An energy-stable convex splitting for the phase-field crystal equation
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Earth Science and Engineering Program
Materials Science and Engineering Program
Numerical Porous Media SRI Center (NumPor)
Physical Sciences and Engineering (PSE) Division
Permanent link to this recordhttp://hdl.handle.net/10754/594083
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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.
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.
SponsorsKAUST, King Abdullah University of Science and Technology
JournalComputers & Structures