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dc.contributor.authorVignal, Philippe
dc.contributor.authorDalcin, Lisandro
dc.contributor.authorBrown, Donald
dc.contributor.authorCollier, N.
dc.contributor.authorCalo, Victor M.
dc.date.accessioned2016-01-19T13:21:11Z
dc.date.available2016-01-19T13:21:11Z
dc.date.issued2015-10
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.
dc.identifier.issn0045-7949
dc.identifier.doi10.1016/j.compstruc.2015.05.029
dc.identifier.urihttp://hdl.handle.net/10754/594083
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.
dc.description.sponsorshipKAUST, King Abdullah University of Science and Technology
dc.publisherElsevier BV
dc.subjectB-spline basis functions
dc.subjectIsogeometric analysis
dc.subjectMixed formulation
dc.subjectPetIGA
dc.subjectPhase-field crystal
dc.subjectProvably-stable time integration
dc.titleAn energy-stable convex splitting for the phase-field crystal equation
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentEarth Science and Engineering Program
dc.contributor.departmentMaterials Science and Engineering Program
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Division
dc.identifier.journalComputers & Structures
dc.contributor.institutionConsejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Santa Fe, Argentina
dc.contributor.institutionComputer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN, United States
dc.identifier.arxividarXiv:1405.3488
kaust.personVignal, Philippe
kaust.personDalcin, Lisandro
kaust.personBrown, Donald
kaust.personCalo, Victor M.


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