str_mv |
Reula, Oscar Alejandro; Cécere, Mariana Andrea; Iriondo, Mirta Susana; Parisi, Maria Florencia; Numerical Treatment of Interfaces for Second-Order Wave Equations; Springer/plenum Publishers; Journal Of Scientific Computing; 60; 3; 6-2014; 875-897 0885-7474 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/doi/ 10.1007/s10915-014-9880-7 info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs10915-014-9880-7 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Springer/plenum Publishers |
publisher.none.fl_str_mv |
Springer/plenum Publishers |
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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13.13397 |