An energy-stable convex splitting for the phase-field crystal equation
KAUST DepartmentNumerical Porous Media SRI Center (NumPor)
Materials Science and Engineering Program
Applied Mathematics and Computational Science Program
Earth Science and Engineering Program
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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