An energy-stable time-integrator for phase-field models

Handle URI:
http://hdl.handle.net/10754/622080
Title:
An energy-stable time-integrator for phase-field models
Authors:
Vignal, Philippe ( 0000-0001-5300-6930 ) ; Collier, N.; Dalcin, Lisandro ( 0000-0001-8086-0155 ) ; Brown, D.L.; Calo, V.M.
Abstract:
We introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of these models can lead to expressions that guarantee energy-stability implicitly, which are second-order accurate in time. The spatial discretization relies on a mixed finite element formulation and isogeometric analysis. We also propose an adaptive time-stepping discretization that relies on a first-order backward approximation to give an error-estimator. This error estimator is accurate, robust, and does not require the computation of extra solutions to estimate the error. This methodology can be applied to any second-order accurate time-integration scheme. We present numerical examples in two and three spatial dimensions, which confirm the stability and robustness of the method. The implementation of the numerical schemes is done in PetIGA, a high-performance isogeometric analysis framework.
KAUST Department:
Materials Science and Engineering Program; Extreme Computing Research Center
Citation:
Vignal P, Collier N, Dalcin L, Brown DL, Calo VM (2016) An energy-stable time-integrator for phase-field models. Computer Methods in Applied Mechanics and Engineering. Available: http://dx.doi.org/10.1016/j.cma.2016.12.017.
Publisher:
Elsevier BV
Journal:
Computer Methods in Applied Mechanics and Engineering
Issue Date:
27-Dec-2016
DOI:
10.1016/j.cma.2016.12.017
Type:
Article
ISSN:
0045-7825
Sponsors:
We would like to acknowledge the open source software packages that made this work possible: PETSc [60] and [61], NumPy [62], matplotlib [63], ParaView [64]. We would also like to thank Adel Sarmiento for proofreading the manuscript and providing useful comments. This work was supported by the Center for Numerical Porous Media (NumPor) at King Abdullah University of Science and Technology (KAUST) . This work is part of the European Union’s Horizon 2020 research and innovation programme of the Marie Skłodowska-Curie grant agreement No. 644602. This work was also supported by the Agencia Nacional de Promoción Científica y Tecnológicagrants PICT 2014–2660 and PICT-E 2014–0191, and the National Priorities Research Programgrant 7-1482-1-278 from the Qatar National Research Fund (a member of The Qatar Foundation).
Additional Links:
http://www.sciencedirect.com/science/article/pii/S0045782516317972
Appears in Collections:
Articles; Extreme Computing Research Center; Materials Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorVignal, Philippeen
dc.contributor.authorCollier, N.en
dc.contributor.authorDalcin, Lisandroen
dc.contributor.authorBrown, D.L.en
dc.contributor.authorCalo, V.M.en
dc.date.accessioned2016-12-29T13:20:20Z-
dc.date.available2016-12-29T13:20:20Z-
dc.date.issued2016-12-27en
dc.identifier.citationVignal P, Collier N, Dalcin L, Brown DL, Calo VM (2016) An energy-stable time-integrator for phase-field models. Computer Methods in Applied Mechanics and Engineering. Available: http://dx.doi.org/10.1016/j.cma.2016.12.017.en
dc.identifier.issn0045-7825en
dc.identifier.doi10.1016/j.cma.2016.12.017en
dc.identifier.urihttp://hdl.handle.net/10754/622080-
dc.description.abstractWe introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of these models can lead to expressions that guarantee energy-stability implicitly, which are second-order accurate in time. The spatial discretization relies on a mixed finite element formulation and isogeometric analysis. We also propose an adaptive time-stepping discretization that relies on a first-order backward approximation to give an error-estimator. This error estimator is accurate, robust, and does not require the computation of extra solutions to estimate the error. This methodology can be applied to any second-order accurate time-integration scheme. We present numerical examples in two and three spatial dimensions, which confirm the stability and robustness of the method. The implementation of the numerical schemes is done in PetIGA, a high-performance isogeometric analysis framework.en
dc.description.sponsorshipWe would like to acknowledge the open source software packages that made this work possible: PETSc [60] and [61], NumPy [62], matplotlib [63], ParaView [64]. We would also like to thank Adel Sarmiento for proofreading the manuscript and providing useful comments. This work was supported by the Center for Numerical Porous Media (NumPor) at King Abdullah University of Science and Technology (KAUST) . This work is part of the European Union’s Horizon 2020 research and innovation programme of the Marie Skłodowska-Curie grant agreement No. 644602. This work was also supported by the Agencia Nacional de Promoción Científica y Tecnológicagrants PICT 2014–2660 and PICT-E 2014–0191, and the National Priorities Research Programgrant 7-1482-1-278 from the Qatar National Research Fund (a member of The Qatar Foundation).en
dc.publisherElsevier BVen
dc.relation.urlhttp://www.sciencedirect.com/science/article/pii/S0045782516317972en
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering, 27 December 2016. DOI: 10.1016/j.cma.2016.12.017en
dc.subjectPhase-field modelsen
dc.subjectPetIGAen
dc.subjectHigh-order partial differential equationen
dc.subjectMixed finite elementsen
dc.subjectIsogeometric analysisen
dc.subjectTime integrationen
dc.titleAn energy-stable time-integrator for phase-field modelsen
dc.typeArticleen
dc.contributor.departmentMaterials Science and Engineering Programen
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.eprint.versionPost-printen
dc.contributor.institutionComputer Science and Mathematics Division, Oak Ridge National Laboratory, TN, United Statesen
dc.contributor.institutionConsejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Santa Fe, Argentinaen
dc.contributor.institutionSchool of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdomen
dc.contributor.institutionApplied Geology Department, Western Australian School of Mines, Faculty of Science and Engineering, Curtin University, Perth, Western Australia, 6845, Australiaen
dc.contributor.institutionMineral Resources, Commonwealth Scientific and Industrial Research Organisation (CSIRO), Kensington, WA, 6152, Australiaen
kaust.authorVignal, Philippeen
kaust.authorDalcin, Lisandroen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.