An energy-stable convex splitting for the phase-field crystal equation

Autores
Vignal, P.; Dalcin, Lisandro Daniel; Brown, D.L.; Collier, N.; Calo, V.M.
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Abstract The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. Nonetheless, solving this equation is not a trivial task, as energy dissipation and mass conservation need to be verified for the numerical solution to be valid. This work addresses these issues, and proposes a novel algorithm that guarantees mass conservation, unconditional energy stability and second-order accuracy in time. Numerical results validating our proofs are presented, and two and three dimensional simulations involving crystal growth are shown, highlighting the robustness of the method.
Fil: Vignal, P.. King Abdullah University Of Science And Technology; Argelia
Fil: Dalcin, Lisandro Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina
Fil: Brown, D.L.. King Abdullah University Of Science And Technology; Arabia Saudita
Fil: Collier, N.. Oak Ridge National Laboratory; Estados Unidos
Fil: Calo, V.M.. King Abdullah University Of Science And Technology; Arabia Saudita
Materia
B-Spline Basis Functions
Isogeometric Analysis
Mixed Formulation
Petiga
Phase-Field Crystal
Provably-Stable Time Integration
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/78613
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/78613
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling An energy-stable convex splitting for the phase-field crystal equationVignal, P.Dalcin, Lisandro DanielBrown, D.L.Collier, N.Calo, V.M.B-Spline Basis FunctionsIsogeometric AnalysisMixed FormulationPetigaPhase-Field CrystalProvably-Stable Time Integrationhttps://purl.org/becyt/ford/2.5https://purl.org/becyt/ford/2Abstract The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. Nonetheless, solving this equation is not a trivial task, as energy dissipation and mass conservation need to be verified for the numerical solution to be valid. This work addresses these issues, and proposes a novel algorithm that guarantees mass conservation, unconditional energy stability and second-order accuracy in time. Numerical results validating our proofs are presented, and two and three dimensional simulations involving crystal growth are shown, highlighting the robustness of the method.Fil: Vignal, P.. King Abdullah University Of Science And Technology; ArgeliaFil: Dalcin, Lisandro Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; ArgentinaFil: Brown, D.L.. King Abdullah University Of Science And Technology; Arabia SauditaFil: Collier, N.. Oak Ridge National Laboratory; Estados UnidosFil: Calo, V.M.. King Abdullah University Of Science And Technology; Arabia SauditaPergamon-Elsevier Science Ltd2015-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/78613Vignal, P.; Dalcin, Lisandro Daniel; Brown, D.L.; Collier, N.; Calo, V.M.; An energy-stable convex splitting for the phase-field crystal equation; Pergamon-Elsevier Science Ltd; Computers & Structures; 158; 7-2015; 355-3680045-7949CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.compstruc.2015.05.029info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:04:13Zoai:ri.conicet.gov.ar:11336/78613instacron: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:34982025-10-22 12:04:13.711CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv An energy-stable convex splitting for the phase-field crystal equation
title An energy-stable convex splitting for the phase-field crystal equation
spellingShingle An energy-stable convex splitting for the phase-field crystal equation
Vignal, P.
B-Spline Basis Functions
Isogeometric Analysis
Mixed Formulation
Petiga
Phase-Field Crystal
Provably-Stable Time Integration
title_short An energy-stable convex splitting for the phase-field crystal equation
title_full An energy-stable convex splitting for the phase-field crystal equation
title_fullStr An energy-stable convex splitting for the phase-field crystal equation
title_full_unstemmed An energy-stable convex splitting for the phase-field crystal equation
title_sort An energy-stable convex splitting for the phase-field crystal equation
dc.creator.none.fl_str_mv Vignal, P.
Dalcin, Lisandro Daniel
Brown, D.L.
Collier, N.
Calo, V.M.
author Vignal, P.
author_facet Vignal, P.
Dalcin, Lisandro Daniel
Brown, D.L.
Collier, N.
Calo, V.M.
author_role author
author2 Dalcin, Lisandro Daniel
Brown, D.L.
Collier, N.
Calo, V.M.
author2_role author
author
author
author
dc.subject.none.fl_str_mv B-Spline Basis Functions
Isogeometric Analysis
Mixed Formulation
Petiga
Phase-Field Crystal
Provably-Stable Time Integration
topic B-Spline Basis Functions
Isogeometric Analysis
Mixed Formulation
Petiga
Phase-Field Crystal
Provably-Stable Time Integration
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.5
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv Abstract The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. Nonetheless, solving this equation is not a trivial task, as energy dissipation and mass conservation need to be verified for the numerical solution to be valid. This work addresses these issues, and proposes a novel algorithm that guarantees mass conservation, unconditional energy stability and second-order accuracy in time. Numerical results validating our proofs are presented, and two and three dimensional simulations involving crystal growth are shown, highlighting the robustness of the method.
Fil: Vignal, P.. King Abdullah University Of Science And Technology; Argelia
Fil: Dalcin, Lisandro Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina
Fil: Brown, D.L.. King Abdullah University Of Science And Technology; Arabia Saudita
Fil: Collier, N.. Oak Ridge National Laboratory; Estados Unidos
Fil: Calo, V.M.. King Abdullah University Of Science And Technology; Arabia Saudita
description Abstract The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. Nonetheless, solving this equation is not a trivial task, as energy dissipation and mass conservation need to be verified for the numerical solution to be valid. This work addresses these issues, and proposes a novel algorithm that guarantees mass conservation, unconditional energy stability and second-order accuracy in time. Numerical results validating our proofs are presented, and two and three dimensional simulations involving crystal growth are shown, highlighting the robustness of the method.
publishDate 2015
dc.date.none.fl_str_mv 2015-07
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/11336/78613
Vignal, P.; Dalcin, Lisandro Daniel; Brown, D.L.; Collier, N.; Calo, V.M.; An energy-stable convex splitting for the phase-field crystal equation; Pergamon-Elsevier Science Ltd; Computers & Structures; 158; 7-2015; 355-368
0045-7949
CONICET Digital
CONICET
url http://hdl.handle.net/11336/78613
identifier_str_mv Vignal, P.; Dalcin, Lisandro Daniel; Brown, D.L.; Collier, N.; Calo, V.M.; An energy-stable convex splitting for the phase-field crystal equation; Pergamon-Elsevier Science Ltd; Computers & Structures; 158; 7-2015; 355-368
0045-7949
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.compstruc.2015.05.029
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
dc.publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
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 12.982451

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