An Energy Stable and Convergent Finite-Difference Scheme for the Modified Phase Field Crystal Equation

By C. Wang, Steven M. Wise. SIAM Journal on Numerical Analysis, 2011

342 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computational Theory and Mathematics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/3e989e0d2fbc2aa8803ca650fa6d8cdf74414f38

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Citations in the corpus

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview (2012, methodology): “In contrast, the wavelike dynamics, the second-order time derivatives of the MPFC-type EOMs realize, leads to a solute trapping behaviour similar to the predictions of Galenko et al. [236].”
A MIXED DISCONTINUOUS GALERKIN, CONVEX SPLITTING SCHEME FOR A MODIFIED CAHN-HILLIARD EQUATION AND AN EFFICIENT NONLINEAR MULTIGRID SOLVER (2013, methodology): “For the time discretization we use the convex-splitting (CS) approach popularized by David Eyre [16] and used in several other settings [12, 18, 29, 33].”
A Second-Order Energy Stable BDF Numerical Scheme for the Cahn-Hilliard Equation (2018, background): “See the related works for the phase field crystal (PFC) equation and the modified phase field crystal (MPFC) equation [3, 4, 28, 35, 37]; epitaxial thin film growth models [8, 10, 32, 34]; non-local Cahn-Hilliard-type models [22, 23]; the CHHS and related models [9, 13, 20, 36]; et cetera.”
Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows (2015, background): “The difficulty (iii) is also well studied recently: two classes of methods, one based on stabilization [44, 40, 33, 42] and the other based on convex splitting [8, 9, 39, 6], have proved to be effective.”
Classical dynamical density functional theory: from fundamentals to applications (2020, methodology): “Many of them address PFC models [773–782], the Allen-Cahn and Cahn-Hilliard equations [783–789], the Swift-Hohenberg equation [790], or the PoissonNernst-Planck (PNP) equations [791].”
An unconditionally energy-stable method for the phase field crystal equation (2012, positive): “Thermodynamically consistent methods have been previously studied in the context of solid [3,39,44,45] and fluidmechanics [30,36,47,48], but remain less investigated for phase-field equations (significant works on this topic include [16,20,22,24,27,31,51–53]).”