Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation
By Zhengzheng Hu, Steven M. Wise, Cheng Wang, John S. Lowengrub. Journal of Computational Physics, 2009
342 citations recorded by the source corpus.
Subfields: Aerospace Engineering, Computational Theory and Mathematics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/7e99f90a3c9bb3e2c02023e3e34588531351859f
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Aerospace Engineering
- Xiaoming Wang
- Hector Gomez
- Hartmut Löwen
- Raphael Wittkowski
- Jie Shen
- Andreas C. Aristotelous
- Ohannes A. Karakashian
- Steven M. Wise
In Computational Theory and Mathematics
- Xiaoming Wang
- Hector Gomez
- Steven M. Wise
- Jie Shen
- Xesús Nogueira
- Cheng Wang
- Andreas C. Aristotelous
- Ohannes A. Karakashian
In Materials Chemistry
- Xiaoming Wang
- Steven M. Wise
- Jie Shen
- Cheng Wang
- Hector Gomez
- Andreas C. Aristotelous
- Ohannes A. Karakashian
- Hartmut Löwen
Citations in the corpus
- An unconditionally energy-stable method for the phase field crystal equation (2012, background): “The solution presents similar features to those obtained in [18,34].”
- Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich-Schwoebel Type Energy: Application to Thin Film Epitaxy (2012, methodology): “Further details of the test can be gleaned from [14].”
- Unconditionally stable schemes for equations of thin film epitaxy (2010, background): “Higher-order (in particular, second-order) convex-splitting schemes can be developed as well [11] that preserve the unconditional energy stability and unconditional solvability aspects of the first-order convex splitting schemes.”
- A MIXED DISCONTINUOUS GALERKIN, CONVEX SPLITTING SCHEME FOR A MODIFIED CAHN-HILLIARD EQUATION AND AN EFFICIENT NONLINEAR MULTIGRID SOLVER (2013, result): “The result is a pseudocrystallization of the domain, similar to that predicted by the phase field crystal (PFC) equation [6, 22].”
- 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].”
- 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.”