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
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/78613
Ver los metadatos del registro completo
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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 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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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 |
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eng |
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info:eu-repo/semantics/altIdentifier/doi/10.1016/j.compstruc.2015.05.029 |
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openAccess |
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https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
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application/pdf application/pdf |
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Pergamon-Elsevier Science Ltd |
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Pergamon-Elsevier Science Ltd |
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