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

Philippe Vignal, Lisandro Dalcin, Donald Brown, N. Collier, Victor M. Calo

Research output: Contribution to journalArticlepeer-review

53 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)355-368
Number of pages14
JournalComputers & Structures
StatePublished - Oct 2015

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: KAUST, King Abdullah University of Science and Technology


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