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

Handle URI:
http://hdl.handle.net/10754/594083
Title:
An energy-stable convex splitting for the phase-field crystal equation
Authors:
Vignal, P.; Dalcin, L.; Brown, D. L.; Collier, N.; Calo, V. M.
Abstract:
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. © 2015 Elsevier Ltd.
KAUST Department:
Numerical Porous Media SRI Center (NumPor); Materials Science and Engineering Program; Applied Mathematics and Computational Science Program; Earth Science and Engineering Program
Citation:
Vignal P, Dalcin L, Brown DL, Collier N, Calo VM (2015) An energy-stable convex splitting for the phase-field crystal equation. Computers & Structures 158: 355–368. Available: http://dx.doi.org/10.1016/j.compstruc.2015.05.029.
Publisher:
Elsevier BV
Journal:
Computers & Structures
Issue Date:
Oct-2015
DOI:
10.1016/j.compstruc.2015.05.029
Type:
Article
ISSN:
0045-7949
Sponsors:
KAUST, King Abdullah University of Science and Technology
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Earth Science and Engineering Program; Materials Science and Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorVignal, P.en
dc.contributor.authorDalcin, L.en
dc.contributor.authorBrown, D. L.en
dc.contributor.authorCollier, N.en
dc.contributor.authorCalo, V. M.en
dc.date.accessioned2016-01-19T13:21:11Zen
dc.date.available2016-01-19T13:21:11Zen
dc.date.issued2015-10en
dc.identifier.citationVignal P, Dalcin L, Brown DL, Collier N, Calo VM (2015) An energy-stable convex splitting for the phase-field crystal equation. Computers & Structures 158: 355–368. Available: http://dx.doi.org/10.1016/j.compstruc.2015.05.029.en
dc.identifier.issn0045-7949en
dc.identifier.doi10.1016/j.compstruc.2015.05.029en
dc.identifier.urihttp://hdl.handle.net/10754/594083en
dc.description.abstractAbstract 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. © 2015 Elsevier Ltd.en
dc.description.sponsorshipKAUST, King Abdullah University of Science and Technologyen
dc.publisherElsevier BVen
dc.subjectB-spline basis functionsen
dc.subjectIsogeometric analysisen
dc.subjectMixed formulationen
dc.subjectPetIGAen
dc.subjectPhase-field crystalen
dc.subjectProvably-stable time integrationen
dc.titleAn energy-stable convex splitting for the phase-field crystal equationen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.contributor.departmentMaterials Science and Engineering Programen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentEarth Science and Engineering Programen
dc.identifier.journalComputers & Structuresen
dc.contributor.institutionConsejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Santa Fe, Argentinaen
dc.contributor.institutionComputer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN, United Statesen
kaust.authorVignal, Philippeen
kaust.authorDalcin, Lisandroen
kaust.authorBrown, Donalden
kaust.authorCalo, Victor M.en
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